# Price Responsiveness of Residential Demand for Natural Gas in the United States

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [1]. Specifically, it is often seen as a bridge fuel for displacing coal and oil [2,3] in the US path of deep decarbonization [4,5]. Further, an electric grid’s reliable integration of emissions-free but intermittent solar and wind resources may benefit from natural gas-fired generation’s flexible capacity with quick start and fast ramping capability [6] (The EIA’s Annual Energy Outlook 2021 press release provides a graphical depiction of renewable capacity expansion. See: https://www.eia.gov/pressroom/presentations/AEO2021_Release_Presentation.pdf (accessed on 22 April 2022)).

**KG1**: None of the studies considers how price responsiveness has changed over time.**KG2**: None of the studies investigates how price responsiveness differs by season.**KG3**: Little is known about how the parametric specification employed in the study may yield different results. While the critical issue of parametric specification is decades old [36], all 13 studies presume a particular specification (e.g., the double-log or GL) sans consideration of known alternatives like the linear, CES, and TL.**KG4**: None of the studies estimates the impact of cross-section dependence (CD) on the resulting price elasticity estimates.**KG5**: Regional variations in the responsiveness of natural gas to price changes has not been updated recently, as the study by [37] is already 35 years old.**KG6**: None of the studies uses own-price elasticity estimates to quantify natural gas shortage costs, thus overlooking demand response (DR) programs for efficient shortage management.

- (1)
- The US residential demand for natural gas is price inelastic, with statistically significant (p-value ≤ 0.05) estimates of −0.271 to −0.486 for the static own price elasticity, −0.238 to −0.555 for the short run own price elasticity, and −0.323 to −0.796 for the long-run own price elasticity, matching the mid-range estimates of the studies listed in Table A1.
- (2)
- Parametric specification, CD presence, and partial adjustment have statistically significant effects on the own-price elasticity estimates of the US residential natural gas demand.
- (3)
- Erroneously ignoring the highly significant presence of CD tends to shrink the size of the own-price elasticity estimates of the US residential natural gas demand.
- (4)
- The US residential natural gas demand’s own-price elasticity estimates vary seasonally and regionally.
- (5)
- The US residential natural gas demand’s price responsiveness exhibits a nonlinear time trend.
- (6)
- A hypothetical one-day natural gas shortage that triggers curtailment of 10% of residential demand increases residential energy cost by less than 1%.

## 2. Materials and Methods

#### 2.1. Nonlinear Pricing of Residential Natural Gas Consumption

#### 2.2. Five Parametric Specifications

_{1}(Mcf) at price P

_{1}($/Mcf), along with fuel oil Y

_{2}(gallon) at P

_{2}($/gallon) (We do not consider propane for two reasons. First, none of the studies uses propane price as a regressor. Second, residential propane consumption is relatively minor in the US), and electricity Y

_{3}(kWh) at price P

_{3}($/kWh) to minimize its monthly energy cost for producing an intermediate output Z = increasing function of end-use requirements for space heating, water heating, cooking, etc.:

_{1}Y

_{1}+ P

_{2}Y

_{2}+ P

_{3}Y

_{3}.

_{1}= β

_{0}+ β

_{1}ln(P

_{1}/P

_{3}) + β

_{2}ln(P

_{2}/P

_{3}) + β

_{Z}lnZ.

_{1}, does not vary by consumption level or across time and states. Since the data for Z are unobservable, we assume that lnZ is a linear function of employment X, cooling degree days CDD and heating degree days HDD. This assumption makes sense because rising employment implies less time at home but higher income in turn affects end-use requirements. Further, space and water heating requirements are lower in warm weather than cold weather.

_{1}= α

_{0}+ α

_{1}(P

_{1}/P

_{3}) + α

_{2}(P

_{2}/P

_{3}) + α

_{Z}Z.

_{1}(P

_{1}/P

_{3})/Y

_{1}.

_{1}/P

_{3}) and Y

_{1}, it varies by consumption level, price ratios, and across states and time. Thus, the estimated ε value for the entire US is the arithmetic mean of state- and month-specific estimates of the panel.

_{1}/Y

_{3}) = φ

_{0}+ φ

_{1}ln(P

_{1}/P

_{3}),

_{0}is a linear function of the variables X, CDD, and HDD to account for possible dependence of ln(Y

_{1/}Y

_{3}) on non-price factors. The own-price elasticity is:

_{1}(1 − S),

_{1}Y

_{1}/C is the cost share for natural gas ([3]). Since ε varies across states and time, the overall national value is the arithmetic mean of the state- and month-specific estimates of the panel.

_{1}= b

_{11}+ b

_{12}(P

_{2}/P

_{1})

^{1/2}+ b

_{13}(P

_{3}/P

_{1})

^{1/2}+ b

_{1Z}Z.

_{12}(P

_{2}/P

_{1})

^{1/2}+ b

_{13}(P

_{3}/P

_{1})

^{1/2}]/Y

_{1}.

_{1}+ a

_{11}ln(P

_{1}/P

_{3}) + a

_{12}ln(P

_{2}/P

_{3}) + a

_{1Z}lnZ,

_{1}Y

_{1}/C = natural gas cost share. Equation (9) assumes that lnZ is a simple linear function of the variables X, CDD, and HDD. The own-price elasticity is:

_{11}+ S

^{2}− S)/S.

#### 2.3. Long-Run Elasticity

#### 2.4. Estimation of Residential Shortage Cost

- (1)
- Consider a one-day shortage of natural gas that triggers curtailment of D% of the residential customer class’s total demand. The size of D is the same for all customer classes if the shortage triggers proportional rationing. However, D may vary by customer class, depending on the established curtailment protocol. For safety and health reasons, the protocol may curtail residential demand relatively less than non-residential demand.
- (2)
- Find the virtual price VP
_{1}≡ (1 + ΔlnP_{1}) that renders D unnecessary, where ΔlnP_{1}= −(D/ε) [44]. - (3)
- Estimate the cost of a one-day shortage of natural gas as a percentage of C:SC = (ΔC/C) ÷ 30 days,
_{1}] ΔP_{1}= Y_{1}ΔP_{1}using Shephard’s Lemma [45]. Since (ΔP_{1}/P_{1}) = ΔlnP_{1}, we find:SC = (P_{1}Y_{1}/C) (ΔP_{1}/P_{1}) ÷ 30 days = −S (D/ε) ÷ 30 days.

#### 2.5. Data Description

_{1}and the other variables. Y

_{1}is negatively correlated with P

_{1}(r = −0.247) as well as the price ratio (P

_{1}/P

_{3}) (r = −0.144) but uncorrelated with (P

_{2}/P

_{3}) (r = 0.002). Y

_{1}is also positively correlated with X (r = 0.115) and HDD (r = 0.824) but not with CDD (r = −0.458). These correlation coefficients are largely consistent with our expectations, though they fail to measure the marginal impacts of price ratios, employment, and weather on the US residential natural gas demand. Thus, we undertake the estimation strategy described below.

#### 2.6. Estimation Strategy

_{i}represents the state-specific fixed effect, μ

_{it}represents the random error, i = 1 to 48 denotes the state, t = 2 to 360 denotes the time period and cross-section averages are indicated by a bar on top of the variable. When the estimate of φ is positive and statistically significant, short- and long-run elasticities may be estimated using the formulas presented in Section 2.3.

- (1)
- Test for CD in the variables using the test developed by [50].
- (2)
- Determine whether the variables are non-stationarity using the [51] panel unit root test that accounts for CD.
- (3)
- For each parametric specification, estimate the coefficients of Equation (13) with IV and non-IV estimation for the four cases formed by (a) φ = 0 vs. φ > 0; and (b) CD presence vs. CD absence. The instruments for the current month’s price-ratio are the lagged price ratios in the prior three months (The lagged price ratios in month t are pre-determined variables as they use average prices based on billing data in the prior three months. As the lagged price ratios are suitable instruments as they are highly correlated with the current price ratio (r ≥ 0.8)).
- (4)
- For each parametric specification, use the Durbin-Wu-Hausman test [52] to determine if current price ratios are endogenous and whether IV estimation is necessary.

## 3. Results

#### 3.1. Tests of Cross-Section Independence and Non-Stationary Variables

#### 3.2. General Observations

^{2}values ≥ 0.95 that indicate remarkable goodness of fit. Second, the hypothesis of cross-section independence is decisively rejected (p-value < 0.01) for each of the specifications. Third, our application of the Durbin-Wu-Hausman test suggests that the current price ratio data do not cause estimation bias under the empirically valid assumption of CD presence. These observations lead to our preferred regression results by specification, which are shaded in light green in the panels of Table 4. All preferred regressions are based on CD presence and non-IV estimation.

#### 3.3. Regression Details

_{1}.

_{1}/Y

_{3}) declines with ln(P

_{1}/P

_{3}) for the CES specification. The estimated coefficients on CDD and HDD suggest that weather has a small but statistically significant impact on the natural gas-electricity consumption ratio, while the estimated coefficient for employment is not statistically significant. The static own-price elasticity estimate is −0.271, and the short- and long-run estimates are −0.238 and −0.323. Hence, the CES specification generates estimates which are smaller than those based on the double-log and linear specifications.

#### 3.4. Seasonal Pattern of Own-Price Elasticity Estimates

**KG2**, Panel F of Table 4 presents seasonal own-price elasticity estimates for each model. The winter elasticity estimates are smaller in size than non-winter estimates, due chiefly to a household’s winter space heating requirement.

#### 3.5. Factors Affecting the US Residential Demand’s Empirical Price Responsiveness

**KG3**and

**KG4**, a simple OLS dummy variable regression is used to delineate factors which affect our estimates of the price responsiveness of residential natural gas demand in the US. The results in Table 5 lead to the following inferences. First, the statistically insignificant coefficient estimates for F

_{j}for j = 1 to 3 indicate that the double-log specification’s elasticity estimates resemble those of the linear, CES, and GL specifications. The large and significant estimate for F

_{4}reflects TL specification’s potential of yielding oddly positive price elasticity estimates. While the use of IV estimation does not seem to matter, ignoring CD presence can lead to smaller elasticity estimates due to the bias that CD absence introduces to the regression [47].

#### 3.6. Time Trend of Own-Price Elasticity Estimates

**KG1**. The first rolling-window period is Jan-1990 to Dec-2009, while the last period is Jan-2010 to Dec-2019. Figure 2 depicts a non-linear trend in the own-price elasticity of residential natural gas demand in the US, as confirmed by the results of OLS regressions appearing in Table 6. Nonetheless, the static and short-run estimates are between −0.4 and −0.5 and the long-run estimates are between −0.5 and −0.6, revealing the price-inelastic nature of US residential natural gas demand.

#### 3.7. Residential Shortage Costs

**KG6**, Table 7 reports shortage costs (SC) estimates for various parametric specifications and types of elasticities under the assumption of a one-day shortage that triggers curtailment of D = 10% of the residential demand for natural gas. We use the elasticity estimates from the preferred regressions shaded in light green in Table 4. For comparison, we also calculate SC using elasticity estimates from the regressions with CD absence and non-IV estimation. After dismissing the TL specification’s anomalous results, Panel A of Table 7 shows that residential shortage cost for a 10% demand curtailment is less than 1% of residential energy cost. Some of Panel B’s SC estimates are counter-intuitive, due chiefly to the empirically erroneous assumption of CD absence.

#### 3.8. Final Checks

**KG5**, the last check investigates regional price responsiveness. Table 8 shows that the Midwest and Northeast regions in Figure 3 have smaller (in absolute value) own-price elasticity estimates than the South and West regions. This makes sense because households residing in the Midwest and Northeast regions have higher space heating requirements caused by more severe winter weather than the South and West regions.

## 4. Conclusions and Policy Implications

#### 4.1. Conclusions

#### 4.2. Policy Implications

#### 4.3. Limitations and Future Research

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Own-price elasticity estimates from thirteen selected studies of residential demand for natural gas (NG) in the US.

Study | Sample Period | Regional Coverage | Data Type | Data Frequency | Non−NG Energy Prices | Parametric Specification | Estimation Method | Static | Short Run | Long Run |
---|---|---|---|---|---|---|---|---|---|---|

Beierlein et al. (1981) [56] | 1967–1977 | Nine Northeast states | Panel | Annual | Electricity, fuel oil | Double-log with partial adjustment | Error components—seemingly unrelated regressions | −0.353 | −3.440 | |

Barnes et al. (1982) [57] | 1972–1973 Consumer expenditure survey | The US | Cross section | Annual | None | Double-log | Instrumental variable estimation | −0.68 | ||

Blattenberger et al. (1983) [58] | 1960–1974 | The US | Panel | Annual | Electricity | Double-log with partial adjustment | Cross-section/time-series regressions | −0.049 to −0.32 | −0.264 to −0.393 | |

Liu (1983) [59] | 1967–1978 | The US | Time series | Annual | Electricity, fuel oil | Double-log | OLS | −0.318 to −0.490 | ||

Lin et al. (1987) [37] | 1967–1983 | Nine regions of the US | Panel | Annual | Electricity, fuel oil | Double-log with partial adjustment | Error components-seemingly unrelated regressions | −0.154 | −1.215 | |

Garcia−Cerruti (2000) [60] | 1983–1997 | 44 counties of California | Panel | Annual | Electricity | Double-log with partial adjustment | Dynamic random variables models | −0.041 to −0.071 | −0.53 to −0.193 | |

Bernstein and Griffin (2005) [61] | 1997–2003 | Lower 48 states | Panel | Annual | Electricity | Double-log with partial adjustment | Panel data analysis with fixed effects | −0.12 | −0.36 | |

Payne et al. (2011) [62] | 1970–2007 | Illinois | Time series | Annual | Electricity | Linear | Error correction model with autoregressive distributed lag | −0.185 | −0.264 | |

Lavin et al. (2011) [54] | Residential Energy Consumption Survey for 1993 | The US | Cross section | Annual | Electricity | Double-log and linear | −0.007 to −0.72 | |||

Charles (2016) [28] | 2001–2014 | Lower 48 states | Panel | Monthly | Electricity | Double-log with and without partial adjustment | OLS with fixed effects | −0.297 | −0.211 | −0.360 |

Auffhammer and Rubin (2018) [39] | 2003–2014 | California | Panel | Monthly | None | Double-log | Instrumental variable estimation | −0.17 to −0.23 | ||

Gautam and Paudel (2018) [63] | 1997–2011 | Nine Northeast states | Panel | Annual | Electricity, fuel oil | Double-log with autoregressive distributed lag | Pooled Mean Group (PMG) and Dynamic Fixed Effects (DFE) | −0.061 | −0.200 | |

Woo et al. (2018b) [3] | 2001–2016 | Lower 48 states | Panel | Monthly | Electricity, fuel oil | Generalized Leontief (GL) system of energy intensities with and without partial adjustment | Iterated seemingly unrelated regressions | −0.455 | −0.271 | −0.684 |

Burns (2021) [64] | 1970–2016 | The US | Time series | Annual | None | Double-log with time-varying elasticities | Maximum likelihood with Kalman filter | −0.08 to −0.18 |

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**Figure 1.**US annual natural gas consumption by end-use customer class in 1991–2019, recognizing that annual industrial consumption data are unavailable for years prior to 1997 (Data source: US Energy Information Agency).

**Figure 2.**Rolling-window own-prices elasticity estimates. The solid black line portrays an elasticity estimate; the lower and upper solid grey lines show the 95% confidence interval; and the dashed line is the time trend of the estimate.

Study | Short Run | Long Run |
---|---|---|

Gillingham et al. (2009) [9] | −0.14 to −0.44 | −0.32 to −1.89 |

Al-Sahlawi (1989) [10] | −0.05 to −0.68 | −1.06 to −3.42 |

Bohi and Zimmerman (1984) [11] | −0.05 to −0.60 | −0.26 to −3.17 |

**Table 2.**Descriptive statistics for monthly data from Jan-1990 to Dec-2019 for the lower 48 states; number of observations = 17,280.

Variable (Source) | Definition | Mean | Standard Deviation | Minimum | Maximum | Correlation with Y_{1} |
---|---|---|---|---|---|---|

Y_{1} (EIA and BLS) | Per capita consumption of natural gas (Mcf) | 1.77 | 1.69 | 0.02 | 11.61 | 1.0 |

Y_{3} (EIA and BLS) | Per capita consumption of electricity (kWh) | 618.40 | 956.64 | 21.47 | 11,598.17 | −0.044 |

P_{1} (EIA) | Natural gas price ($/Mcf) | 11.10 | 4.89 | 2.42 | 41.56 | −0.247 |

P_{2} (EIA) | Fuel oil price ($/gallon) | 1.56 | 0.96 | 0.34 | 4.34 | −0.057 |

P_{3} (EIA) | Electricity price ($/kWh) | 0.010 | 0.003 | 0.00 | 0.02 | −0.122 |

P_{1}/P_{3} | Natural gas—electricity price ratio | 1138.66 | 431.51 | 364.46 | 4664.42 | −0.144 |

P_{2}/P_{3} | Fuel oil—electricity price ratio | 154.44 | 84.37 | 27.57 | 574.36 | 0.002 |

X (BLS) | Per capita industrial employment | 0.59 | 0.05 | 0.43 | 0.83 | 0.115 |

CDD (NOAA) | Cooling degree days | 91.01 | 144.01 | 0 | 761 | −0.458 |

HDD (NOAA) | Heating degree days | 435.19 | 422.63 | 0 | 2111 | 0.824 |

Variable | H_{0}: Cross-Section Independence | H_{0}: Non-Stationarity |
---|---|---|

Y_{1} | 584.87 (0.000) | −6.120 (0.000) |

P_{1}/P_{3} | 459.84 (0.000) | −5.132 (0.000) |

P_{2}/P_{3} | 614.44 (0.000) | −4.643 (0.000) |

X | 401.97 (0.000) | −3.403 (0.000) |

CDD | 569.56 (0.000) | −6.190 (0.000) |

HDD | 605.90 (0.000) | −6.190 (0.000) |

**Table 4.**Regression results by specification; coefficient and elasticity estimates which are statistically significant (p-value ≤ 0.10) are in

**bold**; coefficient and elasticity estimates with an unexpected sign are in italic; and each specification’s preferred results shaded in light green.

Variable | CD Presence | CD Absence | |||
---|---|---|---|---|---|

IV Estimation: No | IV Estimation: Yes | IV Estimation: No | IV Estimation: Yes | ||

Panel A.1: Double-log specification without partial adjustment | |||||

RMSE | 0.12 | 0.12 | 0.23 | 0.23 | |

Adjusted R^{2} | 0.98 | 0.99 | 0.92 | 0.92 | |

ln(P_{1/}P_{3}) = ln(natural gas price/electricity price) | −0.396 | −0.334 | −0.326 | −0.507 | |

ln(P_{2/}P_{3}) = ln(fuel oil price/electricity price) | 0.309 | 0.262 | −0.013 | 0.046 | |

X = per capita employment | −0.419 | −0.326 | 1.203 | 2.068 | |

CDD = cooling degree days | 0.000 | 0.000 | −0.001 | −0.001 | |

HDD = heating degree days | 0.001 | 0.001 | 0.002 | 0.002 | |

Static own-price elasticity | −0.396 | −0.334 | −0.326 | −0.507 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.995 | 0.017 | |||

Panel A.2: Double-log specification with partial adjustment | |||||

RMSE | 0.09 | 0.09 | 0.15 | 0.15 | |

Adjusted R^{2} | 0.99 | 0.99 | 0.97 | 0.97 | |

ln(P_{1/}P_{3}) = ln(natural gas price/electricity price) | −0.336 | −0.013 | −0.167 | 0.019 | |

ln(P_{2/}P_{3}) = ln(fuel oil price/electricity price) | 0.186 | 0.029 | −0.017 | −0.076 | |

X = per capita employment | 0.171 | 0.045 | 1.446 | 0.641 | |

CDD = cooling degree days | 0.000 | 0.000 | −0.001 | −0.001 | |

HDD = heating degree days | 0.001 | 0.001 | 0.002 | 0.002 | |

Lagged lnY_{1} | 0.271 | 0.296 | 0.308 | 0.316 | |

Short-run own-price elasticity | −0.336 | −0.013 | −0.167 | 0.019 | |

Long-run own-price elasticity | −0.460 | −0.018 | −0.242 | 0.028 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.352 | 0.000 | |||

Panel B.1: Linear specification without partial adjustment | |||||

RMSE | 0.00 | 0.00 | 0.00 | 0.00 | |

Adjusted R^{2} | 0.98 | 0.98 | 0.93 | 0.93 | |

(P_{1}/P_{3}) = (natural gas price/electricity price) | −0.0002 | −0.0003 | 0.0000 | −0.0003 | |

(P_{2}/P_{3}) = (fuel oil price/electricity price) | 0.0013 | 0.0017 | −0.0011 | −0.0005 | |

X = per capita employment | 0.0000 | 0.0001 | −0.0016 | −0.0001 | |

CDD = cooling degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

HDD = heating degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Static own-price elasticity | −0.486 | −0.684 | 0.018 | −0.651 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.617 | 0.042 | |||

Panel B.2: Linear specification with partial adjustment | |||||

RMSE | 0.00 | 0.00 | 0.00 | 0.00 | |

Adjusted R^{2} | 0.99 | 0.99 | 0.97 | 0.97 | |

(P_{1}/P_{3}) = (natural gas price/electricity price) | −0.0002 | −0.0001 | 0.0001 | 0.0001 | |

(P_{2}/P_{3}) = (fuel oil price/electricity price) | 0.0012 | 0.0009 | −0.0009 | −0.0010 | |

X = per capita employment | −0.0002 | −0.0004 | 0.0001 | 0.0000 | |

CDD = cooling degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

HDD = heating degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Lagged Y_{1} | 0.303 | 0.304 | 0.299 | 0.301 | |

Short-run own-price elasticity | −0.555 | −0.337 | 0.177 | 0.262 | |

Long-run own-price elasticity | −0.796 | −0.485 | 0.253 | 0.375 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.437 | 0.591 | |||

Panel C.1: CES specification without partial adjustment | |||||

RMSE | 0.13 | 0.13 | 0.26 | 0.26 | |

Adjusted R^{2} | 0.98 | 0.98 | 0.91 | 0.91 | |

ln(P_{1/}P_{3}) = ln(natural gas price/electricity price) | −0.354 | −0.277 | −0.518 | −0.627 | |

X = per capita employment | −0.765 | −0.756 | 1.182 | 1.564 | |

CDD = cooling degree days | −0.001 | −0.001 | −0.003 | −0.003 | |

HDD = heating degree days | 0.001 | 0.001 | 0.001 | 0.001 | |

Static own-price elasticity | −0.271 | −0.212 | −0.396 | −0.480 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.672 | 0.186 | |||

Panel C.2: CES specification with partial adjustment | |||||

RMSE | 0.10 | 0.10 | 0.18 | 0.18 | |

Adjusted R^{2} | 0.99 | 0.99 | 0.96 | 0.96 | |

ln(P_{1/}P_{3}) = ln(natural gas price/electricity price) | −0.311 | −0.016 | −0.284 | −0.132 | |

X = per capita employment | 0.014 | −0.218 | 1.135 | 0.713 | |

CDD = cooling degree days | −0.001 | −0.001 | −0.003 | −0.003 | |

HDD = heating degree days | 0.001 | 0.001 | 0.001 | 0.001 | |

Lagged lnY_{1} | 0.263 | 0.290 | 0.327 | 0.340 | |

Short-run own-price elasticity | −0.238 | −0.012 | −0.217 | −0.101 | |

Long-run own-price elasticity | −0.323 | −0.017 | −0.323 | −0.153 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.100 | 0.769 | |||

Panel D.1: GL specification without partial adjustment | |||||

RMSE | 0.00 | 0.00 | 0.00 | 0.00 | |

Adjusted R^{2} | 0.98 | 0.98 | 0.93 | 0.93 | |

(P_{2}/P_{1})^{1/2} = (fuel oil price/natural gas price) ^{1/2} | 0.0001 | 0.0002 | 0.0004 | 0.0008 | |

(P_{3}/P_{1})^{1/2} = (electricity price/natural gas price) ^{1/2} | 0.0010 | 0.0008 | −0.0010 | −0.0010 | |

X = per capita employment | −0.0003 | 0.0004 | −0.0015 | −0.0005 | |

CDD = cooling degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

HDD = heating degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Static own-price elasticity | −0.453 | −0.427 | −0.041 | −0.408 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.117 | 0.065 | |||

Panel D.2: GL specification with partial adjustment | |||||

RMSE | 0.00 | 0.00 | 0.00 | 0.00 | |

Adjusted R^{2} | 0.99 | 0.99 | 0.97 | 0.97 | |

(P_{2}/P_{1})^{1/2} = (fuel oil price/natural gas price) ^{1/2} | 0.0003 | −0.0008 | 0.0001 | 0.0001 | |

(P_{3}/P_{1})^{1/2} = (electricity price/natural gas price) ^{1/2} | 0.0007 | 0.0029 | −0.0008 | −0.0008 | |

X = per capita employment | −0.0001 | −0.0012 | 0.0000 | −0.0001 | |

CDD = cooling degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

HDD = heating degree days | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Lagged Y_{1} | 0.305 | 0.297 | 0.295 | 0.297 | |

Short-run own-price elasticity | −0.453 | −0.237 | 0.138 | 0.206 | |

Long-run own-price elasticity | −0.651 | −0.336 | 0.197 | 0.293 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.763 | 0.234 | |||

Panel E.1: TL specification without partial adjustment | |||||

RMSE | 0.02 | 0.02 | 0.04 | 0.04 | |

Adjusted R^{2} | 0.97 | 0.98 | 0.87 | 0.87 | |

ln(P_{1/}P_{3}) = ln(natural gas price/electricity price) | 0.087 | 0.093 | 0.101 | 0.074 | |

ln(P_{2}/P_{3}) = ln(fuel oil price/electricity price) | 0.010 | 0.008 | −0.021 | −0.012 | |

X = per capita employment | −0.134 | −0.134 | 0.118 | 0.252 | |

CDD = cooling degree days | −0.0001 | −0.0001 | −0.0003 | −0.0003 | |

HDD = heating degree days | 0.0001 | 0.0001 | 0.0002 | 0.0002 | |

Static own-price elasticity | 0.377 | 0.459 | 0.562 | 0.207 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.684 | 0.393 | |||

Panel E.2: TL specification with partial adjustment | |||||

RMSE | 0.02 | 0.02 | 0.03 | 0.03 | |

Adjusted R^{2} | 0.98 | 0.98 | 0.95 | 0.95 | |

ln(P_{1/}P_{3}) = ln(natural gas price/electricity price) | 0.075 | 0.061 | 0.080 | 0.094 | |

ln(P_{2/}P_{3}) = ln(fuel oil price/electricity price) | 0.007 | 0.015 | −0.016 | −0.020 | |

X = per capita employment | 0.021 | 0.034 | 0.099 | 0.039 | |

CDD = cooling degree days | −0.0001 | −0.0001 | −0.0002 | −0.0002 | |

HDD = heating degree days | 0.0001 | 0.0001 | 0.0002 | 0.0002 | |

Lagged lnY_{1} | 0.344 | 0.361 | 0.396 | 0.390 | |

Short-run own-price elasticity | 0.223 | 0.043 | 0.294 | 0.480 | |

Long-run own-price elasticity | 0.340 | 0.068 | 0.487 | 0.788 | |

p-value for testing H_{0}: CD is absent | − | − | 0.000 | 0.000 | |

p-value for testing H_{0}: natural gas price ratio data are exogeneous | 0.766 | 0.005 | |||

Panel F. Seasonal pattern of elasticity estimates based on CD presence and non-IV estimation | |||||

Specification j | Static Own−Price Elasticity Estimate | Short−Run Own−Price Elasticity Estimate | Long−Run Own−Price Elasticity Estimate | ||

Results for all 12 months | |||||

- (1)
- Double-log
| −0.396 | −0.336 | −0.460 | ||

- (2)
- Linear
| −0.486 | −0.555 | −0.796 | ||

- (3)
- CES
| −0.271 | −0.238 | −0.323 | ||

- (4)
- GL
| −0.453 | −0.453 | −0.651 | ||

- (5)
- TL
| 0.377 | 0.223 | 0.340 | ||

Results for the spring months of March, April and May | |||||

- (1)
- Double-log
| −0.396 | −0.336 | −0.460 | ||

- (2)
- Linear
| −0.292 | −0.334 | −0.478 | ||

- (3)
- CES
| −0.259 | −0.227 | −0.308 | ||

- (4)
- GL
| −0.328 | −0.327 | −0.470 | ||

- (5)
- TL
| 0.005 | −0.095 | −0.144 | ||

Results for the summer months of June, July and August | |||||

- (1)
- Double-log
| −0.396 | −0.336 | −0.460 | ||

- (2)
- Linear
| −0.951 | −1.086 | −1.557 | ||

- (3)
- CES
| −0.314 | −0.276 | −0.374 | ||

- (4)
- GL
| −0.799 | −0.799 | −1.149 | ||

- (5)
- TL
| 1.219 | 0.935 | 1.425 | ||

Results for the fall months of September, October and November | |||||

- (1)
- Double-log
| −0.396 | −0.336 | −0.460 | ||

- (2)
- Linear
| −0.577 | −0.659 | −0.945 | ||

- (3)
- CES
| −0.281 | −0.247 | −0.335 | ||

- (4)
- GL
| −0.532 | −0.529 | −0.761 | ||

- (5)
- TL
| 0.413 | 0.250 | 0.381 | ||

Results for the winter months of December, January and February | |||||

- (1)
- Double-log
| −0.396 | −0.336 | −0.460 | ||

- (2)
- Linear
| −0.124 | −0.141 | −0.202 | ||

- (3)
- CES
| −0.229 | −0.201 | −0.272 | ||

- (4)
- GL
| −0.155 | −0.155 | −0.223 | ||

- (5)
- TL
| −0.127 | −0.197 | −0.301 |

**Table 5.**OLS dummy variable regression; the regressand is the own-price elasticity estimate for US residential natural gas demand; sample size = 60 observations = 5 specifications × 2 estimation methods × 3 elasticity types × 2 CD assumptions.

Estimate | Standard Error | p−Value | |
---|---|---|---|

Adjusted R^{2} | 0.571 | ||

RMSE | 0.235 | ||

Intercept | −0.249 | 0.076 | 0.002 |

F_{1} = 1 if linear specification, 0 otherwise | −0.013 | 0.106 | 0.903 |

F_{2} = 1 if CES specification, 0 otherwise | 0.001 | 0.080 | 0.992 |

F_{3} = 1 if GL specification, 0 otherwise | 0.048 | 0.079 | 0.541 |

F_{4} = 1 if TL specification, 0 otherwise | 0.590 | 0.083 | 0.000 |

IV = 1 if IV estimation, 0 otherwise | 0.063 | 0.061 | 0.306 |

SR = 1 if short−run, 0 otherwise | 0.181 | 0.070 | 0.012 |

LR = 1 if long−run, 0 otherwise | 0.174 | 0.081 | 0.036 |

CD = 1 if CD present, 0 otherwise | −0.260 | 0.061 | 0.000 |

**Table 6.**OLS time trend regression: Own-price elasticity estimate = intercept + b

_{1}ID + b

_{2}ID

^{2}+ error; sample size = 241 observations for each elasticity type.

Variable | Estimate | Standard Error | p−Value |
---|---|---|---|

Panel A: Static elasticity | |||

Regressand’s mean | −0.452 | ||

Adjusted R^{2} | 0.715 | ||

RMSE | 0.024 | ||

Intercept | −0.473 | 0.004 | 0.000 |

ID | 0.0012 | 0.0001 | 0.000 |

ID^{2} | −6.63 × 10^{−6} | 3.38 × 10^{−7} | 0.000 |

Panel B: Short−run elasticity | |||

Regressand’s mean | −0.407 | ||

Adjusted R^{2} | 0.734 | ||

RMSE | 0.014 | ||

Intercept | −0.469 | 0.003 | 0.000 |

ID | 0.001 | 0.00005 | 0.000 |

ID^{2} | −2.95 × 10^{−6} | 2.05 × 10^{−7} | 0.000 |

Panel C: Long−run elasticity | |||

Regressand’s mean | −0.504 | ||

Adjusted R^{2} | 0.829 | ||

RMSE | 0.019 | ||

Intercept | −0.593 | 0.005 | 0.000 |

ID | 0.001 | 0.0001 | 0.000 |

ID^{2} | −1.98 × 10^{−6} | 3.07 × 10^{−7} | 0.000 |

Parametric Specification | Static | Short−Run | Long−Run | |||
---|---|---|---|---|---|---|

e_{1} | SC | e_{1} | SC | e_{1} | SC | |

Panel A. CD presence and non−IV estimation | ||||||

Double−log | −0.396 | 0.2% | −0.336 | 0.2% | −0.46 | 0.1% |

Linear | −0.486 | 0.1% | −0.555 | 0.1% | −0.796 | 0.1% |

CES | −0.271 | 0.2% | −0.238 | 0.3% | −0.323 | 0.2% |

GL | −0.453 | 0.1% | −0.453 | 0.1% | −0.651 | 0.1% |

TL | 0.377 | −0.2% | 0.223 | −0.3% | 0.340 | −0.2% |

Panel B. CD absence and non−IV estimation | ||||||

Double−log | −0.326 | 0.2% | −0.167 | 0.4% | −0.242 | 0.3% |

Linear | 0.018 | −3.7% | 0.177 | −0.4% | 0.253 | −0.3% |

CES | −0.396 | 0.2% | −0.217 | 0.3% | −0.323 | 0.2% |

GL | −0.041 | 1.6% | 0.138 | −0.5% | 0.197 | −0.3% |

TL | 0.562 | −0.1% | 0.294 | −0.2% | 0.487 | −0.1% |

Region Definition | Static Elasticity | Short−Run Elasticity | Long−Run Elasticity |
---|---|---|---|

Midwest | −0.380 | −0.317 | −0.376 |

Northeast | −0.148 | −0.166 | −0.300 |

South | −0.439 | −0.357 | −0.492 |

West | −0.508 | −0.400 | −0.605 |

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## Share and Cite

**MDPI and ACS Style**

Li, R.; Woo, C.-K.; Tishler, A.; Zarnikau, J.
Price Responsiveness of Residential Demand for Natural Gas in the United States. *Energies* **2022**, *15*, 4231.
https://doi.org/10.3390/en15124231

**AMA Style**

Li R, Woo C-K, Tishler A, Zarnikau J.
Price Responsiveness of Residential Demand for Natural Gas in the United States. *Energies*. 2022; 15(12):4231.
https://doi.org/10.3390/en15124231

**Chicago/Turabian Style**

Li, Raymond, Chi-Keung Woo, Asher Tishler, and Jay Zarnikau.
2022. "Price Responsiveness of Residential Demand for Natural Gas in the United States" *Energies* 15, no. 12: 4231.
https://doi.org/10.3390/en15124231