Taxes versus Standards (Again): Misallocation and Productivity
Consequences of Energy and Emission Intensity Targets
Trevor Tombe and Jennifer Winter∗
September 2012
Preliminary and Incomplete - Comments Welcome
Abstract
Various policies, from energy taxes to emission intensity limits, promote energy conservation and emission reduction, and have potentially different effects on aggregate productivity and GDP. Theory and evidence regarding the
superiority of either policy is mixed, leading some jurisdictions to adopt energy taxes and others to adopt intensity
standards. We contribute to this debate by developing a tractable quantitative model reflecting the industrial structure
and energy use patterns of developed economies. In contrast with most existing literature, we explicitly incorporate
productivity dispersion across firms in multiple industries. This is important as policies can (1) differentially burden
firms, leading some to exit, and (2) create factor-market distortions, lowering aggregate productivity. In the model,
calibrated to Canadian data, a flat energy tax is usually superior to intensity standards, as the tax does not cause
factor-market distortions, though it does induce firm exit. The cost of a firm-specific standard is mainly driven by
factor-market distortions while the cost of a sector-specific standard is mainly from firm exit. In special cases where
standards are superior to a flat tax, an alternative tax scheme – where firm-specific rates increase with energy intensity
– dominates the standard. The scope for market-based emission reduction policies is therefore larger than previously
recognized.
JEL Classification: Q4, Q5, H2, E6
Keywords: Energy intensity, energy tax, productivity
∗ Tombe: Assistant Professor, Department of Economics, University of Calgary. Email: ttombe@ucalgary.ca. Winter: Research Associate,
The School of Public Policy, University of Calgary. Email: jwinter@ucalgary.ca. We would like to thank Jevan Cherniwchan and Scott Taylor
for valuable comments and suggestions. We gratefully acknowledge the financial support of The School of Public Policy and the Social Sciences
and Humanities Research Council of Canada.
1
Introduction
Environmental policy evaluation is deeply concerned with the most efficient method of achieving emission reductions.
Despite common goals, governments vary in their choice of policies, with some opting for energy taxes and others for
regulations directly governing emissions and energy intensity.1 The effectiveness of market-based versus commandand-control policies has been long debated in the academic literature.2 Few studies, however, evaluate environmental
policy in the presence of rich productivity dispersion across firms. Recently, theoretical work by Li and Shi (2012)
finds intensity standards dominate if productivity dispersion is sufficiently low and market power sufficiently high.3
We approach the question quantitatively, with a new and tractable model of energy use that features firm productivity
dispersion and maps cleanly into industry-level data on production and input use. We find a flat tax dominates a
standard under a wide range of parameterizations. Even when it does not, we show that a tax whose rate increases
sufficiently rapidly with firm energy intensity does. The scope for market-based emissions reductions policies to
dominate regulatory standards is therefore larger than previously recognized.
Productivity dispersion is important to consider for two reasons. First, environmental policy regulations can differentially burden firms, especially low productivity firms. For example, limits on energy intensity are easier for high
productivity firms to achieve than for low productivity firms. Many of these low productivity firms will be induced to
shut down, leading to welfare loses from reduced product variety. Second, even for the firms that continue to operate,
policies with differential burdens create differences in the marginal revenue product of inputs across firms, which lowers aggregate productivity. This applies even if all firms face identical intensity improvement targets relative to their
own baseline, as differences in production technologies across industries means achieving the target is more costly for
some firms than others. There is also a reallocation of factors and production from high productivity industries (which
tend to be energy intensive) to low productivity industries. The aggregate productivity costs of misallocations across
firms and industries have been the subject of a large and growing literature in recent years; we incorporate a number of
insights from this research.4
To investigate the quantitative effects of various emission reduction policies, we develop a tractable (albeit highly
parametric) multi-sector model that accurately reflects the industrial structure and energy use patterns of most developed nations. Within each industry, a continuum of firms produce horizontally differentiated varieties. Production
requires energy and labour, so that all varieties are “dirty” but vary in their “dirtiness” according to energy use. While
1 Examples of recent intensity targets in environmental regulations include Argentina’s (1999) goal of adopting an intensity target under the
Kyoto Protocol, the UK Climate Change Levy Agreement (2002), the Bush Administration (2002) targets and subsequent National Commission on
Energy Policy (2004) recommendations, and Canada’s recent Regulatory Framework for Industrial Greenhouse Gas Emissions (2007).
2 See, e.g., Weitzman (1974) or, more recently, Mandell (2008).
3 That market power leads quantity regulations to dominate corrective taxes was first demonstrated by Buchanan (1969). He shows when a
monopoly produces a good with a negative externality, a corrective tax lowers total welfare. This is in stark contrast to the case of a perfectly
competitive market.
4 See, e.g., Gollin, Parente and Rogerson (2004, 2007); Restuccia, Yang and Zhu (2008); Restuccia and Rogerson (2008); Hsieh and Klenow
(2009); Song, Storesletten and Zilibotti (2011), or Brandt, Tombe and Zhu (2012), among many others.
1
emissions from energy use are only a subset of emissions, they are a key determinant of greenhouse gas emissions.5
This contrasts with existing approaches that consider emissions as a by-product of production. The structure allows us
to evaluate current emission reduction policies and quantify their relative efficiency in addressing the desired reductions. A firm’s optimal input choice between labour and energy also builds in a simple abatement mechanism: adopt a
more labour intensive input bundle. This choice will respond cleanly to changes in input prices and provides a simple
and natural alternative to modeling a specific abatement technology.
With this model, calibrated to Canadian data, we compare a flat tax on energy use to various types of emissions
standards.6 Specifically, we consider three energy intensity targets that encapsulate many forms of emission regulations: firm-specific, sector-specific, and threshold-based. The firm-specific targets require firms lower their own energy
intensity by a given amount relative to their own baseline. Sector-specific policies require firms meet or exceed a common target based on the sector’s overall average. Threshold-based policies will require improvements only for large
emitters. For all policies, we find a flat tax on energy use dominates in terms of aggregate TFP and GDP per worker
(welfare). We also find sector-specific targets are extremely inefficient, resulting in little reduction in energy use and
large economic costs. For example, we find requiring firms within energy intensive industries to not exceed an energy
intensity 18% lower than their sector’s baseline average will lower total energy use by less than 3%, cause over onethird of firms to exit, and lower aggregate GDP and welfare by nearly 2%. A tax that achieves the same total energy
reduction will lower GDP and welfare by an order of magnitude less.
These results depend on the degree of substitutability between varieties and the extent of productivity dispersion,
but the tax dominates the standard for all parameters within what evidence suggests is a reasonable range.7 There
are, however, parameterizations where standards dominate flat energy taxes. Specifically, when the between-industry
elasticity of substitution is sufficiently large relative to the within-industry elasticity, and when productivity dispersion
is sufficiently low, we find standards dominate flat taxes. That being said, we introduce an alternative energy tax – one
where the rate increases with a firm’s energy intensity – that can dominate the standard, even in this parameter space.
The scope for a tax-based approach to reducing emissions is, therefore, larger than previous research has recognized.
Important for these results is the relationship between productivity and energy intensity, for which the evidence is
fairly strong. First, in Section 2 we use data for the majority of OECD countries and show industry-level productivity is
positively related to energy intensity. Over time, productivity is negatively related to energy intensity within industries.
While we lack firm-level data, Martin (2012) finds a clear inverse relationship between productivity and energy inten5 The US EIA estimates 87% of US GHGs are related to energy consumption (Energy in Brief, 21 June 2012). Statistics Canada infers GHG
emissions from energy use data in the Materials and Energy Flow Accounts. Specifically, emissions per quantity of various forms of energy is
calculated and combined with data on energy use by industry. The data on energy use, which we use to calibrate the model, includes ten energy
commodities: coal, natural gas, liquid petroleum gases, electricity, coke, motor gasoline, diesel fuel, aviation fuel, light fuel oil and heavy fuel oil.
6 Other recent work that uses Canadian data to evaluate environmental policy questions includes Wigle (2001); Dissou et al. (2002); Jaccard et
al. (2003); Chris Bataille and Rivers (2006); Murphy et al. (2007); Rivers and Jaccard (2010), and Li and Sun (2011) among many others.
7 For estimates of the elasticity of substitution between goods within industries, for various degrees of aggregation, see Broda and Weinstein
(2006) and others that follow. For the inverse relationship between within-industry substitutability and productivity dispersion, see Syverson (2004).
Many researchers investigate the extent of productivity dispersion; for details and citations see our discussion in Section 4.
2
sity using firm-level data from India. Second, in a number of case studies, Gray and Shadbegian (1995); Shadbegian
and Gray (2003, 2005) find a negative relationship between productivity and abatement costs. That is, it is easier for
high productivity firms to lower emissions than for low productivity firms. Consequently, paper mills with 10 percent
higher productivity have 2.5 percent lower emissions (Shadbegian and Gray, 2003). These facts demonstrate there are
differences in how firms use energy and their productivity, both between and within industries. These differences mean
environmental policies can cause misallocations that lower productivity.
Our work also fits within a substantial literature regarding the costs of reductions in energy use and greenhouse
gas emissions. This literature can be classified into three areas: quantifying the economic cost of policy reforms;
research concerned with comparing the costs of various policy reforms; and research concerned with terms-of-trade
effects. This paper fits within the first and second branches: we quantitatively evaluate the cost of environmental
policies aimed at reducing energy use (which is proportional to greenhouse gas emissions) in the presence of firmlevel heterogeneity. While firm heterogeneity has been introduced via limited cost heterogeneity, rich productivity
differences were introduced only recently. In particular, Li and Sun (2011) and Li and Shi (2012) compare a tax to a
regulatory standard for reducing emissions in the presence of plant-level heterogeneity. Li and Sun find an emissions
standard with abatement outperforms a tax due to price distortions from monopolistically competitive firms. This
indicates models without firm heterogeneity underestimate the cost of emission reduction. In contrast, Li and Shi
find that a tax generates higher welfare in the absence of an abatement technology, and with abatement, the standard
generates higher welfare if firms have sufficiently large market power and productivity dispersion is low. In this paper,
we view abatement in terms of a firm’s choice over variable inputs. We also incorporate multiple industries, each
with varying degrees of energy intensity, as exhibited in the data. Finally, we introduce a new variable energy tax that
dominates the evaluated standards within the parameter space where standards dominate a flat tax.
We proceed in the following section to an investigation of the relationship between productivity and energy use,
across industries and over time for multiple countries. The data patterns documented here will provide key calibration
targets for our model of energy use and production, which is outlined in Section 3 and fully calibrated in Section 4. With
the model, we perform a number of quantitative evaluations of various forms of energy intensity targets, comparing
their economic costs to simple (flat) energy taxes, in Section 5. To ensure the results hold generally across a variety of
settings, we explore alternative parameterizations in Section 6. We also outline an alternative, variable energy tax that
dominates an intensity standard even when a flat energy tax does not. We conclude in Section 7.
2
Key Data and Patterns
The relationship between productivity and energy intensity is an important component of our modeling exercise and
a source of the misallocation and productivity effects that we find. We document two facts about the relationship
3
between productivity and energy intensity. First, in a cross-section, energy intensity and productivity are positively
related. That is, energy-intensive sectors are more productive. The second fact is that when examining within-industry
variation over time, the relationship between productivity and energy intensity is negative. As productivity increases,
energy intensity declines within all industries. The first fact holds for sixteen of the countries examined, while the
second holds for all but one. While we lack firm-level data, this second fact is consistent with productivity and
energy intensity being inversely related to firm-level productivity within industries, which other research has found
(Martin, 2012). These facts are important for two reasons. Environmental policies can reallocate factors from highly
energy intensive industries (which are more productive), and can burden low productivity firms more heavily than high
productivity firms. The facts also motivate a simple modeling choice: a standard Cobb-Douglas production technology,
where the energy-elasticity of output is positively related to average sectoral TFP, is consistent with these observations.
We explore the relationship between productivity and energy intensity using the EU KLEMS dataset covering 24
countries for 11 industries. We perform the same exercise using Canadian data for 16 industries from Statistics Canada,
as this also allows us to analyse the relationship between productivity and greenhouse gas emissions.
2.1
OECD Countries
To evaluate the relationship between productivity and energy intensity for the majority of OECD countries, we use the
2008 version of the EU KLEMS database. It provides data on productivity and inputs including energy for twenty-four
OECD countries from 1970 to 2007 (1995 to 2007 for some). In the KLEMS data, output is assumed to be a constant
returns to scale function of capital, labour, intermediate inputs, and technology.8 With this framework, we can construct
a measure of productivity and energy inputs to examine the relationship between productivity and energy intensity.
In many respects this is excellent data for our purposes, as it allows direct cross-country comparison and has
consistent statistical accounting. However, while the value of our variables of interest (such as gross output, value
added, energy inputs) are reported in local currency, the quantity of these variables are reported as an index, with a
base year of 1995. This means we are unable to compare the relationship between productivity and energy intensity
across industries using a quantity measure. A second issue is that unless an industry faces the same energy input prices
over time, measuring energy intensity as the value of energy inputs over gross output cannot be used to evaluate the
relationship within each industry over time. We address these issues by considering two measure of productivity and
two measures of energy intensity. We outline both below.
To establish the positive relationship between energy intensity and overall industry productivity, we regress a measure of energy spending relative to total revenue on a measure of total factor productivity. Specifically, we estimate
8 See
Timmer et al. (2007) and O’Mahoney and Timmer (2009) for a description of the data and the construction methodology.
4
separately for each country
eit qt
ln
yit
yit
= β0 + β1 ln αi
lit (qt eit )1−αi
+ γt + εit ,
(1)
where qt is the price of energy, lit and eit are the labour and energy inputs, yit is output, and γt is a set of year fixed
effects. Note that we have no data on yit , only pit yit together as revenue. We infer real output in a manner consistent
with the model developed in Section 3 by assuming a particular elasticity of demand and backing out a quantity of
σ /(σ −1)
pit yit
output. Specifically, consistent with Hsieh and Klenow (2009), yit =
, where σ is the elasticity
N p y
∑i=1 it it
of substitution between goods within each industry. We also perform the regression with energy’s share of output
(eit qt /pit yit ) as the dependent variable. Unfortunately, the price component of the value of energy inputs (qit ) is not
known, so our measure of TFP is less than ideal. If input shares (αi ) were identical across industries, the energy price
would be absorbed into the constant. We do not require equal input shares, and the data clearly shows unequal shares,
and so the bias from variation in qt1−αi is not fully removed.
When estimating the within-industry relationship between productivity and energy intensity through time, we use
the following specification
ẽit
ln
yit
= β0 + β1 ln
yit
i
litαi ẽ1−α
it
!
+ γi + εit ,
(2)
where ẽit is the quantity index measure of energy use for each industry. Given the industry fixed effects (γi ), differences
in the actual quantity in the base year of the index (1995) has no consequences.
Table 1 displays the regression results by country for the relationship between energy intensity and productivity.
The year fixed effects specification captures the generally positive relationship between an industry’s energy intensity
(in terms of energy-elasticity of output) and its overall productivity. The industry fixed effects specification captures
the inverse relationship, within industries, between productivity and energy inputs per unit of output. The first column
has as its dependent variable the log of energy intensity (measured by the value of energy inputs over the value of
gross output). The second column has an alternative measure of energy intensity, energy’s share of output over energy
plus labour’s share of output. The third column has as its dependent variable energy intensity using the quantity
index. The regressions omit the Finance, Insurance, Real Estate and Business Services industries, as these industries
are characterized by extremely high productivity and low energy use, and it is not clear productivity is accurately
represented by the data. Electricity, Gas and Water Supply are also omitted as they are considered inputs into the other
industries’ production processes.
Of the twenty-four countries examined, twelve show a strong positive relationship between productivity and energy intensity across industries, and five show a slightly weaker relationship. All but Japan show a strong negative
5
relationship between productivity and energy intensity within industries. This indicates that in the majority of developed countries, the more productive industries are also the most energy intensive. Moreover, within industries, higher
productivity is associated with lower energy intensity.
2.2
Canada
Though Canada is included in the EU KLEMS data, there is more detailed information available from Statistics Canada.
While data from the Productivity Accounts faces the same constraint as with the KLEMS data - energy inputs are
available as a value or a quantity index - the System of Environmental and Resource Accounts has energy use and
greenhouse gas emissions by industry. Both of these are quantity measures that can be mapped to each industry. There
are two benefits to this data; the first is that it allows us to explore the relationship between productivity and GHG
emissions. The second is that this separate data on energy use provides a measure of energy intensity unrelated to the
energy shares used to calculate productivity.
Productivity is calculated using the Productivity Accounts (CANSIM Table 383-0022). When examining the relationship within industries, productivity is constructed using the volume index of energy inputs. When examining the
relationship across industries, productivity is constructed using the value of energy inputs. Otherwise, the specifications used here are identical to what is detailed above for the cross-country analysis. We examine sixteen Canadian
industries at the two-digit System of National Accounts aggregation level, equivalent to two-digit NAICS.
2.2.1
Energy Use
Table 2 displays regressions results for the relationship between productivity and energy intensity, using different
measures of energy intensity. In regression (1), energy use is the cost of intermediate energy inputs in current dollars.
In regression (2), energy intensity is the adjusted energy input share. In regression (3), energy use is a volume index
of intermediate energy inputs. In regressions (4) and (5), energy use is terajoules (denoted eit ). The regressions with
year fixed effects - (1), (2) and (4) - show the generally positive relationship between an industry’s energy intensity
(in terms of energy-elasticity of output) and its overall productivity. The industry fixed effects specifications - (3) and
(5) - capture the inverse relationship, within industries, between productivity and energy inputs per unit of output.
Specifications (1), (2) and (3) correspond to the regressions for Canada in Table 1, while specifications (4) and (5) have
true energy intensity as the dependent variable.
There is a clear negative relationship between productivity and energy intensity, and the point estimates are relatively similar when comparing energy intensity defined by the quantity index and energy intensity defined by the
actual quantity. The similarity in the estimates of the energy-elasticity of output indicate using a quantity index does
not appreciably effect the results, lending support to the estimates reported in Table 1. There is also a clear positive
6
relationship between productivity and energy intensity across industries.
2.2.2
Greenhouse Gas Emissions
As GHG emissions are highly correlated with fossil fuel consumption, we should expect similar relationships between
GHG intensity and productivity. Although GHG emissions are available from Statistics Canada as a quantity, we
face the same problem with productivity as before. In regression (1), productivity is calculated using the cost of
intermediate energy inputs in current dollars. In regression (2), productivity is calculated using a volume index of
intermediate energy inputs. We provide the results of this exercise in Table 3. The same patterns hold as before:
productive industries have higher greenhouse gas emission intensity and productivity growth lowers greenhouse gas
emission intensity.
2.3
Summary of Results
Overall, this - admittedly simple - analysis suggests two conclusions:
1. Energy intensive industries are more productive than others industries; and,
2. Productivity growth is associated with lower energy intensity.
The second fact is suggestive of other research that finds highly productive firms within the same industry have lower
energy intensities. Modeling production using a Cobb-Douglas production function, where input weights are industryspecific and energy’s weight is positively related to average industry TFP, will be consistent with these facts. It is to
this model that we now turn.
3
A Multi-Sector Model of Energy Use with Heterogeneous Firms
In this section, we outline a model that incorporates productivity dispersion across firms in multiple industries. This
dispersion is supported in equilibrium through horizontally differentiated varieties produced by each firm. These
varieties are aggregated into a single final good consumed by a representative household that earns income from lumpsum transfers and through labour income. Labour is inelastically supplied by the household in a competitive labour
market. Emissions result from use of a dirty input in the production process (thought of as energy), such that all
industries are “dirty” but vary in their “dirtiness.” A government can tax dirty input use and will rebate any earnings
to the household as a lump-sum transfer. Endogenous entry and exit is incorporated as in Melitz (2003), where firms
decide whether to produce or not depending on their marginal production costs relative to their output prices. Many
aspects of the model closely follow Eaton, Kortum and Kramarz (2011), without the international trade components,
and aggregate productivity will be calculated following Brandt, Tombe and Zhu (2012).
7
3.1
Households and the Final Good
A representative household consumes a single final good using labour earnings (wL) and lump-sum transfers. The
transfers come from (1) tax revenue earned by the government from energy taxes, and/or (2) firm profits. Labour is
supplied inelastically, the total supply of which is normalized to unity (L = 1). Utility is linear in the consumption of
the final good.
The final good is produced using a constant elasticity of substitution (CES) aggregation of output from N industries,
!ρ/(ρ−1)
N
Y
=
∑
(ρ−1)/ρ
ξiYi
,
(3)
i=1
where ρ ≥ 1 is the elasticity of substitution across the various industries, and ξi is industry-i’s weight with ∑Ni=1 ξi = 1
imposed. The final good producer minimizes the cost of producing the final good, given the prices of individual
industry goods, and earns zero profit. This results in total expenditures (X) being allocated to expenditures on output
from each industry (Xi ) as
Xi
ρ
= ξi X
1−ρ
Pi
,
P
(4)
with prices given by the aggregate price index, P, and individual price of each industry’s output, Pi . The CES structure
implies the price of the final good is
"
P =
N
∑
#1/(1−ρ)
1−ρ
ξ ρ Pi
,
i=1
which we normalize to one (P = 1).
3.2
Industry Output and Intermediate Varieties
Within each industry, a continuum of firms (denoted by j) produce horizontally differentiated varieties. These are
intermediate inputs into the production of final output in each industry, which uses the CES aggregator
ˆ
Yi
=
yi ( j)(σ −1)/σ d j
σ /(σ −1)
,
(5)
with elasticity of substitution σ > 1. This results in demand for an individual intermediate good- j within industry-i of
Xi ( j) = Xi
8
pi ( j)
Pi
1−σ
.
(6)
The production of individual varieties (yi ( j)) is through a constant returns to scale technology that converts labour
(li ( j)) and a dirty input (ei ( j), loosely thought of as energy) into output. Emissions that result from production are
proportional to energy use. Input markets are perfectly competitive, and therefore input prices (wages, w, and the dirty
input price, q) are common across all firms in the economy. We introduce taxes, τi ( j) ≥ 1, on the use of the dirty input
that may vary across firms and equal one for all (i, j) in the no tax case. With total factor productivity denoted by Ai ( j),
the production function for each variety is
yi ( j) = Ai ( j)li ( j)αi ei ( j)1−αi ,
(7)
and the marginal cost for firm- j in industry-i is
1
Ai ( j)
ci ( j) =
w
αi
αi qτi ( j)
1 − αi
1−αi
.
(8)
Note that labour’s share of output (αi ) varies across industries but does not vary across firms within industries. Given
the monopolistically competitive market structure, firms charge a price in excess of marginal cost. Let m =
σ
σ −1
be the
price-cost markup that depends only on the substitutability across varieties within a firm’s industry. Given demand for
a particular variety- j (Xi ( j)), gross profit will be positive. We assume firms face an industry specific fixed entry cost,
εi . Total profit is therefore
Xi ( j)
− εi ,
pi ( j)
ci ( j)
pi ( j) 1−σ
=
1−
Xi
− εi ,
pi ( j)
Pi
mci ( j) 1−σ
= 1 − m−1 Xi
− εi ,
Pi
Xi mci ( j) 1−σ
− εi ,
=
σ
Pi
Πi ( j) = Xi ( j) − ci ( j)
where the second line incorporates demand for individual intermediate goods from equation 6. A firm will choose to
shut down if profits are negative, which gives an upper bound on an operating firm’s marginal cost of
c̄i
=
Xi
σε
1
σ −1
Pi
.
m
(9)
Any firm in industry-i with ci ( j) > c̄i will not operate. The aggregate mass of firms that enter and produce within
industry-i is given by the fraction with sufficiently low costs (c < c̄i ). Denote the set of entrants in industry-i by Mi .
Each individual producer draws its productivity prior to deciding whether to produce or not. The distribution of
9
productivity across firms follows a Pareto distribution. That is, firm productivity within industry-i (Ai ( j)) follows the
CDF
F(z) = 1 − (zi /z)θ .
(10)
The parameter zi is the lower bound on productivity draws, which varies across industries. The variance of this
2
θ
i
distribution is given by θz−1
θ −2 , which means higher values of θ correspond to lower productivity variation. We
assume, for this variance to exist, that θ > 2. Given that costs vary inversely with productivity, and that prices charged
by individual variety producers are a constant markup over marginal cost, there also exists a non-degenerate distribution
of prices across firms within an industry. For a price index to exist for a given industry, we must impose a restriction
the degree of productivity variation across firms. Specifically, we assume θ > σ − 1. To see this clearly, we consider a
special case where factor prices are constant across firms. The price for industry-i’s output is a function of the prices
of each underlying intermediate varieties,
ˆ
Pi
=
1−σ
pi ( j)
ˆ
= m
c̄
c
1−σ
1/(1−σ )
,
dj
1/(1−σ )
,
dµi (c)
0
where the second line uses the distribution of marginal costs, the price-cost markup, and the firm entry decisions. The
distribution of costs, µ, can be derived from equations 8 and 10. The fraction of firms in industry-i with costs no more
than c is
µi (c) = φi cθ ,
(11)
1−αi −θ
αi
q
where φi = z1 αwi
captures an industry’s overall competitiveness and is common across firms
1−αi
i
within industry-i. Using this distribution of costs, Eaton, Kortum and Kramarz (2011) demonstrate that the industry’s
price index can be expressed as
Pi
where κ =
h
θ
θ −(σ −1)
− θ1
= m (κφi )
i
. So, finite κ requires θ > σ − 1.
10
Xi
σε
1−
θ
1
σ −1
,
(12)
3.3
Supply of the Dirty Input
We suppose that dirty input production requires labour (le ) and natural resources (n), with decreasing returns in each
β
input, using E = le n1−β . Natural resources are rented at a price qn , are owned by the government, and all revenues
raised from natural resource sales are rebated lump-sum to households. There is a fixed stock of natural resources
available for rent in any given period, which we set to unity (ns = 1). The cost of purchasing a unit of dirty input to a
β 1−β
qn
goods-producing firm equals the marginal cost of production, q = βw
. For the remainder of the paper,
1−β
we will view energy and “dirty input” as synonymous.
3.4
Market Clearing Conditions and Equilibrium
We close the model by requiring labour and energy markets clear,
N
L̄ ≡ 1
=
ˆ
∑
li ( j)d j + le ,
∑
ei ( j)d j ,
j∈Mi
i=1
N ˆ
=
E
j∈Mi
i=1
and the demand for natural resources by the dirty input producer equals the available supply,
ns ≡ 1
= n.
The equilibrium is defined as a set of input prices {w, qn , q} such that these markets clear. The output and prices of
each industry can be determined from the system of equations outlined in the previous sections.
3.5
Two Measures of Aggregate Productivity
We represent productivity using two metrics. First, we consider economy-wide productive efficiency as an aggregate
of TFP across industries, which is itself an aggregate across individual firms. Second, we measure aggregate labour
productivity (GDP per worker; welfare, in this framework). It is with these two measures that we evaluate the effects
of various energy reduction schemes.
Calculating overall productive efficiency as an aggregate across a continuum of firms, each facing potentially unique
energy input prices, and across industries with different input intensities, is not trivial. When energy taxes do not vary
across firms, and marginal products are free to equalize, aggregate TFP is
N
A
=
∑
!1/(ρ−1)
ρ (ρ−1)
ξi Ai
i=1
11
,
where
ˆ
σ −1
Ai ( j)
=
Ai
1/(σ −1)
,
dj
These expressions, however, do not hold when there are firm-specific input prices, as marginal products are no longer
equalized. We rely on a recent and growing literature investigating the effect of firm-specific distortions on productivity.
Specifically, we follow Brandt, Tombe and Zhu (2012) to measure aggregate TFP. It is first useful to define a (harmonic)
mean energy tax within each industry, weighted by an adjusted measure of firm-specific productivity, as
´
=
τi
´
Ãi ( j)σ −1 d j
Ãi ( j)σ −1 τi 1( j) d j
,
where Ãi ( j) = Ai ( j) /τi ( j)1−αi . Similarly, we define the mean energy tax for the entire economy as
ρ ρ−1
where Ãi =
´
Ãi ( j)σ −1 d j
1/(σ −1)
∑Ni=1 ξi Ãi
=
τ
ρ ρ−1 1
τi
∑Ni=1 ξi Ãi
,
. With these terms defined, we can introduce a useful proposition.
Proposition 1: Aggregate and sectoral TFP in the presence of firm-specific input price distortions are given by
"
A
=
#1/(ρ−1)
N
∑
ρ
ξi
Ãi τ
1−αi ρ−1
,
i=1
and
Ai
= Ãi τi1−αi .
Proof: See proof of Proposition 2 from Brandt, Tombe and Zhu (2012).
For greater transparency, we report aggregate welfare and final goods per worker (labour productivity) for each
policy experiment. For this, we simply report the aggregate amount of the final good produced, Y . Given the representative household size is normalized to unity, this represents aggregate real output per worker. Equivalently, the value Y
can be considered the household utility level, as replacing the final goods aggregator with a utility function of the same
form would have no consequence.
12
4
Calibrating the Model to Match Canadian Data
In this section, we calibrate certain parameters of the model to match key moments in the Canadian data. We consider
16 industries at the SNA two-digit level and use information on gross output (PiYi ), labour compensation (wLi ), energy
spending (qEi ), capital input spending, and spending on intermediate inputs.9 We ignore input-output linkages between
sectors and therefore do not consider intermediate input spending from the data. We focus on only two inputs (labour
and energy) and absorb capital (k) into firm productivity. This allows us to consider the following production function,
yi ( j) = Ãi ( j) li ( j)α˜il ei ( j) α˜ie ki ( j) α˜ik ,
≡ Ai ( j) li ( j) αi ei ( j) 1−αi ,
where Ai ( j) = Ãi ( j)
α̃ α˜i
ik
r
k
and αi = α̃il /(1− α̃ik ). Note that capital can be rented at price r in a perfectly competitive
global rental market, which implies ki ( j) = α̃ik yi ( j)/r holds for all i and j. This allows us to ignore capital in the
remaining analysis. We can measure each input’s share of output as the fraction of total spending on that input in
industry-i relative to the industry’s value added; for example, α̃i =
wLi
PiYi −psi si ,
where psi si is spending on intermediate
inputs by industry-i. From this point forward, value-added will be synonymous with output and denoted by y.
Calibrating the distribution for each firm’s draw of Ai ( j), with the CDF F(z) = 1 − (zi /z)θ , is more challenging.
First, we exogenously set θ = 4, in line with existing research. For instance, using plant-level data, Bernard, Eaton,
Jensen and Kortum (2003) find θ = 3.6. Ricardian trade models in particular infer productivity dispersion from price
and trade flow data. For example, Simonovska and Waugh (2011) find θ = 4.1, with a range between 2.5 and 5.5.
zi and
Using wages and trade, Eaton and Kortum (2002) find θ = 3.6. Given θ , the mean of the Pareto distribution is θθ−1
we set this equal a measure of each industry’s overall TFP. That is, zi = Ai (θ − 1)/θ , where Ai is the overall TFP of
industry-i. Since we do not have information on each industry’s price index (Pi ), we infer real output for each industry
within the context of our model. Note that
Yi
where
PiYi
PY
= PY
PiYi
PY
ρ/(ρ−1)
is industry-i’s share of total nominal output PY . With data on nominal shares, aggregate total output across
all industries, and a value for the cross-industry elasticity ρ, we can set
Ai
9 Data
,
=
Yi
,
αi 1−αi
Li Ei
extracted from Statistics Canada CANSIM Table 383-0022.
13
and therefore
zi
=
θ −1
Yi
.
α
i
θ Li Ei1−αi
We list these values for each industry in Table 4. As a final note on implementing this productivity distribution, we
consider the maximum draw as the 99.99-percentile. That is, we restrict the support of the distribution from zi to
0.0001−1/θ zi .
Finally, we calibrate the remaining model parameters. The preference weights across industries, ξi , are set such that
nominal output shares
PiYi
PY
in the model match the data. The industry-specific entry costs, εi , are set such that in each
industry the fraction of firms that enter equals 0.75 - roughly the fraction of new businesses that do not go bankrupt
in the first year of operation. Admittedly, this introduces a certain degree of arbitrariness into the calibration of entry
costs. However, the results we present below are not very sensitive to this parameter. We report results under alternative
assumptions where appropriate. The elasticities of substitution are set such that σ > ρ ≥ 1, in line with research that
finds elasticities increasing in the level of disaggregation (Broda and Weinstein, 2006). The specific values chosen are
ρ = 1.5 and σ = 4. The between-industry elasticity is chosen in line with evidence from international real business
cycle models, which finds an elasticity between 1 and 2.10 The mean value of the within-industry elasticity in Broda
and Weinstein (2006) is 4. We explore the sensitivity of our results to alternative values of these parameters. We also
allow the within-industry elasticity and productivity dispersion parameters to vary across industries.
5
The Effect of Intensity Targets on Productivity
In this section, we outline the effect of various energy and emission reduction policies that differentially burden firms.
We incorporate the effect of policies on firm choices through taxes on the use of energy. This tax is a reduced-form
means of capturing all burdens placed on firms that lead them to meet particular targets. We will not question whether
the targets can or will be met but seek only to quantify the costs of the policies taken at face value.
Before moving to particular regulatory schemes, it is useful to note the effect of energy taxes on input choices.
With competitive input markets, the optimal ratio of labour to energy satisfies
li ( j)
ei ( j)
=
αi qτi ( j)
.
1 − αi w
Combining this with the firm production function yields
αi qτi ( j)
yi ( j) = Ai ( j)ei ( j)
1 − αi w
10 See
αi
,
Ruhl (2008) for a more detailed exploration of the conflicting evidence for various elasticity values.
14
which gives the optimal energy intensity of a representative firm
ei ( j)
yi ( j)
=
1
Ai ( j)
1 − αi w
αi qτi ( j)
αi
.
The federal government regulates emissions intensity for a subset of industries in the Canadian economy.11 In
particular, the regulations cover the sources for approximately 50% of Canada’s total emissions, focusing on Electricity
Generation, Oil and Gas, Forest Products, Smelting and Refining, Iron and Steel, certain Mining sectors, and Cement,
Lime, and Chemical producers. A separate emissions framework regulates greenhouse gas emissions, and applies to
many of the same industries just listed as well as Potash, Fertilizer Production, Pulp and Paper, and others. In terms of
our model, we (roughly) approximate these policies by imposing regulations within the model on Agriculture, Forestry,
and Fishing, Mining and Oil and Gas, Utilities, and Manufacturing. We will refer to these as the regulated industries.
This overstates the coverage of the regulations, particularly in Manufacturing, but our focus is on comparing two types
of policies, a standard versus a tax applied to the same industries. There are a variety of types of standards imposed
and we cover each of them separately in the subsections below.
5.1
Facility-Specific Targets
These are emission intensity targets that are plant-specific and apply, for example, to facilities producing chemicals or
fertilizers or those involved in upstream oil and gas or metal smelting. Under these regulations, plants are required to
lower their emissions intensity by 18% relative to each facility’s own base-year intensity. Using the above expression
for energy intensity, we can create an expression for the tax required to meet this target,
τi ( j) = 1.181/αi .
Two firms within the same industry will face the same tax. Two firms in different industries, with different labour
shares, will face different tax rates and, therefore, aggregate productivity will be lowered due to this distortion. For
example, consider two industries: one with labour’s share equal to 75% and the other equal to 95%. The energy tax
1
1
rate will differ between firms in one industry and firms in the other by nearly 5% (1.18 0.75 − 0.95 ). These differences will
lead the marginal revenue product of energy to differ across industries, which is the source of the misallocation and the
aggregate productivity loss. In addition, since energy intensive industries (low αi ) will face higher tax rates, and these
are typically industries with higher productivity, the reallocation across industries will lower aggregate productivity.
Firm exit will also be higher in energy intensive industries, leading to a loss of welfare from fewer varieties.
We re-solve the model imposing the above tax on producers in the regulated industries and report the results in
11 For
details, see the Regulatory Framework for Air Emissions at http://www.ec.gc.ca/doc/media/m_124/report_eng.pdf
15
the first column of Table 5. Total energy use declines by nearly 11% under the standard and TFP falls by nearly one
percent, as does aggregate labour productivity (welfare). The standard leads consumers to shift expenditure away from
the regulated industries, lowering demand and shutting down approximately 3.7% of firms in those sectors. To gauge
the efficiency with which this facility-specific standard achieves this level of energy conservation, we compare it to a
uniform tax on energy that achieves the same reduction in energy use, and report the results in the second column of
Table 5. With a tax rate of 14.4%, we find that TFP falls by less than 0.1% and labour productivity and welfare fall by
0.94%. The number of firms in the regulated industries still declines, as their price increases relative to other industries
due to their higher energy-elasticity of output, but by only 1.84% - nearly half the number the standard induces to exit.
Overall, a tax is superior to facility-specific targets.
5.2
Sector-Specific Targets
In other industries, such as Pulp and Paper, Aluminum, and Cement, the federal government also seeks to reduce
emissions intensity by 18%. It does this, however, in a subtly (but importantly) different way. It imposes on all
producers within a given industry an emissions intensity equal to 18% less than the sector’s average emissions intensity
in the base period. Since, as we saw, energy intensity is decreasing in a firm’s productivity, this regulatory approach
will introduce a clear distortion across firms even within industries. To see this, denote the target intensity as ey
¯ i and
solve for an equivalent tax resulting in this target,
τi ( j) =
1
Ai ( j)ey
¯i
1/αi
1 − αi w
.
αi q
A firm with twice the productivity of another within the same industry will face an effective energy tax rate 2−1/αi
times lower. For an industry such as Mining and Oil and Gas Extraction, the more productive firm would face a tax rate
roughly 41% the size of its less productive peer. We illustrate the implied energy tax for an example industry, Mining
and Oil and Gas, in Figure 1. This tax will create far more significant misallocations, since the marginal revenue
product differences induced by different tax rates also exist within industries. These distortions will lower productivity
much more than a uniform energy tax would.
We re-solve the model with this firm-specific tax to achieve the sector-specific energy intensity target. We report the
results in the third and fourth columns of Table 5. Productive firms that already have energy intensities less than their
sector’s target will not be taxed at all. The differences between a tax and a standard are even more dramatic than under
the facility-specific target. Aggregate TFP declines by 1.88% under the standard but by a tiny 0.02% under the uniform
tax achieving an identical reduction in energy use. Labour productivity falls by 1.71% under the standard but by only
0.23% under the tax. The most dramatic difference is with the number of exiting firms. The standard, which imposes
a huge burden on low productivity firms relative to high productivity firms within an industry, causes over one-third
16
of firms exit. Under the flat tax, only 0.46% of firms exit. The overall level of energy reduction achieved through this
costly policy is also small: less than 3%. To lower energy use by this amount with a uniform energy tax requires a rate
of just over 3.5%. It is clear that policies which impose common energy intensity targets are significantly more costly
than those that are firm-specific.
5.3
Targets for Large Emitters
The final regulatory scheme we investigate is a firm-specific intensity target where only a subset of firms are required
to comply. This regulation uses an emissions threshold, below which a firm is not required to comply. Alberta, for
example, imposes a firm-specific emissions intensity reduction target of 12% for firms in certain sectors that emit more
than 100,000 tonnes of carbon per year. For the covered industries, this threshold leaves 30% of industrial emitters
unregulated and, hence, introduces energy tax rate differences between firms within an industry. To mirror this scheme
in the model, we find the threshold that covers 70% of firms and impose a tax similar to Section 5.1 but with a 12%
target: τi ( j) = 1.121/αi .
The results of this experiment also reveals the benefit of a uniform energy tax relative to a standard. TFP and
welfare decline by about two-thirds of a percent, while a tax only reduces TFP by 0.06%. The number of firms that
exit under the standard is 2.5% and only 1.27% under the tax. The total level of energy use is reduced by 7.68% and
an energy tax just below 10% is required to achieve the same reduction. The results are reported in detail in the final
two columns of Table 5.
6
Discussion and Robustness
The results in Section 5 strongly point to uniform energy taxes as a superior means of lowering energy use, and therefore
a superior way to lower total emissions. We find productivity losses to achieve a given level of energy conservation
far lower with a tax than various regulatory standards on energy intensity. We also find losses in GDP per worker, and
equivalently consumer welfare, to be lower with a tax than a standard. Li and Shi (2012) make clear in their theoretical
work, however, that this conclusion will depend on the elasticities of substitution between and within industries and on
the degree of productivity dispersion between firms. We explore in the next section how a tax on energy use compares
to a sector-specific intensity standard under a wide variety of values for elasticities of substitution and productivity
dispersion.
We also explore a special case where standards can dominate flat energy taxes. Notwithstanding this, we introduce
a new type of energy tax – one where tax rates are firm-specific and increase with a firm’s energy intensity – and
demonstrate that this tax can dominate the standard even when the flat tax cannot. This increases the scope for marketbased policies to achieve emission reduction and energy conservation goals beyond what has typically been recognized
17
in the literature. We conclude the section by decomposing the two margins whereby policies lower productivity: the
extensive margin (firm exit) and the intensive margin (factor-market distortions creating wedges between marginal
revenue products). We do this by re-solving the model and allowing each industry’s cost of entry (εi ) to vary such that
the total mass of firms is unchanged. The resulting costs in each experiment provide an estimate of the intensive margin
alone. The difference between these results and the baseline results provide an estimate of the extent of the extensive
margin.
6.1
Alternative Elasticities of Substitution and Productivity Dispersion
In the baseline case, we assume that the between-variety elasticity of substitution within each industry is the same for
all industries. We also assume the productivity variation between firms within each industry is the same. There is
recent and growing evidence that these assumptions do not hold (see, e.g., Broda and Weinstein, 2006 for elasticities or
Caliendo and Parro, 2011 for productivity dispersion). The results from Li and Shi (2012) suggest regulatory standards
can be superior to uniform taxes when the within-industry elasticity of substitution between varieties and productivity
dispersion are sufficiently low; that is, in our context, when σ is low and θ is high. Indeed, one might expect variation
in productivity amongst commodity producers (or energy intensive firms generally) to be lower than for the economy
as a whole. On the other hand, industries with low productivity variation tend to be industries with high elasticities
of substitution (Syverson, 2004). To explore the quantitative significance of these facts, we explore some alternative
parameter values that vary by industry.
While industry-specific evidence for particular values of θ are few, recent work by Caliendo and Parro (2011) which identifies productivity variation using the sensitivity of trade flows to tariff rates using a vary general framework
- suggests this value is as high as 15 in Mining, 11 in Forestry, 8 in Basic Metals, and 51 in Petroleum Processing.
Overall, their economy-wide average is approximately 4, the value we used for our baseline simulations. In other
regulated industries this variation is lower, however, such as 4.75 for Chemicals. To reflect the lower productivity
variation between firms in the regulated industries we use θregulated = 10 and θunregulated = 4. As for the withinindustry elasticity of substitution, we set σregulated = 5 to correspond to the average within-sector elasticity found by
Broda and Weinstein (2006) for commodity related sectors (specifically, those with one-digit SITC revision 3 codes
from zero to four). We leave σunregulated = 4 as before. The results of the Section 5 exercises under this alternative
parameterization are provided in the third panel of Table 5. Overall, the results are very close to those reported in the
first panel. We conclude that the conditions for a standard to out-perform a tax are not likely to be present among the
set of energy intensive industries.
To systematically explore the relative superiority of a tax, we perform counterfactuals for a complete set of withinand between-sector elasticities and productivity dispersion parameters. First, for the same between-industry elasticity
18
of substitution (ρ = 1.5), we compare the cost of achieving equivalent energy reductions under a tax relative to a sectorspecific standard. We report in Table 6 the welfare and productivity costs of achieving energy use reductions using a
tax relative to using the sector-specific intensity targets. That is, if a sector-specific intensity standard results in a 2%
welfare loss but a tax that achieves equivalent reductions in energy use results in only a 0.5% loss, then the relative
cost of a tax reported in the table will be 0.25. For all values considered (which we believe represents the relevant
range of elasticities and productivity dispersions) the tax dominates the standard. In Tables 7 and 8, we consider a
Cobb-Douglas aggregation of industry output to form the final good (ρ = 1) and a more elastic case (ρ = 2).12 In both
cases, the tax achieves the energy reduction with lower costs than a standard.
Common to all results is that as productivity dispersion declines (as θ increases) and as the within-sector elasticity
of substitution declines (as σ decreases) the cost of the tax grows relative to the standard. This gradient is consistent
with Li and Shi (2012); they find that for a sufficiently low elasticity and for sufficiently low productivity dispersion
the standard dominates the tax. We find the tax dominates the standard but the degree to which this holds declines in a
manner consistent with their model. Differences arise as our framework opts for a structure in line with data, features
energy use as the source of emissions, and we select parameter ranges in line with evidence. Unique to our paper,
we find the advantage of a tax declines as the between-industry elasticity of substitution grows (as ρ increases). In
fact, as this between-industry elasticity grows sufficiently high, the tax will become less efficient at achieving energy
reductions than the standard. We explore the implication of choosing parameters that result in a standard dominating a
flat tax in the next section.
6.2
Energy Taxes with Variable Rates
While the above exercises suggest energy taxes are a more efficient mechanism to reduce energy use, there are parameter ranges in our framework where this does not hold. Specifically, we consider the case where the between-sector
elasticity is larger than the within-sector elasticity (ρ = 4 and σ = 1.5) and productivity dispersion is low (θ = 10).
While we do not feel these parameter ranges are reasonable (see the previous section for simulation results within our
preferred range), we investigate the performance of a new type of tax and compare it to the standard. We consider a tax
on energy with a variable rate that increases with a firm’s energy intensity. That is, firms with higher levels of energy
use per unit of output will pay a higher tax rate on all units of energy purchased. Specifically, consider
τi ( j) = τ̄
12 Note
ei ( j)
yi ( j)
ζ
,
1−αi
that when ρ → 1, the expression for aggregate productivity approaches A = ∏N
i=1 ξi Ãi τ
as before.
19
ξi
, where τ = ∑N
i=1 ξi /τi
−1
; Ãi and τi are
where ζ is the elasticity of the tax rate with respect to energy intensity and τ̄ is a rate faced by all firms. If taxes are flat
(ζ = 0) then the rate faced by all firms in all industries is τ̄ (with τ̄ = 1 in the no tax case). Variable taxes that increase
with energy intensity require ζ > 0.
This tax will fall heavily on low productivity firms, as a sector-specific standard does. Unlike the standard, we find
that a variable tax that declines sufficiently with energy intensity will dominate the standard. To put it another way, we
can find a market-based mechanism to lower energy use that dominates a regulatory standard even when the standard
dominates a flat energy tax. We display the difference in welfare and productivity costs between the variable tax relative
to the standard in Figure 2. Negative values imply the standard dominates the variable tax. For sufficiently high values
of ζ , the variable tax dominates the standard. We interpret these results to imply that the scope for market-based
mechanisms to lower emissions are broader than has been previously recognized.
6.3
Intensive and Extensive Margins
There are two sources for productivity and welfare losses from taxes and regulatory standards. First, given our model
features endogenous entry and exit, a policy that differentially impacts low productivity firms will induce some degree
of exit. This results in a loss in welfare due to a smaller set of varieties available for consumption. The second margin
for losses, the intensive margin, results from differences in the marginal revenue product of energy across producing
firms. These differences result in aggregate productivity losses from a misallocation of factors across firms. To gauge
the importance of each channel under the various policies, we repeat the three policy experiments without allowing
firms to enter or exit. We report the results in the second panel of Table 5.
The costs of a sector-specific intensity target attributable to firm exit, and the resulting loss of product variety, is
large while the costs for firm-specific and threshold-based targets are predominantly from between-firm distortions and
misallocation. To see this, compare the figures in the second panel of Table 5 with the corresponding figures in the
first panel. For facility-specific targets, the loss to TFP and welfare when the extensive margin is shut down is 0.84%
and 0.95%, respectively. The total losses when endogenous entry and exit is permitted are 0.95% and 1.05%. So, we
conclude that costs associated with facility-specific targets are mostly (90%) driven by misallocation across producing
firms. Indeed, this is not surprising given that only 3.7% of firms exit under the facility-specific standard. For sectorspecific targets, the figures are dramatically different. TFP losses when firms cannot enter are only 0.47%, compared to
1.88% overall. Thus, when firms are subjected to an intensity target based on their sector’s overall average, a substantial
number of firms exit and costs associated with the policy are substantially higher. We conclude three-quarters of the
costs of using this type of regulation is from the extensive margin (firm exit). The final case, threshold-based regulation,
is similar to the facility-specific results: most costs are from between-firm distortions and misallocation.
20
7
Conclusion
To investigate the effect of various energy conservation and emission reduction policies, we develop a new multi-sector
model of energy use with heterogeneous firms. Incorporating productivity differences between firms has important
implications for whether taxes or regulatory standards are the superior means of achieving emission reduction goals.
If policies disproportionately burden some producers relative to others, then firm exit and factor misallocations result.
Firm exits will lower welfare through a reduced set of varieties available for consumption. Factor misallocation causes
lower aggregate productivity whenever the marginal revenue product of energy is not equal across firms. We model
emissions as proportional to energy inputs used by firms, which allows for a simple and natural abatement mechanism,
substitution away from energy. If energy prices increase relative to other factors, firms adjust their input choices and
use less energy. Our model cleanly maps to available industry-level data on production and input use and allows for
tractable and transparent policy analysis.
We specifically consider three types of standards: (1) targets that are firm-specific; (2) sector-specific targets that
are common across firms within an industry; and (3) targets that apply only to sufficiently large emitters. In all cases,
and especially for sector-specific targets, we find that a flat tax on energy results in lower welfare and productivity
losses for a given reduction in energy use. This result holds across a wide range of parameters, well within the range
suggested by other research. We decompose productivity losses into an intensive margin, input factor misallocation,
and an extensive margin, firm exit. We find that for a sector-specific standard, over three-quarters of the costs results
from firm exit. For the other standards, 90% of the costs are from misallocation. Both of these costs are only apparent in
a model that features productivity dispersion across heterogeneous firms. Finally, for parameter values where standards
dominate flat taxes, we propose a new tax with a rate that increases with a firm’s energy intensity. This firm-specific
variable tax can, if it rises sufficiently quickly with energy intensity, dominate a standard even when a flat tax does
not. We conclude that to encourage energy conservation and emissions reductions the scope for market-based policies,
rather than regulatory standards, is larger than previously recognized.
21
References
Bernard, Andrew B., Jonathan Eaton, J. Bradford Jensen, and Samuel Kortum, “Plants and Productivity in
International Trade,” American Economic Review, 2003, 93 (4), 1268–1290.
Brandt, Loren, Trevor Tombe, and Xiaodong Zhu, “Factor Market Distortions Across Time, Space and Sectors in
China,” 2012.
Broda, Christian and David E. Weinstein, “Globalization and the Gains from Variety,” The Quarterly Journal of
Economics, 2006, 121 (2), 541–585.
Buchanan, James M, “External Diseconomies, Corrective Taxes, and Market Structure,” American Economic Review,
1969, 59 (1), 174–77.
Caliendo, Lorenzo and Fernando Parro, “Estimates of the Trade and Welfare Effects of NAFTA,” 2011.
Dissou, Yazid, Carolyn Mac Leod, and Mokhtar Souissi, “Compliance costs to the Kyoto Protocol and market
structure in Canada: a dynamic general equilibrium analysis,” Journal of Policy Modeling, 2002, 24 (7-8), 751–779.
Eaton, Jonathan and Samuel Kortum, “Technology, Geography, and Trade,” Econometrica, 2002, 70 (5), 1741–
1779.
,
, and Francis Kramarz, “An Anatomy of International Trade: Evidence From French Firms,” Econometrica,
2011, 79 (5), 1453–1498.
Gollin, Douglas, Stephen L. Parente, and Richard Rogerson, “Farm Work, Home Work, and International Productivity Differences,” Review of Economic Dynamics, 2004, 7 (4), 827–850.
,
, and
, “The food problem and the evolution of international income levels,” Journal of Monetary Economics,
2007, 54 (4), 1230–1255.
Gray, Wayne B. and Ronald J. Shadbegian, “Pollution Abatement Costs, Regulation, and Plant-Level Productivity,”
NBER Working Papers 4994, National Bureau of Economic Research 1995.
Hsieh, Chang-Tai and Peter J. Klenow, “Misallocation and Manufacturing TFP in China and India,” The Quarterly
Journal of Economics, 2009, 124 (4), 1403–1448.
Jaccard, John Nyboer Chris Bataille Mark and Nic Rivers, “Towards General Equilibrium in a Technology-Rich
Model with Empirically Estimated Behavioral Parameters,” The Energy Journal, 2006, 0 (Special I), 93–112.
22
Jaccard, Mark, Richard Loulou, Amit Kanudia, John Nyboer, Alison Bailie, and Maryse Labriet, “Methodological contrasts in costing greenhouse gas abatement policies: Optimization and simulation modeling of microeconomic effects in Canada,” European Journal of Operational Research, 2003, 145 (1), 148–164.
Li, Zhe and Jianfei Sun, “Environmental Policy with Heterogeneous Plants,” 2011.
and Shouyoung Shi, “Emission Tax or Standard? The Role of Productivity Dispersion,” 2012.
Mandell, Svante, “Optimal mix of emissions taxes and cap-and-trade,” Journal of Environmental Economics and
Management, 2008, 56 (2), 131–140.
Martin, Leslie, “Energy efficiency gains from trade: greenhouse gas emissions and India’s manufacturing sector,”
2012.
Melitz, Marc J., “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 2003, 71 (6), 1695–1725.
Murphy, Rose, Nic Rivers, and Mark Jaccard, “Hybrid modeling of industrial energy consumption and greenhouse
gas emissions with an application to Canada,” Energy Economics, 2007, 29 (4), 826–846.
O’Mahoney, Mary and Marcel P. Timmer, “Output, Input and Productivity Measures at the Industry Level: The EU
KLEMS Database,” The Economic Journal, 2009, 119 (538), F374–F403.
Restuccia, Diego and Richard Rogerson, “Policy Distortions and Aggregate Productivity with Heterogeneous
Plants,” Review of Economic Dynamics, 2008, 11 (4), 707–720.
, Dennis Tao Yang, and Xiaodong Zhu, “Agriculture and aggregate productivity: A quantitative cross-country
analysis,” Journal of Monetary Economics, 2008, 55 (2), 234–250.
Rivers, Nicholas and Mark Jaccard, “Intensity based climate policy in Canada,” Canadian Public Policy, 2010, 36
(4), 409–428.
Ruhl, Kim, “The International Elasticity Puzzle,” 2008.
Shadbegian, Ronald J. and Wayne B. Gray, “What Determines Environmental Performance at Paper Mills? The
Roles of Abatement Spending, Regulation, and Efficiency,” The B.E. Journal of Economic Analysis & Policy, 2003,
0 (1).
and
, “Pollution abatement expenditures and plant-level productivity: A production function approach,” Ecolog-
ical Economics, 2005, 54 (2-3), 196–208.
23
Simonovska, Ina and Michael E. Waugh, “The Elasticity of Trade: Estimates and Evidence,” Working Paper 16796,
National Bureau of Economic Research 2011.
Song, Zheng, Kjetil Storesletten, and Fabrizio Zilibotti, “Growing Like China,” American Economic Review, 2011,
101 (1), 196–233.
Syverson, Chad, “Product Substitutability and Productivity Dispersion,” The Review of Economics and Statistics,
2004, 86 (2), 534–550.
Timmer, Marcel, Ton von Moergastel, Edwin Stuivenwold, and Gerard Ypma, “EU KLEMS Growth and Productivity Accounts: Part I Methodology,” Technical Report, EU KLEMS Consortium 2007.
Weitzman, Martin L, “Prices vs. Quantities,” Review of Economic Studies, 1974, 41 (4), 477–91.
Wigle, Randall, “Sectoral Impacts of Kyoto Compliance,” Technical Report 34, Industry Canada, 2001.
24
A
Figures and Tables
Figure 1: Implied Energy Tax from Sector-Specific Intensity Target (Example: Oil and Gas Sector)
Displays the implied energy tax rate for various firm productivity. This rate is calculated as the rate necessary to achieve a common target for all firms within an
1−α
industry: τi ( j) = (Ai ( j)ey
¯ i )−1/αi α i wq , where ey
¯ i denotes the target. See text for details. Note that the burden of complying with a sector-specific target falls largely on
i
unproductive firms.
25
Figure 2: Comparing a Standard to a Variable Tax
(a) GDP per Worker (Welfare)
(b) Aggregate TFP
Compares the welfare and productivity associated with various energy tax schemes to an energy intensity standard. The standard dominates the typical (flat) energy
tax. When the tax rate, however, declines with energy-intensity, the tax can once again dominate the standard. ζ (zeta) denoates the elasticity of the tax rate to a firm’s
energy intensity.
26
Table 1: Relationship between Energy Intensity and Productivity for Various Countries
(1)
(2)
(3)
Dep. Var.: log(eit qt /yit )
Dep. Var.: log(eit qt /pit yit )
Dep. Var.: log(ẽit /yit )
β̂
s.e.(β̂ )
β̂
s.e.(β̂ )
β̂
s.e.(β̂ )
Austria
0.074*
0.034
0.178***
0.032
-0.144***
0.050
Belgium
0.442***
0.051
0.719***
0.052
-0.264***
0.062
Canada
0.007
0.024
0.153***
0.024
-0.937***
0.011
Czech Republic
0.088
0.061
0.268***
0.055
-0.935***
0.083
0.135***
0.031
0.293***
0.031
-0.953***
0.022
0.040
0.043
0.206***
0.041
-0.706***
0.023
Finland
0.513***
0.026
0.570***
0.020
-0.588***
0.011
France
0.265***
0.036
0.386***
0.039
-0.897***
0.033
Germany
-0.231***
0.029
-0.239***
0.032
-1.054***
0.025
-0.039
0.069
0.023
0.074
-0.452***
0.105
Hungary
-0.297***
0.054
-0.149*
0.068
-0.927***
0.032
Italy
0.178***
0.026
0.255***
0.027
-1.040***
0.022
0.025
Denmark
Spain
Greece
Japan
0.047
0.031
0.180***
0.033
-0.031
Korea
-0.029
0.022
-0.045
0.025
-0.754***
0.015
Luxembourg
0.252**
0.075
0.456***
0.082
-0.754***
0.095
Netherlands
0.317***
0.062
0.292***
0.062
-0.556***
0.043
Poland
-0.016**
0.006
-0.018**
0.007
-0.659***
0.051
Portugal
0.180***
0.022
0.297***
0.020
-0.795***
0.017
Slovakia
-0.152**
0.051
0.042
0.048
-1.088***
0.082
Slovenia
-0.034
0.017
-0.027
0.020
-0.302*
0.130
Sweden
0.320***
0.062
0.513***
0.065
-0.849***
0.042
United Kingdom
0.245***
0.027
0.242***
0.023
-0.752***
0.020
United States
0.457***
0.042
0.486***
0.047
-0.991***
0.013
Median
0.088
0.034
0.242
0.033
-0.754
0.033
Mean
0.114
0.040
0.209
0.041
-0.703
0.046
Max
-0.297
0.006
0.719
0.082
-0.031
0.130
Min
0.513
0.075
-0.239
0.007
-1.088
0.011
Specification:
Year FEs
Yes
Yes
No
Industry FEs
No
No
Yes
* p<0.05, ** p<0.01, *** p<0.001 Note: Source is the EU KLEMS database, 2008 release. Reports β estimates and standard errors from a regression of the
given dependent variable on an industry-specific measure of productivity: log(yit ) = β log(T FPit ) + FEs + εit . See text for details. In regression (1), energy use is the
cost of intermediate energy inputs in current dollars. In regression (2), energy intensity is the energy input share. In regression (3), energy use is a volume index of
intermediate energy inputs. Each regression run separately for each country. The year fixed effects specification captures the generally positive relationship between an
industry’s energy-intensity (in terms of energy-elasticity of output) and its overall productivity. The industry fixed effects specification captures the inverse relationship,
with-industries, between productivity and energy inputs per unit of output.
27
Table 2: Relationship between Energy Intensity and Productivity in Canada
(1)
(2)
(3)
(4)
(5)
Dep. Var.:
Dep. Var.:
Dep. Var.:
Dep. Var.:
Dep. Var.:
log (eit qt /yit )
log (eit qt /pit yit )
log (ẽit /yit )
log (eit /yit )
log (eit /yit )
0.298***
1.211***
-0.935***
0.834***
-0.853***
(0.078)
(0.076)
(0.013)
(0.179)
(0.036)
R2
0.046
0.253
0.936
0.123
0.981
N
768
768
768
270
270
Year FEs
Yes
Yes
No
Yes
No
Industry FEs
No
No
Yes
No
Yes
Industry TFP
Specification:
* p<0.05, ** p<0.01, *** p<0.001. Standard errors in brackets. Note: Data source is CANSIM tables 383-0022 and 153-0032. Reports β estimates and standard
errors from a regression of the given dependent variable on an industry-specific measure of productivity: log(yit ) = β log(T FPit ) + FEs + εit . See text for details. In
regression (1), energy use is the cost of intermediate energy inputs in current dollars. In regression (2), energy intensity is the adjusted energy input share. In regression
(3), energy use is a volume index of intermediate energy inputs. In regressions (4) and (5), energy use is terajoules. The year fixed effects specification captures the
generally positive relationship between an industry’s energy-intensity (in terms of energy-elasticity of output) and its overall productivity. The industry fixed effects
specification captures the inverse relationship, with-industries, between productivity and energy inputs per unit of output.
Table 3: Relationship between GHG Emission Intensity and Productivity in Canada
(1)
(2)
Dep. Var.:
Dep. Var.:
log(GHGit /yit )
log(GHGit /yit )
1.471***
-0.881***
(0.247)
(0.038)
R2
0.145
0.981
N
270
270
Industry TFP
Specification:
Year FEs
Yes
No
Industry FEs
No
Yes
* p<0.05, ** p<0.01, *** p<0.001. Standard errors in brackets. Note: Data source is CANSIM tables 383-0022 and 153-0032. Reports β estimates and standard
errors from a regression of the given dependent variable on an industry-specific measure of productivity: log(yit ) = β log(T FPit ) + FEs + εit . See text for details. In
regression (1), productivity is calculated using the cost of intermediate energy inputs in current dollars. In regression (2), productivity is calculated using a volume
index of intermediate energy inputs. The year fixed effects specification captures the generally positive relationship between an industry’s GHG-intensity (in terms of
GHG-elasticity of output) and its overall productivity. The industry fixed effects specification captures the inverse relationship, with-industries, between productivity and
GHG emissions per unit of output.
28
29
11
21
22
23
3A
41
4A
4B
51
54
56
5A
62
71
72
81
Agriculture
Mining and Oil and Gas Extraction
Utilities
Construction
Manufacturing
Wholesale Trade
Retail Trade
Transportation and Warehousing
Information and Culture
Professional, Scientific, and Technical
Administrative/Support, Waste Management
FIRE and Rental and Leasing
Health and Social Services
Arts, Entertainment, and Recreation
Accomodation and Food Services
Other
0.016
0.024
0.121
0.023
0.009
0.028
0.268
0.058
0.056
0.057
0.037
0.052
0.031
0.089
0.021
0.111
Nominal Output
Share
9,853
16,006
140,650
15,466
4,513
19,950
405,294
52,236
50,360
51,256
29,277
44,994
22,522
93,576
13,592
124,566
Real Output
($M)
733
1,116
2,833
904
294
990
3,996
1,897
2,207
1,557
903
2,239
362
916
334
3,042
Wage Bill
($M)
1,764
1,628
8,375
1,826
390
1,417
25,735
5,754
4,613
19,980
677
992
5,344
6,831
6,670
4,798
Energy Bill
($M)
0.92
0.95
0.90
0.93
0.95
0.95
0.80
0.90
0.93
0.67
0.97
0.98
0.64
0.78
0.57
0.94
Labour’s Output
Share
0.08
0.05
0.10
0.07
0.05
0.05
0.20
0.10
0.07
0.33
0.03
0.02
0.36
0.22
0.43
0.06
Energy’s Output
Share
12.49
14.07
44.50
16.27
15.12
19.78
70.35
24.55
21.62
14.27
32.69
20.37
23.66
65.58
11.19
39.91
Total Factor Productivity
Note: Data extracted from Statistics Canada CANSIM Table 383-0022. Real output is an estimate from industry total revenue raised to the power of ρ/(ρ − 1). This reflects the fact that productive industries will
SNA Code
Industry
Table 4: Industry-Level Summary Statistics (2008)
Table 5: Costs of Various Energy Regulation Schemes
Facility-Specific Regulation
Sector-Specific Regulation
Threshold-Based Regulation
Standard
Tax
Standard
Tax
Standard
Tax
Aggregate TFP
GDP/Worker (Welfare)
-0.95%
-1.05%
-0.09%
-0.94%
-1.88%
-1.71%
-0.02%
-0.23%
-0.63%
-0.69%
-0.06%
-0.64%
Number of Firms
Total Energy Use
Uniform Energy Tax Rate
-3.68%
-10.86%
-
-1.84%
-10.86%
14.4%
-35.99%
-2.91%
-
-0.46%
-2.91%
3.55%
-2.50%
-7.68%
-
-1.27%
-7.68%
9.83%
Fixed Mass of Entrants (No Exit or Entry)
Aggregate TFP
GDP/Worker (Welfare)
-0.84%
-0.95%
0.00%
-0.85%
-0.47%
-0.36%
0.00%
-0.16%
-0.56%
-0.63%
0.00%
-0.58%
Number of Firms
Total Energy Use
Uniform Energy Tax Rate
0.00%
-10.83%
-
0.00%
-10.83%
14.39%
0.00%
-2.23%
-
0.00%
-2.23%
2.70%
0.00%
-7.67%
-
0.00%
-7.67%
9.82%
Alternative Parameters: Commodity-Sectors σ = 5 and θ = 10; all others σ = θ = 4
Aggregate TFP
GDP/Worker (Welfare)
-0.98%
-1.06%
-0.11%
-0.98%
-1.72%
-1.57%
-0.04%
-0.33%
-0.65%
-0.70%
-0.08%
-0.67%
Number of Firms
Total Energy Use
Uniform Energy Tax Rate
-3.86%
-11.03%
-
-1.98%
-11.03%
14.59%
-26.46%
-4.08%
-
-0.69%
-4.08%
5.00%
-2.63%
-7.81%
-
-1.36%
-7.81%
9.96%
Displays results of various experiments that simulate regulatory energy and emissions intensity standards. The “Standard” corresponds to: (1) Facility-Specific,
an 18% reduction in energy intensity; (2) Sector-Specific, an energy intensity target for all firms to meet or exceed that corresponds to 18% less than the sector’s prior
average; and (3) Threshold-Based, a 12% energy intensity reduction target that is firm specific for the largest firms (cumulatively account for 70% of total energy use.
The results are contrasted to a flat, economy-wide, energy tax that achieves equivalent conservation effects. All results are reported as percentage point reductions in
the baseline value. The parameter σ is the elasticity of substitution between varieties within industries. The parameter θ governs (inversely) the productivity dispersion
across firms within industries.
30
Table 6: Comparing Tax to Sectoral-Target Standard, ρ = 1.5
(a) Welfare Loss of Tax Relative to Standard
Elasticity of
Substitution, σ
2
3
4
5
6
7
8
9
10
3
0.28
0.14
(Inverse) Productivity Dispersion Parameter, θ
4
5
6
7
8
9
10
0.34 0.39 0.42 0.46 0.49 0.52 0.54
0.22 0.28 0.33 0.37 0.40 0.43 0.46
0.11 0.18 0.24 0.29 0.33 0.36 0.39
0.07 0.15 0.20 0.25 0.29 0.32
0.05 0.12 0.18 0.22 0.26
0.05 0.10 0.15 0.20
0.02 0.08 0.15
0.02 0.10
0.05
(b) Aggregate Total Factor Productivity Loss of Tax Relative to Standard
Elasticity of
Substitution, σ
2
3
4
5
6
7
8
9
10
3
0.20
0.03
(Inverse) Productivity Dispersion Parameter, θ
4
5
6
7
8
9
10
0.26 0.32 0.36 0.40 0.44 0.47 0.50
0.06 0.09 0.12 0.14 0.17 0.19 0.21
0.01 0.03 0.04 0.06 0.07 0.09 0.10
0.00 0.01 0.02 0.03 0.04 0.05
0.00 0.01 0.01 0.02 0.03
0.00 0.00 0.01 0.01
0.00 0.00 0.01
0.00 0.00
0.00
These tables compare the welfare and productivity costs associated with a tax on energy relative to the equivalent sector-specific
energy intensity standard. It displays the relative cost of the tax policy (values less than one imply a tax is superior to a standard) for
various degrees of productivity dispersion and for various elasticities of substitution within-sectors. The between-sector elasticity of
substitution is unchanged from our baseline value of 1.5. We find that the tax always dominates the standard, although the degree to
which this is true declines for low elasticities and for low productivity dispersion.
31
Table 7: Comparing Tax to Sectoral-Target Standard, ρ = 1
(a) Welfare Loss of Tax Relative to Standard
Elasticity of
Substitution, σ
2
3
4
5
6
7
8
9
10
3
0.24
0.16
(Inverse) Productivity Dispersion Parameter, θ
4
5
6
7
8
9
10
0.30 0.35 0.38 0.42 0.45 0.48 0.51
0.19 0.25 0.30 0.34 0.38 0.41 0.44
0.09 0.16 0.21 0.26 0.30 0.34 0.37
0.05 0.13 0.18 0.23 0.27 0.30
0.03 0.10 0.15 0.20 0.24
0.03 0.08 0.13 0.18
0.00 0.07 0.14
0.01 0.09
0.04
(b) Aggregate Total Factor Productivity Loss of Tax Relative to Standard
Elasticity of
Substitution, σ
2
3
4
5
6
7
8
9
10
3
0.17
0.03
(Inverse) Productivity Dispersion Parameter, θ
4
5
6
7
8
9
10
0.23 0.29 0.33 0.37 0.41 0.44 0.47
0.05 0.08 0.11 0.13 0.16 0.18 0.20
0.01 0.02 0.04 0.05 0.07 0.08 0.10
0.00 0.01 0.02 0.03 0.04 0.05
0.00 0.01 0.01 0.02 0.02
0.00 0.00 0.01 0.01
0.00 0.00 0.01
0.00 0.00
0.00
These tables compare the welfare and productivity costs associated with a tax on energy relative to the equivalent sector-specific
energy intensity standard. It displays the relative cost of the tax policy (values less than one imply a tax is superior to a standard) for
various degrees of productivity dispersion and for various elasticities of substitution within-sectors. The between-sector elasticity of
substitution is unity. We find that the tax always dominates the standard, although the degree to which this is true declines for low
elasticities and for low productivity dispersion.
32
Table 8: Comparing Tax to Sectoral-Target Standard, ρ = 2
(a) Welfare Loss of Tax Relative to Standard
Elasticity of
Substitution, σ
3
4
5
6
7
8
9
10
3
0.18
(Inverse) Productivity Dispersion Parameter, θ
4
5
6
7
8
9
10
0.26 0.32 0.37 0.41 0.44 0.47 0.50
0.14 0.21 0.27 0.32 0.36 0.39 0.42
0.09 0.17 0.23 0.28 0.32 0.35
0.07 0.14 0.20 0.24 0.29
0.06 0.12 0.17 0.22
0.03 0.10 0.17
0.03 0.12
0.07
(b) Aggregate Total Factor Productivity Loss of Tax Relative to Standard
Elasticity of
Substitution, σ
3
4
5
6
7
8
9
10
3
0.03
(Inverse) Productivity Dispersion Parameter, θ
4
5
6
7
8
9
10
0.07 0.11 0.14 0.17 0.20 0.22 0.24
0.01 0.03 0.05 0.07 0.09 0.10 0.12
0.01 0.02 0.03 0.04 0.05 0.06
0.00 0.01 0.02 0.02 0.03
0.00 0.01 0.01 0.02
0.00 0.00 0.01
0.00 0.00
0.00
These tables compare the welfare and productivity costs associated with a tax on energy relative to the equivalent sector-specific
energy intensity standard. It displays the relative cost of the tax policy (values less than one imply a tax is superior to a standard)
for various degrees of productivity dispersion and for various elasticities of substitution within-sectors. The between-sector elasticity
of substitution is two. We find that the tax always dominates the standard, although the degree to which this is true declines for low
elasticities and for low productivity dispersion. We report results only for the case where σ > ρ.
33