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The impacts of weather variations on energy demand and carbon emissions
Resource and Energy Economics 22 Ž2000. 295–314 www.elsevier.nlrlocaterECONbase
The impacts of weather variations on energy demand and carbon emissions Timothy J. Considine ) Department of Energy, EnÕironmental and Mineral Economics, The PennsylÕania State UniÕersity, 203 Eric A. Walker Building, UniÕersity Park, PA 16802, USA Received 20 July 1999; received in revised form 29 November 1999; accepted 8 February 2000
Abstract This paper examines the impacts of climate fluctuations on carbon emissions using monthly models of US energy demand. The econometric analysis estimates price, income, and weather elasticities of short-run energy demand. Our model simulations suggest that warmer climate conditions in the US since 1982 slightly reduced carbon emissions in the US. Lower energy use associated with reduced heating requirements offsets higher fuel consumption to meet increased air-conditioning needs. The analysis also suggests that climate change policies should allow some variance in carbon emissions due to short-term weather variations. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: Q41; Q20; C51 Keywords: Weather; Carbon; Energy; Demand
1. Introduction Integrated assessments of climate change often estimate the impacts of energy consumption and carbon emissions on world climate. A substantial portion of total energy consumption, however, is sensitive to short-term fluctuations in climate or
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Corresponding author. Tel.: q1-814-863-0810; fax: q1-814-863-7433. E-mail address: [email protected] ŽT.J. Considine..
0928-7655r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 8 - 7 6 5 5 Ž 0 0 . 0 0 0 2 7 - 0
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weather conditions. For instance, warmer summers increase the demand for air conditioning, electricity, and the derived demand for coal. Colder winters increase the demand for natural gas and heating fuel. This feedback of climate on carbon emissions may be an important element in understanding the global carbon cycle. Moreover, future climate change agreements may need to allow some variance in carbon emissions due to normal climate fluctuations. This study estimates the impacts of climate conditions on US energy demand and carbon emissions. Our approach involves estimation of monthly models of energy demand because monthly data provide more detail on seasonal variations in weather conditions. Estimating the demand for energy in this context poses several challenges. First, price elasticities of demand are likely to be quite small because substitution possibilities are limited in the short-run. Moreover, energy consumers probably do not respond fully to demand and supply shocks within one period. The linear logit model of cost shares developed by Considine and Mount Ž1984. is well suited for this empirical setting. The main advantage of this demand system is that price elasticities are linear functions of parameters and cost shares, which Considine Ž1989. shows reduces the likelihood of incorrectly signed own price elasticities of demand. In addition, this formulation allows relatively flexible, dynamic adjustments in quantities. The empirical analysis presented below uses this specification to estimate the demand for energy in the residential, commercial, industrial, and electric utility sectors of the US economy using monthly data from 1983 to 1997. Section 2 discusses the formulation of the energy demand models. The paper then proceeds with a discussion of the estimates of the substitution, price, income, and weather elasticities. Section 4 presents the simulation model that unifies the demand models, linking electricity demand in the residential, commercial, and industrial sectors with the derived demand for fuels in electric power generation. The simulation analysis addresses two major questions. If our climate is getting warmer, what is the impact on energy consumption and carbon emissions? Do mild winters and the reduced demand for heating offset hot summers and increased demand for air conditioning? Section 5 identifies additional research needs and discusses the policy implications of the findings.
2. Modeling short-run energy demand The focus of this study is on that portion of total energy demand that is weather sensitive. Considine Ž1999. shows that gasoline and jet fuel demands have a strong seasonal component but are not sensitive to heating and cooling degree-days. In contrast, consumption of electricity, natural gas, propane, and heating oil are quite sensitive to weather, in particular temperature. In addition, the derived demand for primary fuels used by electric utilities also moves with temperature as the demand for electricity adjusts to weather shocks.
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297
Our basic strategy in estimating the impacts of climate fluctuations on energy demand and carbon emissions involves estimating two components to the climate signal, a fixed seasonal effect and a random weather surprise. Monthly dummy variables represent fixed seasonal effects that may represent length of day and other fixed monthly effects. Heating and cooling degree-day deviations from their 30 year means represent random weather surprises. A degree-day is the difference between a day’s average temperature in Fahrenheit ŽF. and 658F. The National Oceanographic and Atmospheric Administration ŽNOAA. publishes population weighted monthly totals for heating and cooling days and monthly 30 year means. The monthly deviation of degree-days from its corresponding monthly mean measures the extent to which temperature is above or below normal. This approach is similar to the study of natural gas demand by Berndt and Watkins Ž1977.. The models estimated below assume that monthly energy consumption depends upon economic forces, technological factors, fixed seasonal effects, and random weather surprises. The demand systems for each sector contain energy cost shares. This approach requires an estimate of total energy expenditures to calculate individual fuel consumption. Therefore, our modeling strategy involves a non-homothetic, twostage optimization framework. First, assume an aggregate energy demand relationship for each sector with the simple log-linear function: ln Q t s h q k ln Pt q m ln Yt q f Ht q w Ct 11
q
Ý vm Dm t q q Tt q l ln Qty1 q ´ t
Ž 1.
ms1
where Q t is total energy quantity per day; h , k , m , f , w , v m , q , l are unknown parameters; Pt is a divisia index of aggregate fuel prices in month t; Yt is either income, output, or employment in each sector; Ht and Ct are heating and cooling degree-day deviations per day, respectively; Dm t are monthly dummy variables; Tt is the time trend to represent technological change; and ´ t is a random error term. The total energy quantity in each sector is energy expenditure divided by the divisia price index. The Short Term Integrated Forecasting System by EIA Ž1999a. is the source of all data used in this study. Our specification assumes that the fuels in the energy price index are weakly separable from other factors of production. In other words, the marginal rate of substitution between two fuels is independent of the rate at which aggregate energy substitutes with other goods or factors of production. An alternative specification involves either an expenditure function in the residential sector or a cost function for the other sectors in which energy substitutes with other inputs, such as labor and capital, in production. Data limitations precluded this approach. Moreover, the substitution possibilities between energy and other factors of production are likely to be very limited within the monthly time span considered in this study.
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298
In the second stage, a system of share equations determines the mix of fuels within each sector’s energy aggregate. A common approach in deriving demand functions is to assume the existence of a twice continuously differentiable cost function and then apply the envelope theorem to derive a set of cost share equations or inputroutput equations. Another approach is to approximate the cost share system directly with a logistic function, which ensures adding-up and the non-negativity of shares. Considine and Mount Ž1984. show how to impose zero degree homogeneity and symmetry on a set of logistic cost share equations. Given the non-integrable nature of the model, however, Considine Ž1990. imposes symmetry locally — either at a point with linear parameter restrictions or at each point in the sample using an iterative estimation procedure. This study imposes symmetry at the mean cost shares, which simplifies model simulation for policy analysis and forecasting. The unrestricted linear logit model of cost shares is as follows: Si t s
e f it
Pi t Q i t
s
Ct
n
;i
Ž 2.
Ý e f it js1
where: n
f i t s a i q Ý bi j ln Ž Pjt . q g i Q t q d t h Ht q d i c Ct js1 11
q Ý u i j Djt q t i Tt q c ln Ž Q i ty1 . q ´ iXt
Ž 3.
js1
and where Q i t is the quantity of fuel i in period t, Pi t is the price of fuel i, ´ i t is a random disturbance term, and where a i , bi j , g i , d i h , d i c , u i j , t i , c are unknown parameters. The inclusion of Q t allows non-homothetic demand functions within a two-stage demand model similar to the formulation developed by Segerson and Mount Ž1985.. The time trend permits non-neutral technological change. Substituting Eq. Ž3. into Eq. Ž2., taking logarithms, normalizing on the nth cost share, and imposing symmetry and homogeneity following the procedures developed by Considine and Mount Ž1984., yields the following share system: ln
Si t
ž / Sn t
iy1
s Ž ai y an .
n
Ý Sk)bk)i y Ý ks1
ksiq1
iy1
q Ý Ž b k)i y b k)n . Sk) ln ks1
Sk)bi)k y Si)bi)n ln
Pk t
ž / Pn t
Pi t
ž / Pn t
ny1
q
Ý Ž bi)k y bk)n . Sk) ln ksiq1
Pk t
ž / Pn t
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299
q Ž g i y gn . ln Q t q Ž d t h y dn h . Ht q Ž d i c y dn c . Ct 11
q
Ý Ž u i m y un m . Dm t q Ž t i ,tn . Tt q c ln ms1
qŽ ´i t y ´n t . ,
Q i ty1
ž / Q n ty1
Ž 4.
for all i. The four share systems estimated below take this basic form. A partial adjustment coefficient between zero and one satisfies the Chatelier principle. This model has constant Morishima elasticities of substitution: Mi k s Si) Ž bi)k y bi)i . ,
i/k,
Ž 5.
unlike the non-linear counterparts associated with the translog and Generalized Leontief flexible functional forms. A derivation of Eq. Ž5. is available in Appendix A, available upon request.
3. Econometric results The econometric models for the residential, commercial, industrial, and electric utility sectors each have a share system Ž4. and an aggregate energy demand Ž1. equation. Also included in our econometric analysis is an equation for aggregate propane demand because it is also likely to be weather sensitive. In addition, the analysis below includes models of non-fossil fuel-fired electricity generation, including hydroelectric power, and other sources of electric power, such as imports. Total electricity demand from the residential, commercial, and industrial sectors less these other sources of electricity equals power generated from coal, natural gas, and petroleum. The simultaneity of prices and quantities and the invariance problem with cost share equations require iterative instrumental variable estimation. Iterative three stage least squares does not provide consistent estimates when the instruments are not exogenous Žsee Cumby et al. Ž1983... The instruments may not be exogenous because Hamilton Ž1983. has shown that oil prices may affect macroeconomic aggregates, such as output and income. In this case, the Generalized Method of Moments ŽGMM. estimator developed by Hansen and Singleton Ž1982. provides consistent parameter estimates. GMM requires stationary data. Appendix B, which is available upon request, tests for unit roots in the data using augmented Dickey–Fuller and Phillips–Perron tests. The results reported in Appendix B indicate that nearly all the data are either stationary or trend stationary. The data should be either stationary or all trend stationary so this is a potential problem. The results for models without the
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variables that appeared to have unit roots are very similar to those reported below. Hence, this study retains all variables. In addition, there are no seasonal unit roots in the data using the techniques developed by Franses et al. Ž1995. and Ghysels Ž1994.. The estimates reported below are heteroscedastic-consistent using White’s Ž1980. estimator for the standard errors. In addition, our estimation procedures correct for autocorrelation using the bandwidth methods developed by Newey and West Ž1987a,b. and Andrews Ž1991.. The instrumental variables include lagged prices; lagged quantities; lagged income, lagged output or employment appropriate to each sector; monthly dummies; heating and cooling degree-day deviations, and a time trend. Sample estimation programs in Appendix C are available from the author upon request. The first test concerns the maintained restrictions of the models, such as the linear logit approximation of the cost share equations. The value of the objective function for the GMM estimator is distributed as a x 2 statistic with degrees of freedom equal to the number instruments times the number of equations less the number of parameters. If the test statistic is less than the critical value, rejection is not accepted. As Table 1 illustrates, the x 2 statistics do not support rejection. The R 2 coefficients, reported in Appendix A reflect an excellent fit. Mean squared error decompositions do not indicate any sizeable bias in the predictions. The aggregate energy demand elasticities by sector appear in Table 2 along with the probability that the estimated coefficient is zero. With the exception of trend and the degree-day deviations, all variables are in logarithms so that the coefficients are elasticities. The coefficients on degree-day deviations give the percent change in aggregate energy consumption for a degree day deviation per day. For example, if there were one extra heating degree-day per day for an entire month, residential energy consumption would rise 0.492 percent Ž0.0164 = 30.. Heating degree deviations are highly significant for each of the models reported in Table 2. Cooling degree deviations are significant for the residential, commercial, and electric utilities but not for the industrial sector and propane consumption. The industrial and electric utility sectors have significant and correctly signed own price elasticities of aggregate energy demand.
Table 1 Tests of over-identifying restrictions Sector
x2
Critical value )
Degrees of freedom
Probability value
Residential sector Commercial sector Electric utility sector Industrial sector
13.53 13.95 12.96 18.02
30.14 28.87 24.99 65.17
19 18 15 48
0.81 0.73 0.61 1.00
)
5%.
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301
Table 2 Parameter estimates of aggregate energy demand by sector wwith probability valuesx Variable
Residential
Commercial
Real price
y0.0276 w0.574x 0.093 w0.000x
y0.014 w0.665x
Real disposable income Commercial employment Industrial production Steam electric output Heating degree-day deviations Cooling degree-day deviations Trend Lagged quantity R2 Durbin–Watson
Industrial y0.069 w0.000x
Electric utility
Propane
y0.1048 w0.000x
y0.0925 w0.212x 0.209 w0.058x
0.308 w0.000x 0.0201 w0.242x
0.0164 w0.000x 0.0265 w0.000x
0.0107 w0.000x 0.0162 w0.000x
0.0127 w0.000x 0.0032 w0.294x
0.677 w0.000x 0.98 2.50
0.642 w0.000x 0.98 2.10
0.827 w0.000x 0.93 2.55
0.1830 w0.186x 0.0121 w0.000x 0.0354 w0.000x y0.0005 w0.002x 0.3553 w0.000x 0.94 2.94
0.0206 w0.000x 0.0019 w0.851x
0.462 w0.124x 0.90 2.16
In addition to price and weather, each of the energy demand equations include demand shifters. For the residential sector, the shifter is real personal disposable income. In the commercial sector, employment shifts demand because reliable monthly data on commercial output are not available. Industrial output is available but is insignificant. Total fossil fuel-fired power generation serves as the output variable for electric utilities. This output elasticity is positive but the probability level is 19%. The electric utility sector is the only one with significant technological change. Overall, monthly dummy variables, heating and cooling degree-day deviations, and lagged quantities are generally the most significant explanatory variables in the monthly models of aggregate energy consumption. The Morishima substitution elasticities given by Eq. Ž5. appear in Table 3. To interpret these elasticities, note that they are naturally asymmetric. These elasticities divide the effect of changing PirPj in the ith coordinate direction on the quantity ratio, Q irQ j , into two parts: the effect of Pi on Q j and the effect of Pi on Q i . When the jth price changes with the ith price constant, the Morishima elasticity contains the effect of Pj on Q i and the effect of Pj on Q j . Hence, there is a natural asymmetry in Morishima elasticities. The rows in Table 3 should be viewed as prices that are changing while the columns are the input ratios. For example, for a 1% change in the residential electricity price relative to a fixed
302
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Table 3 Morishima elasticities of substitution wwith probability valuesx Residential sector Natural gas Natural gas Distillate oil Electricity
Distillate oil
Electricity
0.066 w0.487x
0.098 w0.142x 0.100 w0.150x
0.091 w0.144x 0.107 w0.119x
0.131 w0.242x
Natural gas
Distillate oil
Electricity
0.014 w0.734x
0.035 w0.145x 0.025 w0.268x
Commercial sector
Natural gas Distillate oil Electricity
0.019 w0.449x 0.041 w0.079x
0.047 w0.171x
Electric utility sector Natural gas Natural gas Residual and distillate oil Coal
Residual and distillate Oil
Coal
0.038 w0.708x
0.028 w0.490x 0.232 w0.000x
0.210 w0.025x 0.050 w0.102x
0.222 w0.000x
Natural gas
Distillate oil
Residual oil
Steam coal
Electricity
0.140 w0.001x
0.155 w0.000x 0.286 w0.003x
y0.066 w0.022x 0.272 w0.000x 0.226 w0.000x
0.023 w0.168x 0.256 w0.000x 0.204 w0.000x 0.514 w0.000x
Industrial sector
Natural gas Distillate oil Residual oil Coal Electricity
0.272 w0.000x 0.231 w0.000x 0.480 w0.000x 0.015 w0.292x
0.242 w0.008x 0.500 w0.000x 0.116 w0.001x
0.500 w0.000x 0.057 w0.023x
0.567 w0.000x
distillate oil price, there is a 0.131% increase in the ratio of heating oil to electricity use Žsee Table 3..
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Two general conclusions regarding short-run energy substitution emerge from our Morishima elasticities. First, short-run inter-fuel substitution possibilities within the residential and commercial sectors are virtually nil. In contrast, short-run inter-fuel substitution elasticities are significantly different from zero in the electric utility and industrial sectors. These results are consistent with previous studies demonstrating that small, dispersed fuel consumers find it sub-optimal to have the fuel switching capability of large industrial users. Three of the six Morishima elasticities in the electric utility sector are significantly different from zero Žsee Table 3.. The substitution between oil and natural gas in this sector is a good illustration of the asymmetry in the Morishima elasticities. For oil price changes, the oil–natural gas Morishima elasticity is 0.21 while for natural gas price changes, the oil–natural gas elasticity is not significantly different from zero. Higher oil prices also significantly induce substitution of coal for oil. On the other hand, coal prices also affect oil substitution Žsee Table 3.. These findings suggest that in the short-run, changes in oil and coal prices significantly affect natural gas and coal use in electric utilities. Changes in natural gas prices, however, do not significantly induce electric utilities to switch fuels. Inter-fuel substitution is more pervasive in the industrial sector Žsee Table 3.. Eighteen out of the twenty Morishima elasticities of substitution have very low p-values. Unlike the electric utility sector, higher natural gas prices induce significant substitution toward distillate and residual fuel oil. Significant complementarity between natural gas and coal exists as natural gas prices change. This could be due to environmental reasons because gas can be injected into coal boilers to reduce emissions. Changes in oil and coal prices motivate substitution across all fuels, with coal prices inducing the greatest substitution. Industrial gas substitutes quite strongly with residual fuel oil and coal as these prices change. Coal prices induce significant substitution. Finally, higher electricity prices stimulate substitution between purchased electricity and coal, which may reflect the choice producers have between buying or generating their own power. In conclusion, the Morishima elasticities for the industrial sector reflect small but significant inter-fuel competition in the short-run. In addition to relative prices, short-run energy demand depends upon seasonal and stochastic weather shocks. Table 4 presents the partial elasticities that provide a basis for comparing the relative magnitude of these factors. The weather elasticities in Table 4 have the same interpretation as the weather coefficients reported in Table 2. The elasticities in Table 4 are partial in the sense that total energy consumption is constant. All fuel demands in each of the four sectors are price inelastic in the short-run. The own price elasticities of demand are very small and insignificant in the residential and commercial sectors. The residential model includes housing stocks as an explanatory variable. Monthly housing stocks include all single-family dwellings and mobile homes collected by EIA Ž1999a. via DRIrMcGraw-Hill. They estimate housing stocks as St s Ž1 y d . Sty1 q HS t , where d is a deprecia-
304
Residential sector Partial adjustment coefficientsa
0.367 w0.000x
Prices
Natural gas Heat oil Electricity
Total quantity
Natural gas
Heat oil
Electricity
y0.073 w0.161x y0.006 w0.937x 0.026 w0.149x
y0.001 w0.937x y0.092 w0.144x 0.008 w0.346x
0.074 w0.149x 0.098 w0.346x y0.034 w0.081x
Degree-days
Housing stocks
Heating
Cooling
0.419 w0.000x y0.811 w0.002x y0.083 w0.002x
0.049 w0.016x 0.224 w0.003x y0.035 w0.000x
y0.149 w0.000x y0.082 w0.010x 0.059 w0.000x
Total quantity
Degree-days
Commercial sector Prices
0.804 w0.000x
Natural gas Heat oil Electricity
Natural gas
Heat oil
Electricity
y0.027 w0.166x y0.014 w0.643x 0.008 w0.098x
y0.004 w0.643x y0.023 w0.296x 0.002 w0.253x
0.031 w0.098x 0.036 w0.253x y0.010 w0.043x
y0.014 w0.037x y0.547 w0.000x 0.047 w0.000x
Heating
Cooling
0.174 w0.000x 0.218 w0.000x y0.057 w0.000x
y0.014 w0.135x 0.022 w0.273x 0.020 w0.434x
y0.936 w0.000x y1.632 w0.245x 0.460 w0.815x
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Table 4 Estimates of partial adjustment coefficients and partial elasticities of demand wwith probability valuesx
Electric utility sector Prices
Natural gas Oil Coal
Natural gas
Oil
Electricity
y0.023 w0.535x 0.015 w0.828x 0.005 w0.486x
0.008 w0.828x y0.202 w0.001x 0.030 w0.000x
0.016 w0.486x 0.187 w0.000x y0.035 w0.000x
y0.496 w0.006x y0.485 w0.109x 0.235 w0.000x
Degree-days
Trend
Heating
Cooling
y0.024 w0.555x 0.530 w0.000x y0.076 w0.000x
0.093 w0.004x 0.294 w0.000x y0.076 w0.000x
0.000 w0.128x y0.001 w0.000x 0.235 w0.000x
Total quantity
Degree-days
Industrial sector Prices
0.695 w0.000x
Natural gas Distillate oil Residual oil Coal Electricity
Natural gas
Distillate oil
Residual oil
Coal
Electricity
y0.030 w0.023x 0.110 w0.003x 0.126 w0.000x y0.097 w0.000x y0.008 w0.082x
0.025 w0.003x y0.247 w0.000x 0.039 w0.402x 0.025 w0.248x 0.010 w0.007x
0.030 w0.000x 0.040 w0.402x y0.202 w0.000x 0.025 w0.228x 0.003 w0.293x
y0.009 w0.000x 0.011 w0.248x 0.010 w0.228x y0.489 w0.000x 0.025 w0.000x
y0.015 w0.082x 0.086 w0.007x 0.027 w0.293x 0.536 w0.000x y0.030 w0.000x
y0.028 w0.612x 0.045 w0.906x 0.404 w0.420x y0.117 w0.053x y0.033 w0.300x
Trend
Heating
Cooling
y0.036 w0.300x 0.744 w0.003x 0.171 w0.103x 0.151 w0.002x y0.094 w0.000x
y0.065 w0.000x 0.428 w0.004x 0.218 w0.000x 0.016 w0.323x y0.042 w0.001x
0.00059 w0.000x y0.00093 w0.142x y0.002 w0.000x y0.001 w0.000x 0.0001 w0.052x
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0.768 w0.000x
Total quantity
a
Adjustments are in quantities. 305
306
Residential sector Prices
Natural gas Heat oil Electricity
Income
Natural gas
Heat oil
Electricity
y0.079 w0.086x y0.007 w0.902x 0.007 w0.885x
y0.008 w0.702x y0.094 w0.146x y0.011 w0.722x
0.067 w0.251x 0.096 w0.349x y0.053 w0.110x
Degree-days Heating
Cooling
0.131 w0.001x 0.017 w0.451x 0.085 w0.000x
0.333 w0.000x 0.262 w0.000x 0.148 w0.000x
y0.022 w0.106x y0.065 w0.030x 0.141 w0.000x
Employment
Degree-days
Commercial sector Prices
Natural gas Heat oil Electricity
Natural gas
Heat oil
Electricity
y0.030 w0.139x y0.014 w0.628x y0.003 w0.911x
y0.006 w0.552x y0.024 w0.291x y0.008 w0.735x
0.029 w0.151x 0.036 w0.255x y0.021 w0.414x
0.294 w0.000x 0.139 w0.000x 0.321 w0.000x
Heating
Cooling
0.296 w0.000x 0.277 w0.000x 0.080 w0.000x
0.038 w0.004x 0.046 w0.016x 0.059 w0.000x
Trend
Stocks
0.001 w0.300x y0.001 w0.275x 0.000 w0.286x
y0.094 w0.000x y1.632 w0.000x 0.460 w0.000x
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Table 5 Total elasticities of demand wwith probability valuesx
Electric utility sector Prices
Coal
Natural gas
Oil
Electricity
y0.046 w0.224x 0.004 w0.957x y0.066 w0.000x
y0.015 w0.689x y0.213 w0.001x y0.041 w0.022x
y0.007 w0.715x 0.176 w0.000x y0.106 w0.000x
0.092 w0.235x 0.094 w0.402x 0.043 w0.141x
Degree-days
Trend
Heating
Cooling
0.050 w0.104x 0.606 w0.000x 0.106 w0.000x
0.154 w0.000x 0.355 w0.000x 0.071 w0.001x
0.000 w0.030x y0.002 w0.000x 0.000 w0.049x
Output
Degree-days
Industrial sector Prices
Natural gas Distillate oil Residual oil Coal Electricity
Natural gas
Distillate oil
Residual oil
Coal
Electricity
y0.049 w0.000x 0.105 w0.005x 0.121 w0.001x y0.098 w0.000x y0.047 w0.000x
0.006 w0.483x y0.251 w0.000x 0.035 w0.460x 0.024 w0.283x y0.029 w0.000x
0.011 w0.245x 0.036 w0.457x y0.206 w0.000x 0.023 w0.264x y0.036 w0.000x
y0.028 w0.000x 0.006 w0.499x 0.005 w0.507x y0.491 w0.000x 0.014 w0.063x
y0.035 w0.011x 0.008 w0.010x 0.022 w0.380x 0.534 w0.000x y0.070 w0.000x
0.019 w0.242x 0.021 w0.235x 0.028 w0.237x 0.018 w0.244x 0.019 w0.250x
Trend
Heating
Cooling
0.114 w0.005x 0.906 w0.001x 0.388 w0.001x 0.287 w0.000x 0.055 w0.004x
y0.055 w0.001x 0.439 w0.005x 0.233 w0.000x 0.026 w0.081x y0.032 w0.014x
0.0006 w0.000x y0.0009 w0.142x y0.0021 w0.000x y0.001 w0.000x 0.0001 w0.052x
T.J. Considiner Resource and Energy Economics 22 (2000) 295–314
Natural gas Oil
Output
307
308
Aggregate price of utility fossil fuels Total electricity consumption Heating degree day deviations Cooling degree day deviations Trend Lagged value R2 Durbin–Watson
Net imports of electricity
Nonutility generation
Transmission and distribution losses
Nuclear generation
Hydroelectric generation
Renewable generation
0.024 w0.162x
0.187 w0.542x
y0.300 w0.009x
y0.214 w0.020x
0.104 w0.272x
y0.050 w0.616x
y0.004 w0.766x 0.001 w0.120x 0.004 w0.121x 0.000 w0.491x 0.915 w0.000x 0.87 2.11
y0.190 w0.610x y0.010 w0.005x y0.005 w0.695x 0.004 w0.004x 0.690 w0.000x 0.99 1.61
y2.000 w0.001x 0.041 w0.000x 0.116 w0.000x 0.004 w0.001x y0.138 w0.441x 0.90 1.58
0.830 w0.010x y0.006 w0.004x y0.027 w0.000x y0.001 w0.106x 0.669 w0.000x 0.97 1.85
y0.374 w0.435x y0.002 w0.732x 0.011 w0.314x 0.001 w0.190x 0.849 w0.000x 0.87 1.99
y0.110 w0.873x y0.001 w0.771x 0.022 w0.331x 0.000 w0.942x 0.913 w0.000x 0.85 2.22
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Table 6 Parameter estimates of miscellaneous electricity balancing equations
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tion rate and HS t is housing starts. Omission of housing stocks from the residential energy cost share equations results in positive own price elasticities of demand. While slightly larger and more significant, the electric utility and the industrial demand for fuels also are very price inelastic. Table 4 also presents the total quantity elasticities that measure how fuel demands change as the scale of consumption changes. Several of these elasticities are significant illustrating the importance of allowing non-homothetic effects on demand. Small but significant technological change affects fuel demands in the electric utility and industrial sectors. Most of the weather elasticities are significant. Moreover, some of them are quite large; particularly those for oil products. Higher heating degree-days generally increase the demand for primary fuels, such as natural gas and oil. Greater cooling requirements increase the residential and commercial demand for electricity. Higher cooling degree-day deviations reduce residential heating oil consumption due to the reduced heating requirements during the spring and fall. Industrial electricity consumption falls with higher heating and cooling degree-days, which may reflect the presence of interruptible service contracts in which industrial customers reduce their usage of electricity during periods of peak power demands. The total elasticities, which include the indirect effects from changing the level of aggregate energy consumption, appear in Table 5. Given the rather small aggregate price elasticities of demand, the total own and cross price elasticities are not substantially different from the partial price elasticities. The total weather elasticities are substantially larger in several cases. For instance, the elasticity of the residential demand for natural gas with respect to heating degree-days is 0.333. With the exception of natural gas in the electric utility sector, all heating degree-day elasticities are larger than the cooling degree-day elasticities. This suggests that heating degree-days have a greater impact on energy consumption and carbon emissions than cooling degree-days. The electric utility fuel demand equations depend upon fossil fuel-fired electricity generation, which equals total electricity generation less nuclear, hydroelectric, and renewable power generation from. Total electric output is equal to total consumption less imports, non-utility generation, and transmission and distribution losses. The estimates from partial adjustment models for non-fossil fuel generation and other sources of electricity supply appear in Table 6. The explanatory variables include the aggregate price of utility fossil fuels, total electricity consumption, heating and cooling degree-days, trend, and monthly dummy variables, not reported here to conserve space. The presence of total electricity consumption in the miscellaneous electricity balancing equations represents the demand-pull on each of these components. Heating degree-days significantly affect non-utility generation, transmission and distribution losses, and nuclear power generation. Cooling degree-days significantly affect these two components of electricity supply. The magnitude of these parameters is similar to the parameter estimates reported in Table 2.
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4. Model simulation analysis The simulation model includes total energy demand and fuel share equations for each sector and the electricity balancing equations. Total electricity demand
Table 7 Impacts of past weather conditions on energy demand and carbon emissions in percent changes from base simulation Fuel consumption Year
Cooling degree days
Electricity
Natural gas
Cooling season, April through September 1983 6.57 0.79 1.15 1984 0.36 0.18 0.48 1985 y2.22 y0.47 y0.97 1986 3.58 0.10 y0.48 1987 8.23 0.31 y0.48 1988 8.96 0.80 0.33 1989 y3.91 y0.30 0.00 1990 3.43 0.23 0.03 1991 11.11 0.50 y0.63 1992 y13.69 y1.03 y0.20 1993 3.15 0.52 0.52 1994 1.56 y0.02 y0.36 1995 8.20 1.07 0.97 1996 0.16 0.06 0.23 1997 y7.82 y0.16 0.97 Heating degree days
Electricity
Natural gas
Heating season, October through March 1983–1984 3.16 0.17 0.88 1984–1985 y1.08 y0.04 0.00 1985–1986 y3.24 y0.18 y1.15 1986–1987 y3.72 y0.41 y1.44 1987–1988 y0.18 y0.13 y0.22 1988–1989 y1.06 0.02 y0.80 1989–1990 y4.55 y0.47 y1.86 1990–1991 y8.92 y1.01 y2.93 1991–1992 y7.88 y1.10 y3.12 1992–1993 2.05 0.27 0.40 1993–1994 4.63 0.64 1.64 1994–1995 y8.44 y1.23 y3.08 1995–1996 3.09 0.38 1.05 1996–1997 y3.62 y0.33 y1.63
Distillate
Residual
Coal
Propane
Carbon emissions
2.03 0.92 y1.26 y0.28 0.11 0.66 y0.17 0.37 0.21 y0.97 0.39 y0.30 1.56 0.36 0.54
6.01 1.33 y3.03 0.59 2.36 4.84 y1.51 1.68 3.56 y6.12 2.84 0.48 6.21 0.49 y1.22
1.35 0.38 y0.94 0.14 0.69 1.44 y0.56 0.50 1.10 y2.18 0.90 0.00 2.14 0.20 y0.36
1.16 0.71 y1.00 y0.61 y0.93 y0.14 0.16 y0.05 y1.09 0.31 0.46 y0.41 0.71 0.31 1.52
1.79 0.55 y1.12 y0.03 0.44 1.30 y0.43 0.43 0.70 y1.71 0.85 y0.12 1.92 0.24 0.11
Distillate
Residual
Coal
Propane
Carbon emissions
2.18 0.33 y1.41 y2.04 y0.10 y0.99 y1.48 y3.65 y3.80 0.64 2.54 y3.53 1.22 y1.36
2.43 y0.16 y1.28 y2.85 y0.88 y1.05 y3.01 y6.40 y7.01 1.32 3.84 y6.87 2.53 y2.66
0.60 y0.04 y0.40 y0.79 y0.23 y0.05 y0.70 y2.00 y2.08 0.48 1.21 y2.48 0.90 y0.80
1.64 y0.24 y1.20 y1.70 0.02 y0.71 y1.50 y3.90 y3.66 0.53 2.21 y3.88 1.29 y1.63
1.17 y0.02 y0.84 y1.33 y0.24 y0.57 y1.29 y2.69 y2.93 0.47 1.67 y3.07 1.09 y1.20
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and generation are endogenous. The simulation model also computes carbon emissions from the consumption of natural gas, distillate oil, residual oil, and coal based upon the emission coefficients reported by EIA Ž1999b.. While far from providing a basis for projecting long-term climate change, there is evidence that the climate in the US has warmed since 1984. Cumulative cooling degree-days are 2.2% higher than normal and heating degree-days are 1.65% lower. Two model simulations from April 1983 to December 1997 provide a basis to determine the impacts of these changes on carbon emissions. First, there is a base simulation of the model using actual degree-day deviations. The second simulation uses the 30-year means for heating and cooling degree-days. All other exogenous variables, such as energy prices and income are the same in the two simulations. Consequently, the changes from the base simulation reported in Table 7, represent those changes in carbon emissions associated with deviations of weather conditions from their 30-year means. There is an unambiguous, positive relationship between heating degree-days and carbon emissions. With warmer winters the demand for energy and carbon emissions fall. The largest impact occurred during the 1994–1995 winter season when the winter was about 8.5% warmer than normal, which led to a 3% drop in carbon emissions. The effects of cooling degree-days are more ambiguous because some months of the cooling season also contain heating degree-days, which may offset the effects associated with cooling degree-days. Nevertheless, there are several years with warmer than normal summers and slightly higher carbon emissions. Over the entire period, carbon emissions under the base simulation with actual weather are 0.2% lower than those under the alternative simulation using
Fig. 1. Simulated effects of a 10% colder than normal winter on fuel consumption.
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Fig. 2. Simulated effects of a 10% colder than normal winter on carbon emissions.
the 30-year means. This suggests that a warmer climate would slightly lower energy consumption and carbon emissions because lower fuel use associated with reduced heating requirements offsets higher fuel consumption to meet increased cooling demands. Simulating the effects of a 3-month shock to heating and cooling degree-days provides a more controlled experiment. First, consider the effects of a colder than normal winter with heating degree-days 10% above the 30-year mean for 3 months. All fuel demands increase ŽFig. 1.. Total carbon emissions appear in Fig. 2 and increase from 4% to 9% during the first three months. Higher residential and commercial consumption is the principle reason for the roughly 7% to 10% increase in natural gas consumption. In addition, electric utility fuel use, particu-
Fig. 3. Simulated effects of a 10% warmer than normal summer on fuel consumption.
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Fig. 4. Simulated effects of a 10% warmer than normal summer on carbon emissions.
larly oil, increases due to the simulated 2% to 4% increase in electricity consumption. The large estimated elasticity of electric utility oil use with respect to electricity generation accounts for most of the increase in residual fuel consumption. This result may reflect electric utilities using oil-fired generators to service peak power demands. The last simulation estimates the effects of a 3-month 10% increase in cooling degree-days. The impacts on fuel demands and carbon emissions appear in Figs. 3 and 4. As expected, electricity demand increases leading to an increase in the demand for coal and oil. Natural gas consumption increases slightly due primarily to higher consumption in the electric utility sectors. Carbon emissions for this scenario rise between 1.5% and 3.7%.
5. Conclusions This paper examines the link between aggregate US energy demand and weather variations. Our focus is on one important dimension of weather, heating and cooling degree-day deviations. The influence of precipitation, wind speed, and other climatic conditions on energy demand awaits further research. Regional analysis is another research need. Our model simulations suggest that warmer climate conditions slightly reduce energy demand and carbon emissions in the US. These results are not grounds for complacency. The 0.2% reduction in carbon emissions due to the slight warming trend since 1982 pales in comparison to the 7% reduction from 1990 emission levels for the US under the Kyoto Protocol. Nevertheless, this study shows that the impact of short-term climate fluctuations on carbon emissions can be sizeable. Our results suggest that future international agreements on global climate change should allow some variance, perhaps up to 3%, in carbon emissions due to short-term weather variations.
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References Andrews, D.W., 1991. Heteroskedastic and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858. Berndt, E.R., Watkins, G.C., 1977. Demand for natural gas: residential and commercial markets in Ontario and British Columbia. Canadian Journal of Economics 10, 97–111. Considine, T.J., Mount, T.D., 1984. The use of linear logit models for dynamic input demand systems. The Review of Economics and Statistics 64, 434–443. Considine, T.J., 1990. Symmetry constraints and variable returns to scale in logit models. Journal of Business and Economic Statistics 8, 347–353. Considine, T.J., 1999. Markup pricing in a short-run model with inventories, International Society for Inventory Research, invited paper, ASSA Meetings in Boston, MA., January 2000. Cumby, R.E., Huizinga, J., Obstfeld, M., 1983. Two step two-stage least squares estimation in models with rational expectations. Journal of Econometrics 21, 333–355. Energy Information Administration, 1999. Short Term Integrated Forecasting System, http:rr www.eia.doe.govremeursteorpubrcontents.html. Energy Information Administration, 1999. Emissions of Greenhouse Gases in the United States, Appendix A, http:rrwww.eia.doe.govroiafr1605r87-92rptrappa.html. Franses, P.H., Hylleberg, S., Lee, H.S., 1995. Spurious deterministic seasonality. Economics Letters 48, 249–256. Ghysels, E., 1994. On the economics and econometrics of seasonality. In: Sims, C.A. ŽEd.., Advances in Econometrics. Cambridge Univ. Press, Cambridge, pp. 257–316. Hamilton, J.D., 1983. Oil and the macroeconomy since World War II. Journal of Political Economy 91, 228–248. Hansen, L.P., Singleton, K., 1982. Generalized instrumental variable estimation of nonlinear rational expectations models. Econometrica 50, 1269–1286. Newey, W.K., West, K.D., 1987a. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Newey, W.K., West, K.D., 1987b. Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653. Segerson, K., Mount, T.D., 1985. A non-homothetic two-stage decision model using AIDS. Review of Economics and Statistics 67, 630–639. White, H., 1980. A heteroscedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica 48, 817–838.
The impacts of weather variations on energy demand and carbon emissions Timothy J. Considine ) Department of Energy, EnÕironmental and Mineral Economics, The PennsylÕania State UniÕersity, 203 Eric A. Walker Building, UniÕersity Park, PA 16802, USA Received 20 July 1999; received in revised form 29 November 1999; accepted 8 February 2000
Abstract This paper examines the impacts of climate fluctuations on carbon emissions using monthly models of US energy demand. The econometric analysis estimates price, income, and weather elasticities of short-run energy demand. Our model simulations suggest that warmer climate conditions in the US since 1982 slightly reduced carbon emissions in the US. Lower energy use associated with reduced heating requirements offsets higher fuel consumption to meet increased air-conditioning needs. The analysis also suggests that climate change policies should allow some variance in carbon emissions due to short-term weather variations. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: Q41; Q20; C51 Keywords: Weather; Carbon; Energy; Demand
1. Introduction Integrated assessments of climate change often estimate the impacts of energy consumption and carbon emissions on world climate. A substantial portion of total energy consumption, however, is sensitive to short-term fluctuations in climate or
)
Corresponding author. Tel.: q1-814-863-0810; fax: q1-814-863-7433. E-mail address: [email protected] ŽT.J. Considine..
0928-7655r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 8 - 7 6 5 5 Ž 0 0 . 0 0 0 2 7 - 0
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weather conditions. For instance, warmer summers increase the demand for air conditioning, electricity, and the derived demand for coal. Colder winters increase the demand for natural gas and heating fuel. This feedback of climate on carbon emissions may be an important element in understanding the global carbon cycle. Moreover, future climate change agreements may need to allow some variance in carbon emissions due to normal climate fluctuations. This study estimates the impacts of climate conditions on US energy demand and carbon emissions. Our approach involves estimation of monthly models of energy demand because monthly data provide more detail on seasonal variations in weather conditions. Estimating the demand for energy in this context poses several challenges. First, price elasticities of demand are likely to be quite small because substitution possibilities are limited in the short-run. Moreover, energy consumers probably do not respond fully to demand and supply shocks within one period. The linear logit model of cost shares developed by Considine and Mount Ž1984. is well suited for this empirical setting. The main advantage of this demand system is that price elasticities are linear functions of parameters and cost shares, which Considine Ž1989. shows reduces the likelihood of incorrectly signed own price elasticities of demand. In addition, this formulation allows relatively flexible, dynamic adjustments in quantities. The empirical analysis presented below uses this specification to estimate the demand for energy in the residential, commercial, industrial, and electric utility sectors of the US economy using monthly data from 1983 to 1997. Section 2 discusses the formulation of the energy demand models. The paper then proceeds with a discussion of the estimates of the substitution, price, income, and weather elasticities. Section 4 presents the simulation model that unifies the demand models, linking electricity demand in the residential, commercial, and industrial sectors with the derived demand for fuels in electric power generation. The simulation analysis addresses two major questions. If our climate is getting warmer, what is the impact on energy consumption and carbon emissions? Do mild winters and the reduced demand for heating offset hot summers and increased demand for air conditioning? Section 5 identifies additional research needs and discusses the policy implications of the findings.
2. Modeling short-run energy demand The focus of this study is on that portion of total energy demand that is weather sensitive. Considine Ž1999. shows that gasoline and jet fuel demands have a strong seasonal component but are not sensitive to heating and cooling degree-days. In contrast, consumption of electricity, natural gas, propane, and heating oil are quite sensitive to weather, in particular temperature. In addition, the derived demand for primary fuels used by electric utilities also moves with temperature as the demand for electricity adjusts to weather shocks.
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Our basic strategy in estimating the impacts of climate fluctuations on energy demand and carbon emissions involves estimating two components to the climate signal, a fixed seasonal effect and a random weather surprise. Monthly dummy variables represent fixed seasonal effects that may represent length of day and other fixed monthly effects. Heating and cooling degree-day deviations from their 30 year means represent random weather surprises. A degree-day is the difference between a day’s average temperature in Fahrenheit ŽF. and 658F. The National Oceanographic and Atmospheric Administration ŽNOAA. publishes population weighted monthly totals for heating and cooling days and monthly 30 year means. The monthly deviation of degree-days from its corresponding monthly mean measures the extent to which temperature is above or below normal. This approach is similar to the study of natural gas demand by Berndt and Watkins Ž1977.. The models estimated below assume that monthly energy consumption depends upon economic forces, technological factors, fixed seasonal effects, and random weather surprises. The demand systems for each sector contain energy cost shares. This approach requires an estimate of total energy expenditures to calculate individual fuel consumption. Therefore, our modeling strategy involves a non-homothetic, twostage optimization framework. First, assume an aggregate energy demand relationship for each sector with the simple log-linear function: ln Q t s h q k ln Pt q m ln Yt q f Ht q w Ct 11
q
Ý vm Dm t q q Tt q l ln Qty1 q ´ t
Ž 1.
ms1
where Q t is total energy quantity per day; h , k , m , f , w , v m , q , l are unknown parameters; Pt is a divisia index of aggregate fuel prices in month t; Yt is either income, output, or employment in each sector; Ht and Ct are heating and cooling degree-day deviations per day, respectively; Dm t are monthly dummy variables; Tt is the time trend to represent technological change; and ´ t is a random error term. The total energy quantity in each sector is energy expenditure divided by the divisia price index. The Short Term Integrated Forecasting System by EIA Ž1999a. is the source of all data used in this study. Our specification assumes that the fuels in the energy price index are weakly separable from other factors of production. In other words, the marginal rate of substitution between two fuels is independent of the rate at which aggregate energy substitutes with other goods or factors of production. An alternative specification involves either an expenditure function in the residential sector or a cost function for the other sectors in which energy substitutes with other inputs, such as labor and capital, in production. Data limitations precluded this approach. Moreover, the substitution possibilities between energy and other factors of production are likely to be very limited within the monthly time span considered in this study.
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In the second stage, a system of share equations determines the mix of fuels within each sector’s energy aggregate. A common approach in deriving demand functions is to assume the existence of a twice continuously differentiable cost function and then apply the envelope theorem to derive a set of cost share equations or inputroutput equations. Another approach is to approximate the cost share system directly with a logistic function, which ensures adding-up and the non-negativity of shares. Considine and Mount Ž1984. show how to impose zero degree homogeneity and symmetry on a set of logistic cost share equations. Given the non-integrable nature of the model, however, Considine Ž1990. imposes symmetry locally — either at a point with linear parameter restrictions or at each point in the sample using an iterative estimation procedure. This study imposes symmetry at the mean cost shares, which simplifies model simulation for policy analysis and forecasting. The unrestricted linear logit model of cost shares is as follows: Si t s
e f it
Pi t Q i t
s
Ct
n
;i
Ž 2.
Ý e f it js1
where: n
f i t s a i q Ý bi j ln Ž Pjt . q g i Q t q d t h Ht q d i c Ct js1 11
q Ý u i j Djt q t i Tt q c ln Ž Q i ty1 . q ´ iXt
Ž 3.
js1
and where Q i t is the quantity of fuel i in period t, Pi t is the price of fuel i, ´ i t is a random disturbance term, and where a i , bi j , g i , d i h , d i c , u i j , t i , c are unknown parameters. The inclusion of Q t allows non-homothetic demand functions within a two-stage demand model similar to the formulation developed by Segerson and Mount Ž1985.. The time trend permits non-neutral technological change. Substituting Eq. Ž3. into Eq. Ž2., taking logarithms, normalizing on the nth cost share, and imposing symmetry and homogeneity following the procedures developed by Considine and Mount Ž1984., yields the following share system: ln
Si t
ž / Sn t
iy1
s Ž ai y an .
n
Ý Sk)bk)i y Ý ks1
ksiq1
iy1
q Ý Ž b k)i y b k)n . Sk) ln ks1
Sk)bi)k y Si)bi)n ln
Pk t
ž / Pn t
Pi t
ž / Pn t
ny1
q
Ý Ž bi)k y bk)n . Sk) ln ksiq1
Pk t
ž / Pn t
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q Ž g i y gn . ln Q t q Ž d t h y dn h . Ht q Ž d i c y dn c . Ct 11
q
Ý Ž u i m y un m . Dm t q Ž t i ,tn . Tt q c ln ms1
qŽ ´i t y ´n t . ,
Q i ty1
ž / Q n ty1
Ž 4.
for all i. The four share systems estimated below take this basic form. A partial adjustment coefficient between zero and one satisfies the Chatelier principle. This model has constant Morishima elasticities of substitution: Mi k s Si) Ž bi)k y bi)i . ,
i/k,
Ž 5.
unlike the non-linear counterparts associated with the translog and Generalized Leontief flexible functional forms. A derivation of Eq. Ž5. is available in Appendix A, available upon request.
3. Econometric results The econometric models for the residential, commercial, industrial, and electric utility sectors each have a share system Ž4. and an aggregate energy demand Ž1. equation. Also included in our econometric analysis is an equation for aggregate propane demand because it is also likely to be weather sensitive. In addition, the analysis below includes models of non-fossil fuel-fired electricity generation, including hydroelectric power, and other sources of electric power, such as imports. Total electricity demand from the residential, commercial, and industrial sectors less these other sources of electricity equals power generated from coal, natural gas, and petroleum. The simultaneity of prices and quantities and the invariance problem with cost share equations require iterative instrumental variable estimation. Iterative three stage least squares does not provide consistent estimates when the instruments are not exogenous Žsee Cumby et al. Ž1983... The instruments may not be exogenous because Hamilton Ž1983. has shown that oil prices may affect macroeconomic aggregates, such as output and income. In this case, the Generalized Method of Moments ŽGMM. estimator developed by Hansen and Singleton Ž1982. provides consistent parameter estimates. GMM requires stationary data. Appendix B, which is available upon request, tests for unit roots in the data using augmented Dickey–Fuller and Phillips–Perron tests. The results reported in Appendix B indicate that nearly all the data are either stationary or trend stationary. The data should be either stationary or all trend stationary so this is a potential problem. The results for models without the
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variables that appeared to have unit roots are very similar to those reported below. Hence, this study retains all variables. In addition, there are no seasonal unit roots in the data using the techniques developed by Franses et al. Ž1995. and Ghysels Ž1994.. The estimates reported below are heteroscedastic-consistent using White’s Ž1980. estimator for the standard errors. In addition, our estimation procedures correct for autocorrelation using the bandwidth methods developed by Newey and West Ž1987a,b. and Andrews Ž1991.. The instrumental variables include lagged prices; lagged quantities; lagged income, lagged output or employment appropriate to each sector; monthly dummies; heating and cooling degree-day deviations, and a time trend. Sample estimation programs in Appendix C are available from the author upon request. The first test concerns the maintained restrictions of the models, such as the linear logit approximation of the cost share equations. The value of the objective function for the GMM estimator is distributed as a x 2 statistic with degrees of freedom equal to the number instruments times the number of equations less the number of parameters. If the test statistic is less than the critical value, rejection is not accepted. As Table 1 illustrates, the x 2 statistics do not support rejection. The R 2 coefficients, reported in Appendix A reflect an excellent fit. Mean squared error decompositions do not indicate any sizeable bias in the predictions. The aggregate energy demand elasticities by sector appear in Table 2 along with the probability that the estimated coefficient is zero. With the exception of trend and the degree-day deviations, all variables are in logarithms so that the coefficients are elasticities. The coefficients on degree-day deviations give the percent change in aggregate energy consumption for a degree day deviation per day. For example, if there were one extra heating degree-day per day for an entire month, residential energy consumption would rise 0.492 percent Ž0.0164 = 30.. Heating degree deviations are highly significant for each of the models reported in Table 2. Cooling degree deviations are significant for the residential, commercial, and electric utilities but not for the industrial sector and propane consumption. The industrial and electric utility sectors have significant and correctly signed own price elasticities of aggregate energy demand.
Table 1 Tests of over-identifying restrictions Sector
x2
Critical value )
Degrees of freedom
Probability value
Residential sector Commercial sector Electric utility sector Industrial sector
13.53 13.95 12.96 18.02
30.14 28.87 24.99 65.17
19 18 15 48
0.81 0.73 0.61 1.00
)
5%.
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Table 2 Parameter estimates of aggregate energy demand by sector wwith probability valuesx Variable
Residential
Commercial
Real price
y0.0276 w0.574x 0.093 w0.000x
y0.014 w0.665x
Real disposable income Commercial employment Industrial production Steam electric output Heating degree-day deviations Cooling degree-day deviations Trend Lagged quantity R2 Durbin–Watson
Industrial y0.069 w0.000x
Electric utility
Propane
y0.1048 w0.000x
y0.0925 w0.212x 0.209 w0.058x
0.308 w0.000x 0.0201 w0.242x
0.0164 w0.000x 0.0265 w0.000x
0.0107 w0.000x 0.0162 w0.000x
0.0127 w0.000x 0.0032 w0.294x
0.677 w0.000x 0.98 2.50
0.642 w0.000x 0.98 2.10
0.827 w0.000x 0.93 2.55
0.1830 w0.186x 0.0121 w0.000x 0.0354 w0.000x y0.0005 w0.002x 0.3553 w0.000x 0.94 2.94
0.0206 w0.000x 0.0019 w0.851x
0.462 w0.124x 0.90 2.16
In addition to price and weather, each of the energy demand equations include demand shifters. For the residential sector, the shifter is real personal disposable income. In the commercial sector, employment shifts demand because reliable monthly data on commercial output are not available. Industrial output is available but is insignificant. Total fossil fuel-fired power generation serves as the output variable for electric utilities. This output elasticity is positive but the probability level is 19%. The electric utility sector is the only one with significant technological change. Overall, monthly dummy variables, heating and cooling degree-day deviations, and lagged quantities are generally the most significant explanatory variables in the monthly models of aggregate energy consumption. The Morishima substitution elasticities given by Eq. Ž5. appear in Table 3. To interpret these elasticities, note that they are naturally asymmetric. These elasticities divide the effect of changing PirPj in the ith coordinate direction on the quantity ratio, Q irQ j , into two parts: the effect of Pi on Q j and the effect of Pi on Q i . When the jth price changes with the ith price constant, the Morishima elasticity contains the effect of Pj on Q i and the effect of Pj on Q j . Hence, there is a natural asymmetry in Morishima elasticities. The rows in Table 3 should be viewed as prices that are changing while the columns are the input ratios. For example, for a 1% change in the residential electricity price relative to a fixed
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Table 3 Morishima elasticities of substitution wwith probability valuesx Residential sector Natural gas Natural gas Distillate oil Electricity
Distillate oil
Electricity
0.066 w0.487x
0.098 w0.142x 0.100 w0.150x
0.091 w0.144x 0.107 w0.119x
0.131 w0.242x
Natural gas
Distillate oil
Electricity
0.014 w0.734x
0.035 w0.145x 0.025 w0.268x
Commercial sector
Natural gas Distillate oil Electricity
0.019 w0.449x 0.041 w0.079x
0.047 w0.171x
Electric utility sector Natural gas Natural gas Residual and distillate oil Coal
Residual and distillate Oil
Coal
0.038 w0.708x
0.028 w0.490x 0.232 w0.000x
0.210 w0.025x 0.050 w0.102x
0.222 w0.000x
Natural gas
Distillate oil
Residual oil
Steam coal
Electricity
0.140 w0.001x
0.155 w0.000x 0.286 w0.003x
y0.066 w0.022x 0.272 w0.000x 0.226 w0.000x
0.023 w0.168x 0.256 w0.000x 0.204 w0.000x 0.514 w0.000x
Industrial sector
Natural gas Distillate oil Residual oil Coal Electricity
0.272 w0.000x 0.231 w0.000x 0.480 w0.000x 0.015 w0.292x
0.242 w0.008x 0.500 w0.000x 0.116 w0.001x
0.500 w0.000x 0.057 w0.023x
0.567 w0.000x
distillate oil price, there is a 0.131% increase in the ratio of heating oil to electricity use Žsee Table 3..
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Two general conclusions regarding short-run energy substitution emerge from our Morishima elasticities. First, short-run inter-fuel substitution possibilities within the residential and commercial sectors are virtually nil. In contrast, short-run inter-fuel substitution elasticities are significantly different from zero in the electric utility and industrial sectors. These results are consistent with previous studies demonstrating that small, dispersed fuel consumers find it sub-optimal to have the fuel switching capability of large industrial users. Three of the six Morishima elasticities in the electric utility sector are significantly different from zero Žsee Table 3.. The substitution between oil and natural gas in this sector is a good illustration of the asymmetry in the Morishima elasticities. For oil price changes, the oil–natural gas Morishima elasticity is 0.21 while for natural gas price changes, the oil–natural gas elasticity is not significantly different from zero. Higher oil prices also significantly induce substitution of coal for oil. On the other hand, coal prices also affect oil substitution Žsee Table 3.. These findings suggest that in the short-run, changes in oil and coal prices significantly affect natural gas and coal use in electric utilities. Changes in natural gas prices, however, do not significantly induce electric utilities to switch fuels. Inter-fuel substitution is more pervasive in the industrial sector Žsee Table 3.. Eighteen out of the twenty Morishima elasticities of substitution have very low p-values. Unlike the electric utility sector, higher natural gas prices induce significant substitution toward distillate and residual fuel oil. Significant complementarity between natural gas and coal exists as natural gas prices change. This could be due to environmental reasons because gas can be injected into coal boilers to reduce emissions. Changes in oil and coal prices motivate substitution across all fuels, with coal prices inducing the greatest substitution. Industrial gas substitutes quite strongly with residual fuel oil and coal as these prices change. Coal prices induce significant substitution. Finally, higher electricity prices stimulate substitution between purchased electricity and coal, which may reflect the choice producers have between buying or generating their own power. In conclusion, the Morishima elasticities for the industrial sector reflect small but significant inter-fuel competition in the short-run. In addition to relative prices, short-run energy demand depends upon seasonal and stochastic weather shocks. Table 4 presents the partial elasticities that provide a basis for comparing the relative magnitude of these factors. The weather elasticities in Table 4 have the same interpretation as the weather coefficients reported in Table 2. The elasticities in Table 4 are partial in the sense that total energy consumption is constant. All fuel demands in each of the four sectors are price inelastic in the short-run. The own price elasticities of demand are very small and insignificant in the residential and commercial sectors. The residential model includes housing stocks as an explanatory variable. Monthly housing stocks include all single-family dwellings and mobile homes collected by EIA Ž1999a. via DRIrMcGraw-Hill. They estimate housing stocks as St s Ž1 y d . Sty1 q HS t , where d is a deprecia-
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Residential sector Partial adjustment coefficientsa
0.367 w0.000x
Prices
Natural gas Heat oil Electricity
Total quantity
Natural gas
Heat oil
Electricity
y0.073 w0.161x y0.006 w0.937x 0.026 w0.149x
y0.001 w0.937x y0.092 w0.144x 0.008 w0.346x
0.074 w0.149x 0.098 w0.346x y0.034 w0.081x
Degree-days
Housing stocks
Heating
Cooling
0.419 w0.000x y0.811 w0.002x y0.083 w0.002x
0.049 w0.016x 0.224 w0.003x y0.035 w0.000x
y0.149 w0.000x y0.082 w0.010x 0.059 w0.000x
Total quantity
Degree-days
Commercial sector Prices
0.804 w0.000x
Natural gas Heat oil Electricity
Natural gas
Heat oil
Electricity
y0.027 w0.166x y0.014 w0.643x 0.008 w0.098x
y0.004 w0.643x y0.023 w0.296x 0.002 w0.253x
0.031 w0.098x 0.036 w0.253x y0.010 w0.043x
y0.014 w0.037x y0.547 w0.000x 0.047 w0.000x
Heating
Cooling
0.174 w0.000x 0.218 w0.000x y0.057 w0.000x
y0.014 w0.135x 0.022 w0.273x 0.020 w0.434x
y0.936 w0.000x y1.632 w0.245x 0.460 w0.815x
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Table 4 Estimates of partial adjustment coefficients and partial elasticities of demand wwith probability valuesx
Electric utility sector Prices
Natural gas Oil Coal
Natural gas
Oil
Electricity
y0.023 w0.535x 0.015 w0.828x 0.005 w0.486x
0.008 w0.828x y0.202 w0.001x 0.030 w0.000x
0.016 w0.486x 0.187 w0.000x y0.035 w0.000x
y0.496 w0.006x y0.485 w0.109x 0.235 w0.000x
Degree-days
Trend
Heating
Cooling
y0.024 w0.555x 0.530 w0.000x y0.076 w0.000x
0.093 w0.004x 0.294 w0.000x y0.076 w0.000x
0.000 w0.128x y0.001 w0.000x 0.235 w0.000x
Total quantity
Degree-days
Industrial sector Prices
0.695 w0.000x
Natural gas Distillate oil Residual oil Coal Electricity
Natural gas
Distillate oil
Residual oil
Coal
Electricity
y0.030 w0.023x 0.110 w0.003x 0.126 w0.000x y0.097 w0.000x y0.008 w0.082x
0.025 w0.003x y0.247 w0.000x 0.039 w0.402x 0.025 w0.248x 0.010 w0.007x
0.030 w0.000x 0.040 w0.402x y0.202 w0.000x 0.025 w0.228x 0.003 w0.293x
y0.009 w0.000x 0.011 w0.248x 0.010 w0.228x y0.489 w0.000x 0.025 w0.000x
y0.015 w0.082x 0.086 w0.007x 0.027 w0.293x 0.536 w0.000x y0.030 w0.000x
y0.028 w0.612x 0.045 w0.906x 0.404 w0.420x y0.117 w0.053x y0.033 w0.300x
Trend
Heating
Cooling
y0.036 w0.300x 0.744 w0.003x 0.171 w0.103x 0.151 w0.002x y0.094 w0.000x
y0.065 w0.000x 0.428 w0.004x 0.218 w0.000x 0.016 w0.323x y0.042 w0.001x
0.00059 w0.000x y0.00093 w0.142x y0.002 w0.000x y0.001 w0.000x 0.0001 w0.052x
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0.768 w0.000x
Total quantity
a
Adjustments are in quantities. 305
306
Residential sector Prices
Natural gas Heat oil Electricity
Income
Natural gas
Heat oil
Electricity
y0.079 w0.086x y0.007 w0.902x 0.007 w0.885x
y0.008 w0.702x y0.094 w0.146x y0.011 w0.722x
0.067 w0.251x 0.096 w0.349x y0.053 w0.110x
Degree-days Heating
Cooling
0.131 w0.001x 0.017 w0.451x 0.085 w0.000x
0.333 w0.000x 0.262 w0.000x 0.148 w0.000x
y0.022 w0.106x y0.065 w0.030x 0.141 w0.000x
Employment
Degree-days
Commercial sector Prices
Natural gas Heat oil Electricity
Natural gas
Heat oil
Electricity
y0.030 w0.139x y0.014 w0.628x y0.003 w0.911x
y0.006 w0.552x y0.024 w0.291x y0.008 w0.735x
0.029 w0.151x 0.036 w0.255x y0.021 w0.414x
0.294 w0.000x 0.139 w0.000x 0.321 w0.000x
Heating
Cooling
0.296 w0.000x 0.277 w0.000x 0.080 w0.000x
0.038 w0.004x 0.046 w0.016x 0.059 w0.000x
Trend
Stocks
0.001 w0.300x y0.001 w0.275x 0.000 w0.286x
y0.094 w0.000x y1.632 w0.000x 0.460 w0.000x
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Table 5 Total elasticities of demand wwith probability valuesx
Electric utility sector Prices
Coal
Natural gas
Oil
Electricity
y0.046 w0.224x 0.004 w0.957x y0.066 w0.000x
y0.015 w0.689x y0.213 w0.001x y0.041 w0.022x
y0.007 w0.715x 0.176 w0.000x y0.106 w0.000x
0.092 w0.235x 0.094 w0.402x 0.043 w0.141x
Degree-days
Trend
Heating
Cooling
0.050 w0.104x 0.606 w0.000x 0.106 w0.000x
0.154 w0.000x 0.355 w0.000x 0.071 w0.001x
0.000 w0.030x y0.002 w0.000x 0.000 w0.049x
Output
Degree-days
Industrial sector Prices
Natural gas Distillate oil Residual oil Coal Electricity
Natural gas
Distillate oil
Residual oil
Coal
Electricity
y0.049 w0.000x 0.105 w0.005x 0.121 w0.001x y0.098 w0.000x y0.047 w0.000x
0.006 w0.483x y0.251 w0.000x 0.035 w0.460x 0.024 w0.283x y0.029 w0.000x
0.011 w0.245x 0.036 w0.457x y0.206 w0.000x 0.023 w0.264x y0.036 w0.000x
y0.028 w0.000x 0.006 w0.499x 0.005 w0.507x y0.491 w0.000x 0.014 w0.063x
y0.035 w0.011x 0.008 w0.010x 0.022 w0.380x 0.534 w0.000x y0.070 w0.000x
0.019 w0.242x 0.021 w0.235x 0.028 w0.237x 0.018 w0.244x 0.019 w0.250x
Trend
Heating
Cooling
0.114 w0.005x 0.906 w0.001x 0.388 w0.001x 0.287 w0.000x 0.055 w0.004x
y0.055 w0.001x 0.439 w0.005x 0.233 w0.000x 0.026 w0.081x y0.032 w0.014x
0.0006 w0.000x y0.0009 w0.142x y0.0021 w0.000x y0.001 w0.000x 0.0001 w0.052x
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Natural gas Oil
Output
307
308
Aggregate price of utility fossil fuels Total electricity consumption Heating degree day deviations Cooling degree day deviations Trend Lagged value R2 Durbin–Watson
Net imports of electricity
Nonutility generation
Transmission and distribution losses
Nuclear generation
Hydroelectric generation
Renewable generation
0.024 w0.162x
0.187 w0.542x
y0.300 w0.009x
y0.214 w0.020x
0.104 w0.272x
y0.050 w0.616x
y0.004 w0.766x 0.001 w0.120x 0.004 w0.121x 0.000 w0.491x 0.915 w0.000x 0.87 2.11
y0.190 w0.610x y0.010 w0.005x y0.005 w0.695x 0.004 w0.004x 0.690 w0.000x 0.99 1.61
y2.000 w0.001x 0.041 w0.000x 0.116 w0.000x 0.004 w0.001x y0.138 w0.441x 0.90 1.58
0.830 w0.010x y0.006 w0.004x y0.027 w0.000x y0.001 w0.106x 0.669 w0.000x 0.97 1.85
y0.374 w0.435x y0.002 w0.732x 0.011 w0.314x 0.001 w0.190x 0.849 w0.000x 0.87 1.99
y0.110 w0.873x y0.001 w0.771x 0.022 w0.331x 0.000 w0.942x 0.913 w0.000x 0.85 2.22
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Table 6 Parameter estimates of miscellaneous electricity balancing equations
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tion rate and HS t is housing starts. Omission of housing stocks from the residential energy cost share equations results in positive own price elasticities of demand. While slightly larger and more significant, the electric utility and the industrial demand for fuels also are very price inelastic. Table 4 also presents the total quantity elasticities that measure how fuel demands change as the scale of consumption changes. Several of these elasticities are significant illustrating the importance of allowing non-homothetic effects on demand. Small but significant technological change affects fuel demands in the electric utility and industrial sectors. Most of the weather elasticities are significant. Moreover, some of them are quite large; particularly those for oil products. Higher heating degree-days generally increase the demand for primary fuels, such as natural gas and oil. Greater cooling requirements increase the residential and commercial demand for electricity. Higher cooling degree-day deviations reduce residential heating oil consumption due to the reduced heating requirements during the spring and fall. Industrial electricity consumption falls with higher heating and cooling degree-days, which may reflect the presence of interruptible service contracts in which industrial customers reduce their usage of electricity during periods of peak power demands. The total elasticities, which include the indirect effects from changing the level of aggregate energy consumption, appear in Table 5. Given the rather small aggregate price elasticities of demand, the total own and cross price elasticities are not substantially different from the partial price elasticities. The total weather elasticities are substantially larger in several cases. For instance, the elasticity of the residential demand for natural gas with respect to heating degree-days is 0.333. With the exception of natural gas in the electric utility sector, all heating degree-day elasticities are larger than the cooling degree-day elasticities. This suggests that heating degree-days have a greater impact on energy consumption and carbon emissions than cooling degree-days. The electric utility fuel demand equations depend upon fossil fuel-fired electricity generation, which equals total electricity generation less nuclear, hydroelectric, and renewable power generation from. Total electric output is equal to total consumption less imports, non-utility generation, and transmission and distribution losses. The estimates from partial adjustment models for non-fossil fuel generation and other sources of electricity supply appear in Table 6. The explanatory variables include the aggregate price of utility fossil fuels, total electricity consumption, heating and cooling degree-days, trend, and monthly dummy variables, not reported here to conserve space. The presence of total electricity consumption in the miscellaneous electricity balancing equations represents the demand-pull on each of these components. Heating degree-days significantly affect non-utility generation, transmission and distribution losses, and nuclear power generation. Cooling degree-days significantly affect these two components of electricity supply. The magnitude of these parameters is similar to the parameter estimates reported in Table 2.
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4. Model simulation analysis The simulation model includes total energy demand and fuel share equations for each sector and the electricity balancing equations. Total electricity demand
Table 7 Impacts of past weather conditions on energy demand and carbon emissions in percent changes from base simulation Fuel consumption Year
Cooling degree days
Electricity
Natural gas
Cooling season, April through September 1983 6.57 0.79 1.15 1984 0.36 0.18 0.48 1985 y2.22 y0.47 y0.97 1986 3.58 0.10 y0.48 1987 8.23 0.31 y0.48 1988 8.96 0.80 0.33 1989 y3.91 y0.30 0.00 1990 3.43 0.23 0.03 1991 11.11 0.50 y0.63 1992 y13.69 y1.03 y0.20 1993 3.15 0.52 0.52 1994 1.56 y0.02 y0.36 1995 8.20 1.07 0.97 1996 0.16 0.06 0.23 1997 y7.82 y0.16 0.97 Heating degree days
Electricity
Natural gas
Heating season, October through March 1983–1984 3.16 0.17 0.88 1984–1985 y1.08 y0.04 0.00 1985–1986 y3.24 y0.18 y1.15 1986–1987 y3.72 y0.41 y1.44 1987–1988 y0.18 y0.13 y0.22 1988–1989 y1.06 0.02 y0.80 1989–1990 y4.55 y0.47 y1.86 1990–1991 y8.92 y1.01 y2.93 1991–1992 y7.88 y1.10 y3.12 1992–1993 2.05 0.27 0.40 1993–1994 4.63 0.64 1.64 1994–1995 y8.44 y1.23 y3.08 1995–1996 3.09 0.38 1.05 1996–1997 y3.62 y0.33 y1.63
Distillate
Residual
Coal
Propane
Carbon emissions
2.03 0.92 y1.26 y0.28 0.11 0.66 y0.17 0.37 0.21 y0.97 0.39 y0.30 1.56 0.36 0.54
6.01 1.33 y3.03 0.59 2.36 4.84 y1.51 1.68 3.56 y6.12 2.84 0.48 6.21 0.49 y1.22
1.35 0.38 y0.94 0.14 0.69 1.44 y0.56 0.50 1.10 y2.18 0.90 0.00 2.14 0.20 y0.36
1.16 0.71 y1.00 y0.61 y0.93 y0.14 0.16 y0.05 y1.09 0.31 0.46 y0.41 0.71 0.31 1.52
1.79 0.55 y1.12 y0.03 0.44 1.30 y0.43 0.43 0.70 y1.71 0.85 y0.12 1.92 0.24 0.11
Distillate
Residual
Coal
Propane
Carbon emissions
2.18 0.33 y1.41 y2.04 y0.10 y0.99 y1.48 y3.65 y3.80 0.64 2.54 y3.53 1.22 y1.36
2.43 y0.16 y1.28 y2.85 y0.88 y1.05 y3.01 y6.40 y7.01 1.32 3.84 y6.87 2.53 y2.66
0.60 y0.04 y0.40 y0.79 y0.23 y0.05 y0.70 y2.00 y2.08 0.48 1.21 y2.48 0.90 y0.80
1.64 y0.24 y1.20 y1.70 0.02 y0.71 y1.50 y3.90 y3.66 0.53 2.21 y3.88 1.29 y1.63
1.17 y0.02 y0.84 y1.33 y0.24 y0.57 y1.29 y2.69 y2.93 0.47 1.67 y3.07 1.09 y1.20
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and generation are endogenous. The simulation model also computes carbon emissions from the consumption of natural gas, distillate oil, residual oil, and coal based upon the emission coefficients reported by EIA Ž1999b.. While far from providing a basis for projecting long-term climate change, there is evidence that the climate in the US has warmed since 1984. Cumulative cooling degree-days are 2.2% higher than normal and heating degree-days are 1.65% lower. Two model simulations from April 1983 to December 1997 provide a basis to determine the impacts of these changes on carbon emissions. First, there is a base simulation of the model using actual degree-day deviations. The second simulation uses the 30-year means for heating and cooling degree-days. All other exogenous variables, such as energy prices and income are the same in the two simulations. Consequently, the changes from the base simulation reported in Table 7, represent those changes in carbon emissions associated with deviations of weather conditions from their 30-year means. There is an unambiguous, positive relationship between heating degree-days and carbon emissions. With warmer winters the demand for energy and carbon emissions fall. The largest impact occurred during the 1994–1995 winter season when the winter was about 8.5% warmer than normal, which led to a 3% drop in carbon emissions. The effects of cooling degree-days are more ambiguous because some months of the cooling season also contain heating degree-days, which may offset the effects associated with cooling degree-days. Nevertheless, there are several years with warmer than normal summers and slightly higher carbon emissions. Over the entire period, carbon emissions under the base simulation with actual weather are 0.2% lower than those under the alternative simulation using
Fig. 1. Simulated effects of a 10% colder than normal winter on fuel consumption.
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Fig. 2. Simulated effects of a 10% colder than normal winter on carbon emissions.
the 30-year means. This suggests that a warmer climate would slightly lower energy consumption and carbon emissions because lower fuel use associated with reduced heating requirements offsets higher fuel consumption to meet increased cooling demands. Simulating the effects of a 3-month shock to heating and cooling degree-days provides a more controlled experiment. First, consider the effects of a colder than normal winter with heating degree-days 10% above the 30-year mean for 3 months. All fuel demands increase ŽFig. 1.. Total carbon emissions appear in Fig. 2 and increase from 4% to 9% during the first three months. Higher residential and commercial consumption is the principle reason for the roughly 7% to 10% increase in natural gas consumption. In addition, electric utility fuel use, particu-
Fig. 3. Simulated effects of a 10% warmer than normal summer on fuel consumption.
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Fig. 4. Simulated effects of a 10% warmer than normal summer on carbon emissions.
larly oil, increases due to the simulated 2% to 4% increase in electricity consumption. The large estimated elasticity of electric utility oil use with respect to electricity generation accounts for most of the increase in residual fuel consumption. This result may reflect electric utilities using oil-fired generators to service peak power demands. The last simulation estimates the effects of a 3-month 10% increase in cooling degree-days. The impacts on fuel demands and carbon emissions appear in Figs. 3 and 4. As expected, electricity demand increases leading to an increase in the demand for coal and oil. Natural gas consumption increases slightly due primarily to higher consumption in the electric utility sectors. Carbon emissions for this scenario rise between 1.5% and 3.7%.
5. Conclusions This paper examines the link between aggregate US energy demand and weather variations. Our focus is on one important dimension of weather, heating and cooling degree-day deviations. The influence of precipitation, wind speed, and other climatic conditions on energy demand awaits further research. Regional analysis is another research need. Our model simulations suggest that warmer climate conditions slightly reduce energy demand and carbon emissions in the US. These results are not grounds for complacency. The 0.2% reduction in carbon emissions due to the slight warming trend since 1982 pales in comparison to the 7% reduction from 1990 emission levels for the US under the Kyoto Protocol. Nevertheless, this study shows that the impact of short-term climate fluctuations on carbon emissions can be sizeable. Our results suggest that future international agreements on global climate change should allow some variance, perhaps up to 3%, in carbon emissions due to short-term weather variations.
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