A Discrete-Continuous Choice Model of Climate
Change Impacts on Energy*
Erin T. Mansur
Yale University
School of Management and
School of Forestry and Environmental Studies
New Haven, CT
erin.mansur@yale.edu
Robert Mendelsohn
Edwin Weyerhaeuser Davis Professor
Yale University
School of Forestry and Environmental Studies.
New Haven, CT
robert.mendelsohn@yale.edu
Wendy Morrison
Texas A&M University
El Paso Agricultural Research Center
El Paso, TX
mmorrison@elp.rr.com
January 2, 2005
*
We would like to thank Arnulf Grübler, Nat Keohane, and Sheila Olmstead for helpful comments. This work was
supported in part by a grant from the Department of Energy.
Abstract
This paper estimates a multinomial discrete-continuous fuel choice model
of both households and firms in order to determine the sensitivity of national
energy demand to climate change. We find that consumers switch from natural
gas, oil, and other fuels to electricity as climate warms and that overall energy
demand—especially electricity demand—increases. The model implies that
warming will increase American energy expenditures, resulting in welfare
damages that increase as temperatures rise. Increases in electricity expenditures
for cooling are partially offset by reductions in expenditures on other fuels for
heating. Given a five degree Celsius increase in temperature by 2100, we predict
an annual welfare loss of $40 billion, borne primarily by residential customers.
1
Introduction
While many have studied the impacts of energy consumption on climate change,
few have examined how changing the climate is likely to impact the demand for energy.
Energy has been identified as one of the more vulnerable economic sectors to climate
change (McCarthy et al., 2001). This paper develops a multinomial discrete-continuous
choice model of joint decisions regarding fuel choice and energy demand. We then apply
this model to examine the interface between climate and energy demand.
Although discrete-continuous modeling has been used to examine numerous
consumption decisions, it has received relatively little attention in the energy literature.
Further, whereas most consumption decisions involve only two choices, there are many
choices of fuels, requiring a multinomial first stage choice. Using the methodology of
Dubin and McFadden (1984), we estimate a multinomial logit model of fuel choice
followed by fuel-specific conditional demand functions. In the specific case of energy,
we find that there is another important distinction to make between houses that have
access to natural gas (“pipeable”) and households that do not (“non-pipeable”). These
two groups of households make very different fuel and energy choices.
Climate warming is expected to affect the demand for space conditioning energy
by reducing heating needs and increasing cooling needs. Using the estimated relationship
between fuel choice and energy demand across current households and firms, we measure
the climate sensitivity of both the fuel choice and conditional demand equations. The
estimated model is then used to predict the US energy impacts of alternative future
climate change scenarios.
1
Despite the widespread interest in global warming, few studies have calibrated the
impact of climate on energy demand. Most energy-climate studies have focused on
measuring energy use as a source of greenhouse gases (Metz et al., 2001), not as a
potential impact of climate change (McCarthy et al., 2001). Most of the studies that do
consider the impacts of climate on the energy sector rely mainly on expert opinion
(Nordhaus, 1991; Cline, 1992), engineering models (Rosenthal et al., 1995) or case
studies of electricity (Crocker, 1976; Linder et al., 1987; Smith and Tirpak, 1989). The
few empirical studies that consider the entire energy sector use an aggregate expenditure
model that examines all fuels without distinction (Morrison and Mendelsohn, 1999;
Mendelsohn, 2001). Our study analyzes how climate change will alter consumers' fuel
choice and subsequent consumption of energy. The study is based on a special data set
that combines climate and energy information from individual residences and firms
across the United States.
The paper proceeds as follows. The discrete-continuous model is presented in
Section 2. Section 3 presents the theory describing the welfare measurement of long run
climate impacts on energy. Section 4 presents the empirical methodology and data.
Section 5 presents the results of the empirical modeling on fuel choice and conditional
demand. The estimated model is then used, in Section 6, to project the energy impacts for
future climate scenarios. The paper concludes in Section 7 with a discussion of the
energy model results and the welfare implications of climate change for the US energy
sector.
2
2
Discrete-Continuous Choice Model of Energy
Modeling techniques that explicitly consider the discrete and continuous
components of consumer choice are found widely in the literature. Researchers have used
this method to examine a wide range of topics including demand for transportation,
housing, and water.1 For many consumer choices, total demand can be broken down into
a discrete component involving choice over alternatives and a corresponding continuous
component describing demand conditional on that choice.
While energy demand includes a discrete fuel choice and a continuous choice of
consumption level, this approach has received relatively little attention in the energy
literature. Baughman and Joskow (1976) develop a model of fuel choice and energy
consumption for electricity, natural gas, and oil in the commercial and residential sectors
of the United States. Their study, however, does not account for potential interactions
between fuel choice and consumption decisions. As noted by Heckman (1979), if the
decisions are not independent, then the model will suffer from selection bias. For many
consumer choice occasions, the error term in the choice equation is correlated with the
error term in the continuous equation, requiring a selection correction estimation method.
Dubin and McFadden (1984) (hereafter, DM) develop a methodology for
estimating a discrete-continuous model in the polychotomous choice setting that accounts
for section correction. DM apply their method to electricity demand and the choice of
appliance holdings. More recently, Vaage (2000) examines household energy
consumption using a discrete-continuous choice model using Norwegian data.
1
Several studies use this method to examine questions of transportation (see Abdelwahab and Sargious,
1992; Mannering and Winston, 1985; and Hensher and Milthorpe, 1987). Lee and Trost (1978) and King
(1980) look at housing choices with this methodology. Other research examines food and drink (Pompelli
and Heien, 1991; Haines, Guilkey, and Popkin, 1988), shopping (Barnard and Hensher, 1992), and water
(Hewitt and Hanneman, 1995; Olmstead et al., 2004).
3
Households make discrete choices of which appliances to purchase and then how much
energy to use conditional on these choices. He finds a large price elasticity in both
modeling stages and substantial, observed household heterogeneity.
Our paper uses the DM model to perform a comprehensive analysis of fuel choice
and energy consumption in the residential and commercial energy sectors in the United
States. The model tests how climate affects current energy decisions. We then use the
model to forecast how climate change will affect both fuel choice and the level of energy
consumption.
3
Welfare Impacts Of Climate Change
In response to climate change, households and firms may alter: 1) fuel choice, 2)
the quantity of fuel, 3) expenditures on building characteristics, and/or 4) interior comfort
levels. For households, a measure of the welfare impacts of climate change on energy can
be described as the change in income necessary to keep utility constant given climate
change:
∂Y
U *(T *, R*),
∂C
(1)
where Y is income, C is climate, U is utility, T is interior temperature, and R is an index
of all other goods. Interior temperature is assumed to be a function of climate, energy use
(Qf conditional on fuel choice f), and building characteristics (Z):
T = T (C , Q f , Z ),
where C is exogenous and Qf and Z are purchased inputs.
4
If people maintain optimal interior temperatures regardless of climate, there will
be no loss of comfort from climate change. A survey of interior temperatures conducted
across households in the winter revealed that households in all regions of the country
maintained the same winter temperatures (EIA, 1993). If, with increased air conditioning
penetration in the future, the same result holds for the summer, future households and
firms will not alter their interior comfort in response to climate change. The welfare
effect from climate change will simply be the change in expenditure required to maintain
these desired temperatures.2 Increases (decreases) in energy and building expenditures
will measure the welfare loss (gain) from climate change. The change in welfare (∆W)
equals:
∆W = ∫
C0
C1
∂Y
≅ Pq Q0 + Pz Z 0 −Pq Q1 − Pz Z1 ,
∂C
(2)
where Pq and Pz are the prices of energy and building attributes, respectively, and
subscripts 0 and 1 represent the baseline case and climate change scenario, respectively.
As long as firms also hold interior temperatures constant, (2) applies to them as well.
Although changes in both energy and building expenditures provide the desired
measure of welfare change, only energy expenditure data and detailed data about building
characteristics are available. We propose to estimate the long run impacts of climate
change. We consequently do not control for building choices that are climate sensitive in
our energy model. This will yield accurate long run measures of how energy will change
as climate changes because it treats these building characteristics as endogenous.
However, the approach will not capture the change in costs associated with changes in
2
To the extent that comfort levels fall or rise with warming, our measures of the impacts of climate change
will be attenuated.
5
buildings. With changes such as cooling capacity, this will lead to an underestimate of the
costs of warming. With changes such as insulation for winter, it will overestimate the
costs of warming. In earlier analyses of energy expenditures, the analysis compared the
energy costs associated with controlling for endogenous building characteristics (short
run) and omitting them (long run). The analyses found that the energy expenditures did
not change dramatically (Morrison and Mendelsohn, 1999; Mendelsohn, 2001). These
results imply that the bias from omitting endogenous building characteristics is likely to
be small.
Because warming reduces heating costs but increases cooling costs, we expect
that energy has a nonlinear relationship with climate. In very cold places, the heating
effects will dominate and in hot places, the cooling effects will dominate. Somewhere
between is a temperate climate that minimizes both heating and cooling. Climate, of
course, is not a single dimension variable. In addition to annual mean temperatures,
seasonal temperature distribution may also be important. In this study, we will distinguish
between winter and summer temperatures. We will also explore the less important but
still significant role of precipitation. In the discrete-continuous model, we define the
welfare impacts of changes in climate as the change in the expected value of energy
expenditures. The probability that a particular fuel portfolio, f ∈ F , is chosen is defined
as θf. Expenditures are the product of prices Pq and the conditional demand Qf.
6
In this discrete-continuous situation, the estimate of the expected change in
welfare corresponding to (2) is:
∆W ≅ Ε  Pq Q f (C0 )  − Ε  Pq Q f (C1 ) 
=
∑ θ
f ∈F
f
(3)
(C0 ) Pq Q f (C0 ) − θ f (C1 ) Pq Q f (C1 ) 
where E[·] identifies the expected value. Therefore, expenditures over all alternatives are
defined as the sum of prices Pq times the conditional quantities Qf, weighted by the
choice probabilities θf. The link between the model components determining θf and Qf is
further described in Section 4.
For most of the analysis, we assume that energy prices do not change as a result
of climate change. Partially because we do not expect them to change very much and
partially because it is very difficult to project how prices across fuels will actually change
given our results.3 However, if energy prices do change, the welfare calculations are more
complicated.
One must estimate the consumer and producer welfare before and after the
warming. Assuming a linear supply response, this will be equivalent to the estimate
above with an additional term equal to one half of the change in price times the change in
quantity for each fuel. So if energy supply is inelastic and warming increases summer
(decreases winter) energy demand; prices will increase (decrease) and the welfare
estimate of damages (benefits) will be slightly higher. We estimate the magnitude of this
endogenous price effect in the sensitivity analysis.
3
The prices for electricity will rise while the prices of other fuels (used for heating) might decline.
However, if the other fuels are used to produce electricity instead, then their prices will not decline.
7
One must estimate the consumer and producer welfare before and after the
warming. The welfare effect will be approximately equivalent to (3) with an additional
term equal to one half of the change in price times the change in quantity for each fuel:
∆W ≅

∑ θ
f ∈F
f
1
(C0 ) Pq Q f (C0 ) − θ f (C1 ) Pq Q f (C1 ) − ( Pq* − Pq ) Q f (C1 ) − Q*f (C1 )
2
(
),
(4)
where Pq* and Q*f (C1 ) are the equilibrium price and quantity after climate change. The
addition term captures the lost consumer surplus that results from the higher prices. So, if
energy supply is not perfectly elastic and warming increases energy demand, both
equilibrium prices and the welfare estimate of damages will increase. If energy demand
falls, then prices will fall and the benefits will be even greater. We estimate the
magnitude of the effect of endogenous prices on our welfare calculations in the
sensitivity analysis of Section 6.
4
Empirical Methodology and Data
4.1
Empirical Methodology
We model fuel choice and fuel consumption using a discrete-continuous model
based on Dubin and McFadden (1984). This model is a generalization of Heckman's
(1979) two-step selection model. The DM two-step estimation uses a multinomial logit
model in the first stage to choose fuels and then estimates the conditional demand model
for each fuel using ordinary least squares (OLS) with selection terms. Lee (1983)
proposes an alternative polychotomous choice two-step selection model. Both the DM
and the Lee models are widely used.
8
However, Schmertmann (1994) shows that the Lee model places substantial
restrictions on the covariances between the continuous demand and selection choice
models. Schmertmann further finds, using a Monte Carlo study, that the Lee model is
significantly biased when this assumption is violated. Bourguignon, Fournier, and
Gurgand (2004) (hereafter, BFG) support these findings with their own Monte Carlo
study of these polychotomous choice two-step selection models. Both studies find the
DM model to be more robust to various data generating processes. This section outlines
our discrete-continuous DM model using the notation of BFG.
We model energy consumption Qf for fuel choice f among F alternatives:
Qf = x f β f + u f
Q*f = z f γ f + η f ,
(5)
f = 1...F
(6)
where all the variables xf and zf are exogenous, and the disturbance uf has the properties:
E (u f | x, z ) = 0 and V (u f | x, z ) = σ 2f . Energy consumption Qf will be positive only when
fuel f is chosen. This occurs if:
Q*f > max(Q*j ).
j≠ f
(7)
Hence, Q*f is a latent variable of fuel consumption.
If the disturbance terms uf and (ηf)’s are independent, estimation of the parameters
βf and γf is straightforward. When they are not independent, some correlation between the
explanatory variables and the disturbance terms may be introduced into (5) and OLS βf
estimates would be inconsistent. As noted by BFG, condition (7) is equivalent to
z f γ f > ε f , where:
9
ε f = max(Q*j − η f ).
(8)
j≠ f
Following McFadden (1973), we assume the (ηf)’s are i.i.d. with an extreme value
type I distribution. This specification implies the multinomial logit model such that:
θ f ≡ Pr( z f γ f > ε f ) =
exp( z f γ f )
∑ j =1 exp( z jγ j )
F
(9)
.
The (γf)'s can be estimated by maximum likelihood. However, the estimation of the (βf)'s
requires further assumptions.
The DM model assumes the following linearity condition:
E (u f | η1...η F ) = σ f ∑ j ≠ f rj (η j − E (η j )),
with the correlations between uf and ηf summing to zero:
(10)
∑
F
r = 0 . With this
j =1 j
assumption, the conditional demand function for each fuel, as given in (5), can be
written:
 θ j ln(θ j )

F
Q f = x f β f + σ f ∑ j =1 rj 
+ ln(θ f )  + w f ,
 1−θ j



(11)
where wf is an independent error term. This equation can be estimated using OLS.
4.2
Data
The data come from the Department of Energy's Commercial Buildings Energy
Consumption Survey (EIA, 1992) and Residential Energy Consumption Survey (EIA,
1993). These surveys provide detailed data on energy expenditures and consumption as
well as demographics, and building characteristics. The data include several thousand
buildings distributed in random clusters across the continental US and are weighted to
10
represent the true population of buildings. Data are available for the five major residential
fuels: electricity, natural gas, fuel oil, liquid petroleum gas (LPG), and kerosene, as well
as the four major commercial fuels: electricity, natural gas, fuel oil, and district heat. The
original data do not disaggregate energy uses. Although space-conditioning energy is
expected to be most sensitive to climate change, other commercial and residential energy
uses may be affected. Hence, the model is estimated for fuel portfolio choice and
consumption across all energy uses.
The DOE data sets originally measured only degree-days as a proxy for climate.
However, by definition, degree-days go to zero as one approaches an arbitrarily chosen
temperature. For example, heating degree-days using 60°F as a base, assume that there
would be no warming if temperatures rose above 60°F. We wish to test what temperature
leads to the minimum expenditures, not assume it. Consequently, in cooperation with
EIA, climate data from each county was merged with the DOE data sets. The climate data
include average monthly temperature and precipitation for January, April, July, and
October. The climate data were originally collected from the National Climatic Data
Center as 30-year averages for 5,511 meteorological stations in the US. The data by
meteorological station were interpolated to US counties using weighted regressions of all
weather stations within 500 miles of each county (see Mendelsohn et al., 1994).
A number of explanatory variables are expected to influence fuel choice and
consumption. The variables used to predict residential and commercial fuel choice and
consumption are described in Table A1 of the Appendix. In general, explanatory
variables include climate, demographic and firmographic information, and building
characteristics. The building characteristics are divided into climate sensitive and non-
11
sensitive categories. Non-climate sensitive building characteristics such as building size,
type of occupancy, and building age are used to control for exogenous non-climatic
factors that affect energy consumption. Climate sensitive characteristics affecting thermal
efficiency include building material, conservation, the choice of heating and cooling
equipment, and some aspects of the household structure. Recall that we are estimating the
long run welfare impacts of climate change. Therefore, these characteristics are not
included in our model as they are assumed to be endogenous in the long run.
We divide residential customers into two groups: the pipeable and non-pipeable
customers. The distinction between pipeable and non-pipeable households partially
reflects a different set of choices since one group has gas and the other does not.
However, it should be noted that pipeable households might also be systematically
different in other respects as well. For example, these households may be more likely to
be in a metropolitan area. When natural gas is available, households can choose
electricity only, natural gas and electricity (“gas”), or fuel oil and electricity (“oil”). Of
the 3,747 pipeable consumers, 82% opt for gas, 9% pick oil, and the rest choose
electricity only. When gas is not available, they can choose electricity only, fuel oil and
electricity, or other fuels (like LPG and kerosene) and electricity (“other”). Of the 1,283
non-pipeable consumers, 44% choose electricity only, 26% pick oil, and the rest opt for
kerosene or LPG. Commercial customers are estimated jointly. Of the 5,605 firms, 55%
opt for natural gas, 27% pick electricity only, 10% choose oil, and the rest use district
heat (“other”).
12
Table 1 reports the actual expenditures for each customer class. For each fuel,
expenditures equal the sum over all households of the fuel price, the household's demand
of that fuel, and the population weight of the household (ωi). For N households:
Expend f = ∑ i =1 Pqi Q fiωi .
N
(12)
Based on our sample, of the $179 billion (in 1990 dollars) that the residential and
commercial sectors spend on energy, 71% is for electricity. Furthermore, of the overall
expenditures on electricity, 75% is by customers who use other fuels as well. Thus, even
though a large portion of the sample is labeled “natural gas” consumers, most of the
expenditures are on electricity. The share of total expenditures that is for either electricity
or natural gas is over 90%.
5
Results
In this section, we report our estimation results in four subsections and then
examine the sensitivity of the national energy model to climate change. First we discuss
the selection model results for the residential customers. We separately estimate those
households that have access to natural gas and those who do not. Then the residential
conditional demand models are explored for each fuel choice and each subgroup. Next
the commercial selection model results are examined. We do not have information
concerning whether firms have access to natural gas so all firms are estimated in one
common multinomial model. Then the commercial conditional demand models' results
are reported. Finally, we test the sensitivity of energy expenditures in the current
economy to climate change.
13
5.1
Residential Fuel Choice Results
The results of the multinomial logit fuel choice estimation for the residential
sector are shown in Table 2. We report the γf coefficients from estimating the latent
variable model, (6). For both pipeable and non-pipeable groups, the electricity alone
portfolio is the base category where the normalization γ1=0 is imposed. The models fit the
data relatively well. The pseudo-R2 is 0.39 for the pipeable households and is 0.41 for the
others.
Temperature and precipitation variables suggest that climate change will impact
households’ choice of fuel. Many households in warmer regions rely on electricity alone
since, on the cooling side, it is virtually the only option. On the heating side, it has a high
marginal cost but a low fixed cost, making it desirable in moderate winters. The model
results suggest that more households will prefer to move to electricity alone as
temperatures warm.
Given the nonlinearity of the choice model, Table 3 reports the marginal impacts
of temperature and precipitation for January, July, and overall.4 For the pipeable
households, greater January temperatures are likely to result in more households choosing
natural gas instead of oil. A marginal increase in July temperatures increases households'
probability of choosing electricity only but this effect is just weakly significant at the
10% level. Overall, the marginal impact of an increase in temperature is a reduction in
4
The marginal effects are calculated in the following manner:
∂ Pj
∂Cj
= Pj [γ j − ∑ k ≠ j γ k ]
(Green 1993, 666).
Marginal effects are calculated at the sample mean of each independent variable. We assume independence
of the linear and quadratic terms when estimating the standard errors of the marginal effects. A marginal
increase in temperature is measured in degrees Celsius. A marginal increase in precipitation is measured in
inches.
14
the probability of choosing oil of 0.4%. Greater precipitation is likely to result in fewer of
the pipeable households selecting natural gas and more opting for electricity only.
For the households that do not have access to natural gas, the marginal impact of
temperature is substantially larger than for the pipeable households. A marginal increase
in July temperatures results in a 3.5% reduction in the probability of selecting oil and a
5.1% increase in the probability of selecting electricity only. The overall temperature
effects are similar. For these non-pipeable households, precipitation has a negligible
impact.
Table 2 also reports the coefficient estimates for the other factors including
electricity and fuel prices, as well as a number of demographic and structural
characteristics. The price variables significantly influence the choice probabilities. The
own-price effects are negative while the cross price effects are positive, suggesting that
the other options are substitutes. We also note that newer buildings, multi-unit buildings,
and wood burning residents are more likely to select electricity only. Higher income
households are less likely to choose kerosene or LPG. Larger homes select either gas or
oil with greater frequency. Mobile homes tend to use gas or other fuels.
5.2
Residential Conditional Consumption Results
Table 4 presents the results of the residential conditional consumption analysis for
the climate and price variables. Because of nonlinearity of the climate variables, we
report the marginal impact of temperature and precipitation at the sample mean of each
variable. When natural gas is available, the marginal impact of a one degree Celsius
increase in January temperatures, relative to a mean of zero, is a reduction in electricity
15
consumption of 3% for electricity only consumers (the impact is -0.028 on the natural log
of kWh's consumed). Natural gas consumption falls 2% given a similar marginal
increase.
When July temperatures are increased one degree Celsius (relative to a mean of
24°C), electricity consumption increases substantially for all pipeable customers:
electricity only customers increase their consumption 5%, gas customers increase their
demand for electricity by 6%, and oil customers buy 15% more electricity. Consumption
of natural gas falls 2% given a marginal increase in July temperatures, resulting in an
overall reduction of 4%. A one-inch increase in monthly precipitation, relative to a means
of 2.6 inches in January and 3.6 inches in July, results in more consumption by gas users
of both electricity (7%) and of gas (2%).
Of the non-pipeable customers, January temperatures reduce the consumption of
oil by 6%. July temperatures increase electricity consumption for electricity only (4%)
and oil (12%) customers, but decrease consumption for consumers of other fuels (4%).
The overall impact of precipitation is insignificant at the 5% level for these customers.
Overall, the climate variables are behaving as we expect with warmer summers
increasing energy and warmer winters decreasing energy consumption.
The own-price elasticities for electricity consumption range from -0.24 to -1.32
for the six customer groups. The own-price elasticities are -0.5 for natural gas
consumption and -1.3 for the other fuel consumers based on the LPG price. For both the
pipeable and non-pipeable oil consumers, the own price elasticities are 0.5. These
positive oil price elasticities may reflect problems in collecting price data for oil.
Consumers report expenditures and quantities of oil and prices are inferred for oil. It is
16
possible that consumers remember their last oil delivery rather than their monthly
consumption rates. In general, the cross price fuel elasticities are positive.
The other characteristics of the residence, household, and selection control
variables are shown in the Appendix. We report all of the coefficient estimates for the
pipeable (see Table A2) and non-pipeable (see Table A3) customers. In general,
consumption is increasing in home size, income, and age of head of household. At least
one selection term in half of the regressions is weakly significant at the 10% level. To
interpret the coefficients, consider the following case. For households selecting gas, the
coefficient on the electricity-only error term from the selection model is positive. This
implies there is a positive correlation between the error in the conditional demand models
for gas and the error in the choice of electricity only in the selection model. Households
with a greater probability of selecting electricity only tend to consume more gas.
5.3
Commercial Fuel Choice Results
Table 5 presents the results of the multinomial logit fuel choice model for the
commercial sector. Here, all customers are modeled jointly. Electricity alone is the base
category relative to selecting gas, oil, or other (here, other is district heat). The pseudo-R2
is 0.35.
Many of the climate variables are significant, particularly for choosing oil. Table
6 reports the marginal effects of the temperature variables. Most of the climate impacts
result from changes in July temperatures. A one-degree increase results in a 1.6%
increase in the probability of selecting electricity only, while the probability of selecting
17
oil falls by 1.3%. Greater precipitation reduces the number of firms selecting gas and
increases the number selecting electricity only or oil.
Table 5 also reports the coefficient estimates for the other firm characteristics.
The gas and district heat own-price effects are negative while the own price effect of oil
selection is insignificant. Most of the cross price effects are positive. However, greater
electricity and gas prices increase the probability of choosing district heat, suggesting
these are complements relative to the other options. We also note that newer and smaller
buildings are more likely to select electricity only. Multi-building facilities tend to choose
electricity only and district heat. Commercial firms with alternative fuels not listed are
more likely to select electricity only. Buildings with more establishments and more indoor parking tend to select electricity only. Finally, firms in metropolitan areas tend to
select gas or district heat.
5.4
Commercial Conditional Consumption Results
Table 7 presents the results of the commercial conditional consumption analysis
for the climate and price variables. The marginal impact of a one degree Celsius increase
in January temperatures is a reduction in electricity consumption of 3% for electricity
only firms but an increase in electricity consumption of 2% for natural gas firms. The
marginal effect also reduces gas consumption by 3% and oil demand a sizeable 12%.
Marginal increases in July temperatures further reduce gas consumption an additional
3%. A one-inch increase in January and July precipitation results in more consumption of
gas (6%) and of oil (40%).
18
Overall, firms are relatively sensitive to the prices of the fuels they consume. For
electricity consumption, the own-price elasticities range from -1.01 to -1.98 for the four
groups of firms. The own-price elasticities are relatively large in magnitude for natural
gas, -1.8, and for oil, -3.6. In contrast, district heat consumption is inelastic, -0.3. District
heat is characteristically used in non-profit institutions that have multiple buildings such
as universities and hospitals.5 One explanation for the lack of observed price effects for
district heat is that it is a difficult and costly task to change to another fuel. Another
explanation is that the non-profits that dominate this fuel type are poor managers and fail
to respond to prices by encouraging conservation. The cross price elasticities tend to be
insignificant though gas and electricity seem to be complements.
Table A4 reports the coefficients on the other covariates. The size of the building
in square feet strongly influences consumption in all models as expected. The quantity
demanded decreases with the age of the building, suggesting new buildings use more, not
less, energy. Despite the fact that new buildings include more insulation, they also
provide many services such as central air, computer facilities, and vending operations that
could explain the higher energy expenditures. We also note that firms demand more fuel
if their buildings are open for business more months of the year. Demand also increases if
the firm has multi-building facilities. Metropolitan location has a strong positive
influence on consumption for most fuel portfolios, identifying the potential for a heat
island effect in cities. Firms with “alternative fuels” demand less of the selected fuel.
Both the percentage of assembly activities and the percent of the building used as a
warehouse or vacant space have a strong negative influence on consumption across
5
83% of commercial buildings that consume district heat are multi-complex facilities and 93% are in
designated “urban” areas. In addition, the mean energy consumption in BTUs exceeds the mean of the
sample by almost 3 times.
19
portfolios, probably due to lower space conditioning costs. Sample selection variables
impact consumption of electricity and gas. For customers selecting electricity only, the
greater the selection error for choosing gas the greater the electricity consumption while
larger oil selection errors result in less demand.
5.5
Climate Sensitivity Measures
In order to measure the sensitivity of current energy expenditures to climate, we
explore what would happen to the current system with a small increase in warming and
precipitation. For each class of residential customer, as determined by fuel choice and
availability of natural gas, we calculate the predicted change in expenditures from climate
change, using (12). We define the marginal impact of climate change to be a 1°C increase
in temperature, which is approximately an 8% increase in average temperature, and a 7%
increase in precipitation. The energy system is not particularly sensitive to precipitation
so that most of the change will be due to warming. This allows us to determine the
overall sensitivity of each customer class to climate changes holding all else constant.
Given the complexity of the linkages between the variance-covariance matrices of
the climate variable estimates in both stages, we measure the uncertainty over our
predictions using a bootstrapping method. We create 1000 data sets by drawing, with
replacement, from the original residential data. For each sample drawn, we calculate the
discrete-continuous DM model and use the estimated coefficients to measure the changes
in expenditures associated with climate change. In Table 8, we report the median, 5%,
and 95% of the draws. With these last two measures, we construct the 90% confidence
20
interval. We then repeat the exercise for the commercial data. All expenditures are
represented in 1990 dollars.
The overall residential expenditures increase $2.0 billion with a 90% confidence
interval of $1.1 to $2.7 billion. This is about a 2% change, suggesting a relatively small
elasticity of approximately 0.25. Most of the impacts are in electricity expenditures (an
average increase of $3.8 billion for all customers). This is partially offset by less
consumption of oil and natural gas.
Throughout the analysis, we note several interesting patterns. We consistently
observe that consumers spend more on electricity because of greater needs for cooling
but they spend less on other fuels that are primarily used for heating. Another consistent
result is that the increases in expenditures associated with more cooling exceed the
decreases in expenditures associated with less heating as the climate changes.
Another interesting result is that pipeable and non-pipeable customers have very
different responses to warming. The pipeable consumers are sensitive to climate change.
In contrast, the energy expenditures of the non-pipeable consumers hardly change.
Namely, the 90% confidence interval for the non-pipeable response (-0.1 to 1.0 billion)
spans zero. In fact, the only significant impact for these customers is that the electricity
only customers are expected to increase expenditures by $1.2 billion. In contrast, all of
the energy expenditure responses to warming of the pipeable customers are significant at
the 10% level.
We also report the marginal sensitivity of the commercial expenditures to climate
change in Table 8. Warming causes firms to spend more on electricity if it is their only
fuel. When the firm relies on more than one fuel, there is no change in electricity
21
expenditures with warming. Commercial natural gas, oil, and district heat expenditures
are predicted to fall with climate change. These climate change impacts cancel each other
so there is little response from the commercial energy sector.6
6
Climate Change Simulation
We use our discrete-continuous DM model estimates to simulate the impacts of
climate change on energy expenditures under various future scenarios. The early
literature on impacts focused on how climate might affect the current economy as shown
in the exercise above. In practice, climate change will be occur far into the next century.
In this section, we begin by introducing our base case scenarios for 2050 and 2100. For
several climate change scenarios, we discuss how warming would impact these future
economies. Then, we examine the robustness of our main findings to alternative
economic assumptions regarding energy prices (including endogeneity), population
growth, and economic growth.
6.1
Base Case Scenario of Climate Impacts
Population in the United States is projected to grow annually by approximately
0.3% (IPCC, 1990). We assume similar growth of the number of firms. Based on historic
averages, we model income per capita as continuing to grow at 2% per year. We assume
that these changes are proportional across the country. We assume that the age
distribution of the building stock will not change.
6
The median of the bootstrap draws reports a reduction in expenditures of 0.3 billion with a 90%
confidence interval of -1.1 to 0.6 billion.
22
We also predict that fuel prices will increase over the next century. These changes
are likely to occur due to expected reductions in fossil fuel supplies (Hotelling, 1931). In
our base case scenario, we assume that oil, natural gas, and other fuel prices increase 50%
by 2050. We assume that electricity prices will increase only 25% because of the
presence of relatively plentiful coal and nuclear power. As oil and gas prices rise, we
assume that synthetic gases and oils will be made from coal. This backstop technology is
assumed to be abundant, so our prices do not change from 2050 to 2100. All of these
changes will affect the fuel choice, conditional consumption, and the total expenditures of
the forecasts.
Given these baselines, we simulate how climate change may impact the
economies of 2050 and 2100. The scenarios test the change in welfare with and without
the climate changing given baseline conditions. For 2050, we test the impacts of changes
in temperature of 1°C and 2°C with a 7% increase in precipitation. For 2100, we study
increases of 2.5°C and 5°C with a 15% increase in precipitation. All of our climate
change scenarios assume uniform climate change across the US. Current scientific
evidence suggests that changes in climate are not likely to be uniform, and instead are
expected to vary across regions, climate zones and countries. However, climate models
do not agree on within-country variation and their results are difficult to compare. In
contrast, the uniform scenarios for a country are a reasonable approximation of the
expected climate effects (Williams et al., 1998) and they are easy to interpret.
Table 9 reports our base case findings for the four climate scenarios. We focus on
the changes in expenditures. We use our main coefficient estimates shown in Tables 2 to
23
7 to predict our expected change in expenditures from climate change, rather than the
1000 bootstrap estimates.
In the 2050 low climate scenario of a one-degree change, residential expenditures
are predicted to increase by $4 billion while commercial expenditures are not predicted to
change. By doubling the climate impacts in 2050 (from a one to a two degree change),
the expenditures more than double (increasing to $9 billion). For 2100, the low climate
scenario of 2.5C predicts an increase in expenditures of $16 billion, most of which is
attributable to residential consumers. Finally, given a five-degree increase in temperature
and a 15% increase in precipitation, total expenditures are predicted to increase by $40
billion. Almost all of these expenditures, 93%, are attributed to residential consumption.
In the next subsection, we test the sensitivity of our main findings to our key assumptions
regarding the future economy.
6.2
Simulation Results and Sensitivity Analysis
Our sensitivity analysis reveals the interaction between assumptions about the
base case changes in energy and the impact of climate change. The analysis tests whether
the results of the 2100 high climate case are sensitive to alternative assumptions. We
begin by testing the importance of having endogenous energy prices in the welfare
calculation. We also examine the impact of alternative assumptions about price changes,
fuel availability, population growth, and rising income.
Table 10 provides several sensitivity tests. The first row repeats our base case
findings of $40 billion. Our first sensitivity analysis, shown in the second row, explores
what difference it makes if energy prices are endogenous. Obviously, if the supply is
24
relatively elastic, then prices will change very little and there will be almost no additional
effect. Namely, equations (3) and (4) would predict similar changes in welfare. In this
scenario, we assume that the long run supply of every fuel type is unit elastic (the price
elasticity equals 1.0).7
Overall demand for electricity will increase as a result of climate change.8 In this
scenario, we assume that the first resources that power plants would use in order to meet
this increase in demand would be any reductions in the quantities demanded of oil,
natural gas, and other fuels associated with climate change. For each fuel, we convert the
Btu’s of energy into electricity. We assume an efficiency rate of 40%, or equivalently, a
“heat rate” of 8530 Btu/kWh. As consistent with our findings on total expenditures, the
increase in electricity demand is greater than the reduction in energy from the other
sources (converted into kWh’s). The increase in demand of electricity—net of the new
supply from oil, gas, and other fuels’ reserves—will increase the market price for
electricity. However, no other fuel prices will be impacted.
We solve for the equilibrium electricity prices and quantities for all fuels
iteratively. For a given percent increase in electricity prices, we measure the equilibrium
quantities of all fuels. We then calculate the percent increase in net electricity demand.
As we assume unit elastic supply, the equilibrium will exist when the two percent
changes equate. In our model, electricity prices will increase by 9.65% if electricity
supply is unit elastic. Using (4), the change in welfare approximately equals the $39.8
billion from the base case, plus one half times the change in average electricity prices
7
Note that these supply elasticities are for the residual residential and commercial US market only,
ignoring international and industrial customers’ responses.
8
Table 8 shows that overall electricity expenditures increase for a marginal change in climate. In our base
case, a temperature rise of 5°C in 2100 results in the total quantity of electricity demanded increasing by
34%.
25
(
)
($0.0084 per kWh) times the reduction in consumption of electricity, Q f (C1 ) − Q*f (C1 ) .
This reduction is the change in consumption that can be attributed to the price increase,
given that temperatures have risen. For the residential consumers, electricity consumption
decreases 87.3 billion kWh, implying an increase in welfare loss of $367 million. For
commercial customers, consumption decreases 85.1 billion kWh and welfare falls $358
million. The overall additional impact of 0.72 billion that is due to the endogeneity of
prices goes from $39.8 billion in the base case to $40.5 billion.
The remaining sensitivity analyses are focused on changing baseline conditions.
For example, we test the robustness of our main results with two exogenous price
counterfactuals. First, we assume that all energy prices uniformly increase by 50%,
including the electricity prices. Here, expenditures increase $44 billion. The second
exogenous price case allows the prices to increase as in the base case but imposes that oil
supplies, and synthetic oil substitutes, are exhausted. We set oil shares to zero and allow
the other fuel shares to increase proportionally. This is consistent with the independence
of irrelevant alternatives assumption made in multinomial logit models. Expenditures
increase $55 billion as a result of climate change in this case.
We then test the sensitivity of the welfare impacts to other characteristics of the
economy. The fifth row is similar to the base case but we double the population growth
rate. The change in expenditures is $54 billion, a 35% increase over the base case. The
next row doubles the income per capita for residential customers relative to the base case.
Welfare falls by $55 billion as a result of climate change. In the last row, we see that if
26
this substantial amount of climate change occurred in today’s economy, the change in
expenditures would be only $17 billion, less than half of the effect seen in the base case.9
Overall, we conclude that the impacts of climate change on energy expenditures
are quite sensitive to the assumptions of the future. Our base case simulation of the
annual welfare loss associated with a 5°C increase in temperature for 2100 is
approximately $40 billion. In contrast, our predictions that allow for different
assumptions regarding changes in prices, population growth, and income growth range
from $17 to $55 billion.
7
Conclusions
This discrete-continuous model of the impact of climate change on fuel choice
and energy expenditures provides valuable insights regarding the nature of climate
change adjustment in the US energy sector. This is the first study to explicitly consider
how climate change impacts fuel choice in each energy market. The model results
indicate that the fuel choice component is an important aspect of the climate adjustment.
Warming leads both firms and homes to move towards choosing only electricity to heat
and cool. This fuel switch is sometimes more important than changes in the quantities of
fuels chosen.
The model projects that climate change will cause damages in the energy sector
and especially in the residential energy sector. If warming is in the neighborhood of
2.5°C, these damages will be approximately $16 billion in 2100. With a 5°C warming,
9
Note that Tables 7 and 8 report the median of 1000 bootstrap draws while Table 10 is based on the initial
sample only. Both methods provide consistent estimates of expenditures but need not be exactly equal.
27
residential energy damages are expected to rise to $37 billion with another $3 billion of
damages in the commercial side. We find that these estimates are sensitive to
assumptions about price changes, population growth, and economic growth.
Our estimated impacts exceed those predicted by previous studies. Nordhaus
(1991) and Cline (1992) predict electricity damages ranging from $2.4 billion to $11.2
billion and non-electric benefits ranging from $1.7 billion to $1.2 billion, respectively.
Using an engineering methodology, Rosenthal et al. (1995) predict net benefits on the
order of $5 billion. Morrison and Mendelsohn (1999) predict damages of $4 billion with
a 2.5°C warming and $13 billion with a 5°C warming. Partly, our overall welfare impacts
are more severe because our fuel specific model predicts large swings in fuel choice
towards electricity as a result of warming. The explicit modeling of fuel choice allows for
more accurate and more detailed insights into the effects of climate change on energy
demand.
The other major reason why our damage estimates are higher than the earlier
literature is because we are projecting the impacts on a 2100 economy. Nordhaus, Cline,
and Rosenthal all relied on a 1990 economy. Morrison and Mendelsohn projected
forward only to 2060. As our sensitivity analysis reveals, projecting climate change on a
future economy makes a large difference. The impacts of climate change are much larger
if one accounts for the future growth in energy prices, population, and income.
There is further work to pursue in this area. Since climate change is a global
phenomenon, impact estimates are needed around the world. Both the pattern and type of
energy use can vary significantly between developed and developing countries. An
important next step is to study the nature of impacts in developing countries in order to
28
develop an aggregate estimate of world energy impacts. In addition, these results should
be combined with other impact and cost studies in order to develop an integrated
assessment of the costs of controlling climate change and the corresponding benefits.
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31
Table 1: Actual Energy Expenditures by Customer Type
Residential
Natural Gas is
Available
$5.8
Residential
Natural Gas is
Not Available
$14.0
Residential
Total
Commercial
Total
$19.8
$12.1
Electricity Others
$40.1
$11.0
$51.1
$43.6
Natural Gas
$26.4
$26.4
$8.5
$3.9
$7.7
$1.6
$4.0
$4.0
Electricity Only
Oil
$3.8
LPG/Kerosene
District Heat
Total
$3.9
$76.2
$32.9
$109.1
$69.6
Total expenditures are measured in billions of 1990 dollars. For a given fuel,
expenditures equal the sum across households, or firms, of each consumer’s price times
total annual consumption, weighted by the population weights for the sample.
32
33
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level.
January temp
January temp2
July temp
July temp2
January precip
January precip2
July precip
July precip2
log elec. price
log n. gas price
log fuel oil price
log lpg price
log kero. price
log building age
log no. floors
log age of head
log home area
log income
log family size
mobile home
multi unit
metropolitan
burn wood
constant
Table 2: Selection Model for Residential Customers
Natural Gas is Available
Natural Gas is Not Available
Gas
Oil
Oil
Other
0.029
-0.238 **
-0.045
-0.004
-0.001
-0.009 *
-0.002
-0.003
-0.092 #
-0.197
-0.502**
-0.131 #
-0.012
-0.059 *
-0.066**
0.010
-0.233 **
0.042
-0.192
-0.061
#
0.014
0.034
-0.062
0.025 #
-0.101 #
-0.051
0.515**
-0.052
-0.026
0.103 *
-0.139*
0.014
3.500 **
2.566 **
3.327**
3.292**
-2.471 **
4.674 **
-0.317
-2.180 *
1.053
0.208
1.648**
-2.747**
1.161
-2.819**
0.761 **
2.103 **
1.358**
0.523**
-0.322 *
0.698 **
-0.283
-1.420
0.551 **
0.784 *
0.544
0.273
0.431 **
0.488 *
0.854**
-0.146
0.007
-0.027
-0.122
-0.427**
0.633 **
0.806 **
0.268
0.571**
1.259 *
-0.014
0.624
1.175**
#
-0.481 *
-1.375 **
-0.755
-2.012**
-0.109
-0.667 **
0.116
-0.367
-0.677 **
-0.298
-0.705**
-0.414*
2.582
-5.278 #
-3.973
12.301**
Table 3: Marginal Effects of Selection Model for Residential Customers
Panel A: Natural Gas is Available
January temp
July temp
Annual temp
January precip
July precip
Annual precip
Electricity
-0.1%
0.3% #
0.2%
0.9% **
0.3%
1.2% **
Gas
0.4%**
-0.2%
0.2%
Oil
-0.3%**
-0.1%
-0.4%*
-1.2%**
-0.3%
-1.5%**
0.3%*
0.0%
0.3%
Panel B: Natural Gas is Not Available
January temp
July temp
Annual temp
January precip
July precip
Annual precip
Electricity
0.4%
5.1% **
5.6% **
2.1%
-2.1%
0.0%
Oil
-0.4%
-3.5%*
-3.9%**
Other
0.0%
-1.7%
-1.7%
-2.0%
5.5%**
3.5%
-0.1%
-3.4% #
-3.5%
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level.
Marginal effects are calculated at the sample mean of each independent variable. We
assume independents of the linear and quadratic terms when estimating the standard
errors of the marginal effects. A marginal increase in temperature is measured in degrees
Celsius. A marginal increase in precipitation is measured in inches.
34
Table 4: Marginal Climate Effects and Price Elasticity Estimates of the
Conditional Demand Models for Residential Customers
Panel A: Natural Gas is Available
January temp
July temp
Annual temp
Electricity consumption
Only
Gas
Oil
-0.028 **
0.000
-0.041
0.045 **
0.060**
0.153 *
0.017
0.060**
0.113 **
Other fuels
Gas
Oil
-0.020**
-0.029
-0.022**
-0.048
-0.042**
-0.077
January precip
July precip
Annual precip
0.043 #
-0.004
0.039
-0.011
0.035**
0.024**
log elec. price
-0.759 **
log n. gas price
log fuel oil price
0.036**
0.034**
0.070**
0.103
-0.043
0.060
-0.765**
-0.929 **
0.122*
0.217**
-0.041
0.002
-0.038
0.274 #
-0.511**
0.529 **
0.487*
Panel B: Natural Gas is Not Available
January temp
July temp
Annual temp
January precip
July precip
Annual precip
log elec. price
log fuel oil price
log lpg price
log kero. price
Electricity consumption
Only
Oil
Other
-0.008
0.007
0.017
0.039 **
0.122*
-0.043 *
0.031 **
0.129**
-0.027 #
0.009
0.010
0.018
-0.244 **
Other fuels
Oil
Other
-0.057*
-0.018
0.102
-0.016
0.045
-0.034
-0.088
-0.064
-0.152 #
-0.002
0.060 *
0.058 #
-0.003
-0.018
-0.021
-1.324**
-0.736 **
0.125
0.369
0.522
-0.107
-0.131
-0.071
-0.053
-0.124 #
0.370
#
-1.253**
0.805
Notes: Consumption in ln(kWh) for electricity, ln(therms) for natural gas, and ln(gallons) for oil
and other fuels. Marginal increases are measured at the sample means. A marginal increase is
measured in degrees Celsius for temperature and in inches for precipitation. We note significance
by ** at the 1% level, * at the 5% level, and # at the 10% level. Regressions include quadratic
functions of climate variables, log building age, log no. floors, log age of head, log home area,
log income, log family size, mobile home, multi unit, metropolitan, burn wood, selection
variables for each fuel not chosen, and a constant.
35
Oil
-0.064 *
0.003
-0.391 **
-0.039 **
0.499 **
-0.069 **
0.277 **
-0.081 **
0.385 *
0.497 **
0.873
0.395
-1.995 **
0.519 **
0.410 **
0.192 **
-0.771 **
0.240
0.145 **
-0.021 **
0.000
0.011 **
0.005
-0.024 **
-0.011 **
-0.007 **
-5.206 **
36
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level. The excluded percentage of space is for retail or service.
January temp
January temp2
July temp
July temp2
January precip
January precip2
July precip
July precip2
log elec. price
log n. gas price
log fuel oil price
log dist. heat price
alt. fuel used
log building age
log no. floors
log square feet
multi-bldg facility
metropolitan
months open/year
no. establishments
% assembly
% educational activities
% food service activities
% in-door parking
% warehouse/vacant
% office
constant
Gas
0.004
-0.001
-0.065 *
-0.006 #
0.053
-0.019 **
-0.127 **
0.017
0.476 **
-3.381 **
2.709 **
0.442
-2.530 **
0.402 **
0.001
0.199 **
-0.581 **
0.561 **
0.111 **
-0.008 *
0.000
0.003 #
0.010 **
-0.032 **
-0.013 **
-0.005 **
-3.454 **
Table 5: Selection Model for Commercial Customers
Other
-0.012
-0.006**
-0.149**
-0.007
-0.163*
-0.001
0.000
-0.002
-0.501*
-0.494**
2.908**
-1.250**
-3.376**
1.040**
1.086**
0.417**
1.800**
0.894**
0.030
-0.018**
-0.001
0.004 #
0.002
-0.039**
-0.018**
-0.005**
-8.882**
Table 6: Marginal Effects of Selection Model for Commercial Customers
January temp
July temp
Annual temp
January precip
July precip
Annual precip
Electricity
0.1%
1.6% **
1.7% **
-1.0%
1.9% **
0.9%
Gas
0.2%
0.1%
0.3%
-0.1%
-3.7%**
-3.8%**
Oil
-0.2% #
-1.4%**
-1.6%**
Other
-0.1%
-0.3%*
-0.3%*
1.7%**
1.6%**
3.4%**
-0.6%**
0.2%
-0.4%
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level.
Marginal effects are calculated at the sample mean of each independent variable. We
assume independents of the linear and quadratic terms when estimating the standard
errors of the marginal effects. A marginal increase in temperature is measured in degrees
Celsius. A marginal increase in precipitation is measured in inches.
37
Table 7: Marginal Climate Effects and Price Elasticity Estimates of the
Conditional Demand Models for Commercial Customers
Panel A: Electricity consumption
Only
January temp
-0.026 *
July temp
0.046 #
Annual temp
0.020
January precip
July precip
Annual precip
0.011
-0.050 #
-0.039
log elec. price
-1.982 **
log n. gas price
log fuel oil price
log dist. heat price
Gas
0.020**
-0.022 #
-0.002
0.011
0.013
0.024
-1.683**
Other
0.004
-0.010
-0.005
0.140
-0.130 #
0.009
0.057
0.011
0.068
-1.558 **
-1.009**
-0.248*
-0.638 #
0.126
Panel B: Consumption of other fuels
Gas
January temp
-0.030 **
July temp
-0.025 *
Annual temp
-0.055 **
January precip
July precip
Annual precip
Oil
-0.031
0.138 #
0.106
0.030
0.031 #
0.060 **
log elec. price
-0.073
log n. gas price
log fuel oil price
log dist. heat price
-1.816 **
Oil
-0.118**
0.000
-0.117 #
Other
0.020
-0.029
-0.010
0.312**
0.085
0.397**
-0.009
0.013
0.004
0.090
0.017
-3.649**
-0.259 *
Notes: Consumption in ln(kWh) for electricity, ln(therms) for natural gas, ln(gallons) for oil, and
ln(pounds of steam) for district heat. We note significance by ** at the 1% level, * at the 5%
level, and # at the 10% level. Marginal increases are measured at the sample means. A marginal
increase is measured in degrees Celsius for temperature and in inches for precipitation.
Regressions include quadratic functions of climate variables, alt. fuel used, log building age, log
no. floors, log square feet, multi-bldg facility, metropolitan, months open/year, no.
establishments, selection variables for each fuel not chosen, and a constant. In addition, the
regression includes shares of space for assembly, educational activities, food service activities, indoor parking, warehouse/vacant, and office.
38
Table 8: Sensitivity of Energy Expenditures to Climate Change
(in billions of 1990 dollars)
Electricity Only
Electricity Others
Natural Gas
Oil
Other*
Total
Residential
Natural Gas is
Available
0.8
Residential
Natural Gas is Not
Available
1.2
Commercial
Total
[0.5, 1.1]
14%
[0.8, 1.6]
9%
[0.8, 1.5]
9%
1.1
2.1
-0.3
-0.6
[1.7, 2.5]
[-0.8, 0.2]
[-1.3, 0.0]
5%
-3%
-1%
-0.9
n/a
-0.2
[-1.1, -0.7]
[-0.4, -0.1]
-3%
-2%
-0.5
-0.2
-0.3
[-0.8, -0.3]
[-0.5, 0.0]
[-0.4, -0.2]
-13%
-5%
-19%
n/a
-0.1
-0.2
[-0.4, 0.1]
[-0.4, 0.0]
-3%
-5%
1.5
0.5
-0.3
[1, 1.9]
[-0.1, 1]
[-1.1, 0.6]
2%
2%
0%
Notes: The table reports the marginal impact of climate change: a one degree Celsius
increase in all temperatures and a 7% increase in precipitation. We show the median
change, 90% confidence interval of the change, and the percent change in expenditures.
The statistics are calculated using a bootstrapping method with 1000 draws as described
in the text. “Other” is LPG and kerosene for residential and district heat for commercial.
39
Table 9: Base Case Simulation of Welfare Loss Due to Climate Impacts
(in billions of 1990 dollars)
Scenarios
Residential
Commercial
Total
2050 Low Climate
4.0
0.0
4.0
2050 High Climate
8.8
0.3
9.0
2100 Low Climate
15.5
0.5
16.0
2100 High Climate
37.1
2.7
39.8
Notes: For the 2050 and 2100 predictions, we assume that electricity prices will increase
25%, and that other fuel prices will increase 50%. We assume annual growth rates of
0.3% for population and 2% for income per capita. Simulations assume the 1990
distribution of building ages. For each year, a low and high range of temperature change
is given. In 2050, the low and high estimates of change in degrees Celsius are 1 and 2. In
2100, the range is 2.5 and 5. For the 2050 simulations, precipitation increases 7%. For the
2100 simulations, precipitation increases 15%.
40
Table 10: Sensitivity Tests of Welfare Loss to Climate Change for the 2100 High
Climate Case (in billions of 1990 dollars)
Scenarios
Residential
Commercial
Total
Base case
37.1
2.7
39.8
Endogenous prices
37.5
3.1
40.5
Exogenous prices I
42.1
1.5
43.6
Exogenous prices II
39.2
16.2
55.4
Population growth
50.1
3.6
53.6
Income growth
52.1
2.7
54.7
Current economy
14.8
2.0
16.9
Notes: This table reports sensitivity analysis to the aggregate expenditure effects for the
2100 high climate change case from Table 9. In the base case, we assume that electricity
prices will increase 25%, and that other fuel prices will increase 50%. We assume annual
growth rates of 0.3% for population and 2% for income per capita. Temperature increases
five degrees Celsius and precipitation increases 15%. As these changes are based on
projections for 2100, we test the robustness of our findings to various changes that could
occur by 2100. The endogenous price case allows for long run supply functions that are
unit elastic. The first exogenous price case allows all prices to increase by 50%. The
second exogenous case allows the prices to increase as in the base case but imposes that
we will run out of oil. We force the oil shares to be zero and allow the other fuel shares to
increase proportionally (as consistent with the independence of irrelevant alternatives
assumption made in multinomial logit models). The population growth case increases the
number of households and firms based on an annual growth rate of 0.6%. The income
growth increases the income per capita assuming an annual growth rate of 4%. The
current economy is assumes no change in population, income, or prices. All simulations
assume the 1990 distribution of building ages.
41
APPENDIX
Table A1: Data Definitions
Panel A: Definitions of Independent Variables in Residential Regression Models
Variable
burn wood
January temp
January temp2
January precip
July temp
July temp2
July precip
log age of head
log elec. price
log fuel oil price
log kero. price
log income
log lpg price
log nat. gas price
log no. floors
log family size
log square feet
log building age
metropolitan
mobile home
more than 1 unit
select gas
Definition
1 if wood is burned as alternative heat source
average January temperature(demeaned) – degrees C
average January temperature(demeaned) squared
average January precipitation(demeaned) – inches
average July temperature(demeaned) – degrees C
average July temperature(demeaned) squared
average July precipitation(demeaned) – inches
head householder age
average electricity price
average fuel oil price
average kerosene price
average household income for relevant income range
average liquid petroleum gas price
average natural gas price
number of floors
number of household members
size of building in square feet
age of building
1 if in a city (metropolitan statistical area)
1 if home is mobile type
1 if more than 1 unit
sample selection variables for fuel type x
Panel B: Additional Independent Variables in Commercial Regression Models
Variable
alt. fuel used
log dist. heat price
months open/year
multi-bldg facility
no. establishments
% assembly
% educational activities
% food service activities
% in-door parking
% office space
% retail/service
% warehouse/vacant
Definition
1 if alternate fuel is used
average district heat price
number of months open
1 if facility has multiple buildings
number of establishments in building
percent assembly operations
percent non-refrigerated warehouse and vacant
percent food service
percent in-door parking garage
percent office
percent retail/services
percent warehouse/vacant
42
Table A2: Conditional Demand for Residential Customers when Natural Gas is Available
using the Dubin-McFadden Method
Electricity consumption by fuel type
Only
January temp
January temp2
July temp
July temp2
January precip
2
January precip
July precip
July precip2
log elec. price
log n. gas price
log fuel oil price
log building age
log no. floors
log age of head
log home area
log income
log family size
mobile home
multi unit
metropolitan
burn wood
select elec.
select gas
select oil
constant
Gas
-0.029 **
0.000
0.051 **
0.006 **
Oil
Consumption of other fuels
Natural Gas
-0.018**
-0.002**
-0.021**
0.001
-0.025
-0.003
-0.044
0.005
0.048 #
0.039 ** 0.109
-0.008 ** -0.005 ** -0.008
-0.003
0.035 ** -0.041
0.001
0.001
0.004
-0.759 ** -0.765 ** -0.929 **
-0.013
0.003*
0.029**
-0.012**
0.217**
-0.038
-0.004
-0.001
-0.008
0.274 #
0.122 *
-0.511**
#
0.105
-0.068 #
0.100
0.257 **
0.108 **
0.351 **
0.057
-0.049
-0.022
0.051
0.000
-0.041
0.000
0.000
0.060 ** 0.164 *
0.001
0.011
Fuel Oil
-0.077 **
0.014
0.105 **
0.257 **
0.146 **
0.299 **
-0.050
-0.177 **
-0.019
0.087 **
0.138 #
0.160 #
-0.103
-0.079
3.860 ** 3.287 **
0.529 **
-0.095
0.079
-0.117
0.180 **
0.076 *
0.317 **
-0.184
-0.369 **
-0.041
0.100
-0.043
0.015
5.000 **
0.126**
-0.219**
0.060*
0.323**
0.045**
0.184**
0.145**
-0.008
0.062**
-0.011
0.160*
0.033
3.394**
0.487*
0.072
-0.142*
0.159 #
0.355**
0.022
0.069
0.194
0.094
-0.027
-0.070
-0.004
0.074
3.207**
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level.
Consumption of electricity in ln(kWh), natural gas in ln(therms), and fuel oil in ln(gallons).
43
Table A3: Conditional Demand for Residential Customers when Natural Gas is
Not Available using the Dubin-McFadden Method
Electricity consumption by fuel type
Only
January temp
January temp2
July temp
July temp2
January precip
Oil
-0.007
0.010
0.000
-0.002
0.037** 0.139 *
-0.002
0.017 #
Other
Fuel Oil
#
0.018
-0.001 #
-0.036 #
0.007*
0.006
-0.102
0.000
#
January precip
0.020
-0.003
0.004
July precip
0.009
-0.040
0.058*
July precip2
-0.001
0.048 * -0.005
log elec. price
-0.244** -1.324 ** -0.736**
log fuel oil price
0.369
2
log lpg price
log kero. price
log building age
log no. floors
log age of head
log home area
log income
log family size
mobile home
multi unit
metropolitan
burn wood
select elec.
select oil
select other
constant
0.120**
-0.188**
0.010
0.420**
0.087**
0.261**
0.314**
-0.119 #
-0.029
-0.182**
0.012
0.160 #
4.687**
Consumption of other fuels
-0.107
-0.131
-0.163 *
0.035
-0.115
-0.886
-0.076
-0.036
0.207 ** 0.329**
0.199 ** 0.129**
0.235 ** 0.309**
-0.012
0.130
-0.064
0.208
0.073
0.272**
0.063
-0.069
#
0.406
-0.279
0.240
-0.204
3.238 ** 3.233**
Other Fuels
-0.050*
-0.004*
0.123
0.020 #
-0.019
0.001
-0.022
-0.005
-0.020
0.024
-0.023
-0.010
0.125
0.522 #
-0.067
-0.006
-0.050
0.006
0.370
0.078
-0.251
-0.023
0.395**
0.052
-0.040
0.047
0.100
0.086
-0.092
0.113
-0.006
3.122**
-1.253**
0.805
0.105
1.325
0.605**
0.054
0.088
0.174
0.187
0.740
-0.672**
-0.490**
0.275
-0.044
2.862 #
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level.
Consumption of electricity in ln(kWh), fuel oil in ln(gallons), and other fuels in ln(gallons).
44
Table A4: Conditional Demand for Commercial Customers
using the Dubin-McFadden Method
Electricity consumption by fuel type
Only
Gas
Oil
Other
January temp
-0.033*
0.018 ** -0.038
0.005
2
January temp
0.002*
0.000
0.002
0.000
July temp
0.046 #
-0.022 #
0.137 #
-0.010
July temp2
0.000
0.004 #
-0.004
0.000
January precip
0.016
0.023
0.155
0.065
January precip2
-0.006
-0.015 ** -0.020
-0.011
July precip
-0.042
0.013
-0.130 #
0.005
July precip2
0.032** -0.001
-0.001
-0.027
log elec. price
-1.982** -1.683 ** -1.558** -1.009**
log n. gas price
-0.248 *
log fuel oil price
-0.638 #
log dist. heat price
0.126
#
alt. fuel used
-0.283
-0.199
-0.143
-0.143
log building age
-0.162** -0.246 ** -0.169
-0.114
log no. floors
0.105
0.088 *
0.139
0.079
log square feet
0.719**
0.858 **
0.885**
1.000**
multi-bldg facility
-0.037
0.101 #
0.196
0.143
metropolitan
0.559**
0.395 **
0.460**
0.023
months open/year
0.029*
0.049 **
0.135**
0.084**
no. establishments
0.000
0.002
0.009
0.000
% assembly
-0.005** -0.007 ** -0.011** -0.004*
% educational activities
0.000
-0.004 ** -0.004*
-0.006**
% food service activities 0.005 #
0.010 **
0.010**
0.005
% in-door parking
-0.007** -0.008 *
-0.003
-0.012 #
% warehouse/vacant
-0.011** -0.009 ** -0.004
-0.006*
% office
0.004**
0.001 *
0.003
0.003*
select elec.
0.220
-0.319
-0.388
select gas
0.337*
-0.356
0.231
select oil
-0.558*
-0.184
-0.043
select other
0.020
-0.132
0.795 #
constant
-0.782*
-1.075 ** -2.319 #
-1.489
Consumption of other fuels
Gas
Oil
Other
-0.029** -0.126** 0.015
0.000
0.002
0.001
-0.025*
-0.005
-0.028
0.004*
-0.032** 0.005
0.036
0.323** -0.007
-0.009** -0.014
-0.002
#
0.033
0.080
0.008
0.009
-0.017
-0.023
-0.073
0.090
0.017
-1.816**
-3.649**
-0.259*
-0.157
-0.907*
-0.079
-0.049 #
0.424** -0.139
0.102*
-0.088
-0.103
0.622** 0.599** 0.899**
0.163** 0.170
0.359 #
0.057
0.448** -0.288
0.010
-0.009
0.115**
-0.005** 0.000
0.003
-0.003** -0.003 #
-0.005**
-0.001*
0.004*
-0.004**
0.008** 0.003
-0.008
0.000
-0.003
0.001
-0.003** -0.004
-0.003
-0.003** -0.003 #
-0.003*
0.605** -0.786
0.489
0.076
-0.119
-0.200
-0.280
-0.389*
0.587
1.432** -0.311
-1.375
We note significance by ** at the 1% level, * at the 5% level, and # at the 10% level. Shares are
relative to percent retail or service. Consumption of electricity in ln(kWh) natural gas in ln(therms),
fuel oil in ln(gallons), and other (district steam heat) in ln(pounds).
45