Environmental policy and misallocation:The productivity
effect of intensity standards
Trevor Tombe a,n,Jennifer Winter b
a Department of Economics,University of Calgary,2500University Drive NW,Calgary,Alberta,Canada T2N1N4
b Energy and Environmental Policy,The School of Publi
c Policy,University of Calgary,Canada
a r t i c l e i n f o
Article history:currencyexchange
Received18July2014
Available online11June2015
JEL classification:
Q4
Q5
H2
E6
Keywords:
Energy intensity
Energy tax
Productivity
a b s t r a c t
Firm-level idiosyncratic policy distortions misallocate resources between firms,lowering
aggregate productivity.Many environmental policies create such distortions;in particular,
output-bad intensity standards(which limit firms energy u or emissions per unit of
output)are easier for high-productivity firms to achieve.We investigate the productivity
effect of intensity standards using a tractable general-equilibrium model featuring multi-
ple ctors and firm-level heterogeneity.Qualitatively,we demonstrate that intensity
standards are always inferior to uniform taxes,as they misallocate both dirty and clean
inputs across firms and ctors,which lowers productivity.Quantitatively,we calibrate the
model to US data and show that the productivity loss can be large.
&2015Elvier Inc.All rights rerved.
Introduction
impressFirm-level policy distortions–such as differences in tax rates or regulatory treatment across firms–misallocate resources and can substantially lower aggregate productivity(Restuccia and Rogerson,2008;Hsieh and Klenow,2009;Brandt et al.,2013; Bartelsman et al.,2013).Many environme
ntal policies are firm-specific and therefore create such misallocations.In particular, intensity standards(or output-bad regulations)place limits on energy u or emissions per unit of output,which are easier for high-productivity firms to achieve than for low-productivity firms.The policies are increasingly common and a growing literature compares intensity standards to flat energy or emissions taxes.While taxes are often first-best,a number of factors favour intensity standards:market power(Holland,2009;Li and Shi,2012);incomplete regulation or leakage(Holland,2012);learning-by-doing in production(Gerlagh and van der Zwaan,2006);certain pre-existing tax distortions(Parry and Williams,2011);or unexpected business-cycle productivity shocks(Fischer and Springborn,2011).To date,however,there is no quantitative exploration of the misallocation and productivity effects of environmental policy in general and intensity standards in particular. We fill this gap.
What do we mean by misallocation?And how do intensity standards misallocate resources and lower productivity?Inputs to production,such as labour or energy inputs,are misallocated if marginal revenue products differ across producers.With such differences,total output will grow if a worker moves from where she is valued less to where she is valued more.What matters for total output is therefore not only the underlying productivity of individual producers,but also the allocation of resour
ces between them.Environmental policies in general will increa the costs of polluting or the costs of using“dirty”inputs,but intensity
Contents lists available at ScienceDirect
journal homepage:/locate/jeem
Journal of
Environmental Economics and Management
dx.doi/10.1016/j.jeem.2015.06.002
0095-0696/&2015Elvier Inc.All rights
rerved.
n Corresponding author.
E-mail address:ttombe@ucalgary.ca(T.Tombe),jwinter@ucalgary.ca(J.Winter).
Journal of Environmental Economics and Management72(2015)137–163
standards in particular will increa tho costs more for low-productivity firms than for high-productivity firms.As input costs differ,marginal revenue products will also differ across firms in equilibrium,hence the misallocation.We formalize this in the next ction.
The existing literature,starting perhaps with Helfand (1991),highlights two distinct distortions that intensity standards create.First,they impo an implicit tax on a producer's emissions or on its u of dirty inputs.Second,they provide an implicit subsidy to a producer's output.The taxes and subsidies are implicit as neither results in actual payments by or to producers.Instead,intensity standards impo constraints on producer choices that can be equivalently achieved through a tax on dirty inputs with all proceeds rebated to the producer as a subsidy to its output.The output subsidy is important,as marginal costs of production under a standard are lower than under an explicit tax.Holland (2012)demonstrates that this implies that a social planner would choo a higher level of emissions with a standard than it would with an emissions tax.Instead of exploring the optim
al level of emissions,we compare alternative policies that each achieve the same environmental objective.Our focus is therefore on ctoral and aggregate productivity (output per bundle of inputs),and not on welfare.We show that the implicit tax on dirty inputs and the implicit output subsidy both misallocate resources across firms and ctors.Both distortions combine to misallocate dirty inputs –this is cloly related to the widely understood requirement that optimal policy equalizes marginal abatement costs.In addition,the output subsidy misallocates clean inputs –this is a distinct (and previously unexplored)general-equilibrium effect of intensity standards.
We investigate two broad types of intensity standards:(1)improvement targets and (2)level targets.Improvement targets require that firms achieve a given percentage reduction in their energy intensity (relative to their own baline).Level targets,on the other hand,require that firms meet a common energy intensity,which is normally a percentage reduction in the ctor 's average energy intensity.Alternatively,improvement targets are firm-specific and level targets are ctor-specific .A third type of intensity target is a variation on firm-specific targets that apply only to large emitters;we call the threshold-bad targets.For example,the U.S.EPA regulates facilities emitting more than 100,000tons per year of CO 2-equivalent.The Canadian province of Alberta does the same.Each of the policies will have different distortionary effects on energy input costs.Improvement targets incr
ea energy input costs in energy-intensive industries by more than in other industries,while level targets increa energy input costs by more for low-productivity firms.Our model allows us to evaluate the effect of the distortions on allocations,and therefore productivity,across firms and ctors.
To perform this analysis,we build a tractable quantitativemodel that cleanly maps into readily available ctor-level data on production and energy u.The model builds heavily on insights from macroeconomics (in particular,Hsieh and Klenow,2009,and Jones,2013)and provides a uful tool to analyze environmental policies.The broad features of the model can be quickly summarized.Aggregate GDP is a composite of N goods produced by multiple ctors.To produce the goods,each ctor aggregates the output from a continuum of firms that produce horizontally differentiated varieties.At the individual firm level,production is similar to Copeland and Taylor (1994)where firms u labour for production and abatement activities.Firms also require a certain level of energy,that is increasing in production but decreasing in how many workers are ud in abatement.1This structure results in a simple Cobb –Douglas production technology,where all firms are “dirty ”but vary in their “dirtiness ”.
The structure allows for powerful qualitative results and tractable quantitative analysis.We provide ex
pressions that transparently link labour and energy allocations to ctoral and aggregate productivity.With the expressions,we demonstrate that intensity standards change allocations away from the optimum,lowering productivity;energy taxes do not change the optimal allocation.This holds for any admissible parameter values in the model.Building on the propositions,we undertake a variety of illustrative quantitative simulations to show that the magnitude of the effects are often substantial.Sector-specific intensity standards are particularly damaging,resulting in the most misallocation and (in the expanded model)firm exit.For example,a ctor-specific target that lowers total energy u by 10per cent will lower aggregate productivity by nearly 0.15per cent while a uniform tax on energy has zero effect on productivity.If energy u and emissions are proportional,consistent with evidence in the next ction,this is equivalent to the standard costing $35more per tonne of CO 2abated than a uniform energy tax.Our quantitative analysis is only illustrative,but highlights that misallocation from intensity standards can be large.We also extend the model to allow (1)entry and exit of firms and
(2)more general substitution possibilities between industries.Firm exit will amplify the negative effects of intensity standards while more substitutability between ctors dampen them.
Of cour,there are ways to improve the performance of intensity standards.If they are implemented
as tradable permits,their economic costs in our framework are identical to a tax.2Similarly,fines for violating intensity standards,the value of which would not differ across firms,can significantly lower their productivity costs.With a fine equivalent to a 50%tax on energy u –chon for illustrative purpos only –the productivity conquences of a standard falls to less than half our baline estimates.Finally,as we show the costs of intensity standards are even larger when firm exit is considered,policy-makers may consider transfers or other supports to prevent firm exit (though this is not our focus).
1
依恋的意思In Copeland and Taylor (1994),emissions are a by-product of production.The two approaches are largely equivalent,except emissions are free while energy is purchad .This introduces some difficulties for our model calibration and quantitative exercis.In Appendix B we demonstrate that our key qualitative results hold when emissions are a by-product.We explore the empirical relationship between energy u and emissions in the next ction.
2Firms exceeding a mandated intensity can purcha the “spare ”capacity of other firms.In our framework,an efficient trading market would equalize the marginal cost of energy and therefore misal
location costs would be zero.For further reference,Goulder and Schein (2013)show that permit trading is equivalent to an energy tax.For trading schemes that implement intensity standards,e McKitrick (2005).Recently,de Vries et al.(2014)find that cap-and-trade can potentially dominate tradable intensity standards in a model with multiple heterogeneous ctors.T.Tombe,J.Winter /Journal of Environmental Economics and Management 72(2015)137–163
138
Our work fits within a substantial literature in environmental economics,especially tho cited earlier that investigate the efficacy of intensity standards.While we are agnostic about the optimal level of energy reduction,we evaluate the efficiency of various policies in achieving a given objective.Our key contribution is to quantitatively evaluate the cost of environmental policies in the prence of firm-level heterogeneity in productivity.While firm heterogeneity has been introduced via limited cost heterogeneity,rich productivity differences across a continuum of firms has,until recently,not been investigated.Most similar to our paper are Li and Sun(2011)and Li and Shi(2012).They show that firm heterogeneity is important to evaluate environmental policies,though we differ in important ways.First,our model is a quantitative tool that matches key features of production and energy u across multiple industries.Second,the intensity standards we consider differ,and we explore many ty
pes.Third,our substantive focus differs,as we explore the misallocation and productivity costs of intensity standards.Finally,we analytically prove that intensity standards cannot increa productivity, a possibility within their more stylized framework.
Finally,we must emphasize that our approach is conceptually distinct from the large literature on abatement-cost heterogeneity.3In that literature,marginal abatement cost curves are typically exogenously assumed to take a certain functional form.When the marginal costs of inputs differ across firms,there exists a reallocation of abatement responsibilities that lowers the total cost of achieving a given aggregate target.The data requirements to estimate such curves are often prohibitive.As mentioned,some of our analysis is related to abatement cost differences;we discuss this in a later ction.However,misallocation goes beyond this phenomenon.Output distortions in particular will have a distinct, general equilibrium effect on the allocations between firms and ctors.
The next ction begins our analysis with a broad overview of modeling emissions,energy u,and intensity standards. We demonstrate clearly how intensity standards misallocate inputs,how allocations can be equivalently captured by a system of implicit taxes and subsidies,and how inefficient allocations affect productivity.
lpa
Intensity standards and factor misallocation
How do we model emissions and intensity standards?How does the allocation of resources affect aggregate productivity?This ction explores the answers to the basic questions before proceeding to the heart of our analysis.We begin with a well-established modeling approach to incorporate emissions as a free input in production,following Copeland and Taylor(1994).We also argue an alternative approach,where emissions are proportional to costly energy inputs,proves convenient in many applications,especially the quantitative analysis to come.
With the production technologies broadly defined,we proceed to describe how and why resource allocations matter for aggregate productivity.Following the recent macroeconomics literature on the aggregate effect of firm-and ctor-level distortions, we show how intensity standards(and,more broadly,a wide variety of environmental policies)can create implicit taxes that may vary across producers and how this variation lowers productivity.This will prove a powerful modeling approach,both for sharp qualitative results and for fully general equilibrium quantitative simulations.
Emissions as an input:a primer
Copeland and Taylor(1994)show,under certain conditions,emissions that are a by-product of production can be equivalently
modelled as an input.Consider,a firm i that allocates labour L i to production L y
i or emissions abatement L a
眨巴i
.Output is produced
using
Y i¼A i
1Àαi
αi
1Àα
i
L y
i
;ð1Þ
where A i is productivity andαi Að0;1Þ.One can(and should)interpret labour inputs broadly to include any primary input,such as physical or human capital.Emissions are a by-product of production,assumed to follow
E i¼1Àαi
αi
L y
i
alpha是什么L y
过去完成时i
þL a
i
ÀÁα
i
"#1=1Àα
i
:ð2Þ
Without abatement(where L a
i
¼0),emissions per worker areð1ÀαiÞ=αi.As labour is allocated to abatement,L a i increas and emissions decrea.The parameterαi may be interpreted as the effectiveness of the abatement technology.Asαi grows,emissions fall.4
In general,total employment must be allocated to either production or abatement,so L i¼L y
i þL a
brazieri
.With this,Eqs.(1)and
(2)combine to yield
Y i¼A i Lαi
i E1Àαi
i
:ð3Þ
3See,for example,Newell and Stavins(2003)for a complete discussion.
4The Copeland and Taylor(1994)abatement technology is related to that found in Li and Shi(2012).They are identical if the Li and Shi(2012) parameters(b,γ)are b¼γ¼ð1ÀαiÞ=αi.The difference is that Li and Shi allow emissions per worker without abatement(b)to differ from the invers
e
effectiveness of the abatement technology(γ).
T.Tombe,J.Winter/Journal of Environmental Economics and Management72(2015)137–163139
Emissions can therefore be thought of as an input (i.e.,“environmental rvices ”)in the production process along with labour L i .Intuitively,as more labour L i is allocated to abatement,output declines.This effect is captured by a lower E i ,which lowers output Y i .
A powerful alternative to emissions as a by-product is to consider emissions as resulting from purchad energy inputs.This would literally interpret E i as an input purchad at some positive price from an energy supplier.The Copeland and Taylor (1994)structure above is valid,with abatement interpreted as activity of workers that do not contribute directly to production but instead lowers total energy u.5The energy-inputs interpretation dramatically sharpens our qualitative results and eas our calibration and simulation exercis –we maintain this interpretation throughout.In Appendix B,we illustrate how our analysis would differ in a model with emissions as a by-product,and confirm that all our key results hold.In any ca,the basic Cobb –Douglas production technology of Eq.(3)will be ud throughout this paper,though it is instructive to keep Eqs.(1)and (2)i
n mind.As E i =L i falls,for example,labour ud in abatement L a i grows:falling E i =L i is therefore synonymous with incread abatement activity.
This interpretation is also reasonable,as certain emissions at the ctor level are roughly proportional to energy u.To e this,consider the World Input –Output Databa's environmental accounts,which provide two measures of energy inputs:total and emissions-relevant.Importantly,emissions-relevant energy u does not include raw material inputs (such as crude oil ud by refineries)but only energy consumed in the production process,not energy transformed from one form to another.For the United States,the correlation between ctoral emissions-relevant energy u and CO 2emissions is 0.998.Fig.1illustrates this strong relationship.In panel (a)the roughly proportional relationship is clear.This suggests that a 10per cent change in energy u will lead to a 10per cent change in emissions,for example.In panel (b),we compare total energy inputs with emissions-relevant energy inputs.The two are nearly perfectly correlated,with important deviations for only three ctors.We will be careful to calibrate the model using only data for emissions-relevant energy u.
Misallocation and productivity,the basics
red rainHow does input allocations affect productivity?An economy's aggregate productivity depends not only on the productivity of its individual firms but also on the allocation of resources across tho firms.With multiple producers,there will be some optimal allocation between producers.When allocations deviate from that optimum,aggregate productivity falls.
To illustrate this,consider maximizing some aggregate Y ¼F ðy 1;…;y N Þof output y i from N producers.Further suppo all producers have identical αi ,though they may differ in productivity.How should we allocate inputs ðL i ;E i Þ,given some fixed aggregate supply of both,such that Y is maximized and input markets clear?From the first order conditions of the constrained maximization problem,it is straightforward to show that the marginal rates of technical substitution must equalize across firms:
d y i d L i d y i d E i ¼d y j d L j d y j d E j
8i ;j ðÞ:00For the production technology of Eq.(3),or indeed for any technology with constant (and common)elasticities of substitution between inputs,the above implies
E i L i ¼E j L j 8i ;j ðÞ:
take a break
Deviations from equality in input ratios therefore result in lower aggregate output.
Of cour,if input elasticities αi differ across firms then input ratios will optimally differ.But,the general insight is sound:policies that distort firm input decisions away from some optimal allocation will lower aggregate productivity.When the full model is developed,we will derive a clear expression mapping allocations to productivity,both in aggregate and by ctor.Before getting there,we must explore how intensity standards create differences in input ratios between producers.We do this in the next ction.
The effect of intensity standards
Baline energy intensity,from Eqs.(2)and (3),is
E i i ¼1i E i i αi ¼1i 1Àαi αi αi ;ð4Þ
which is clearly decreasing in productivity A i .What is the effect of a binding limit on energy intensity?Imagine the government does not allow E i =L i to exceed some intensity standard s .There is no change to firms that are already below this
5
More broadly,one might looly interpret abatement as any costly activity that lowers the u of emis
sions-relevant energy,such as substitution between different fuel types.We remain focud on general macroeconomic relationships,though such firm-specific considerations may be an interesting avenue for future rearch.T.Tombe,J.Winter /Journal of Environmental Economics and Management 72(2015)137–163
140
threshold,but firms above it must substitute labour for energy to bring E i =L i below s .Precily,
E i Y i ¼min s ;A À1i 1Àαi αi
αi &':If the standard is binding,then E i ¼sY i and Y i ¼A i L αi i E 1Àαi i ¼A 1=α
i i s ð1Àαi Þ=αi L i .This implies that the energy per worker for firms bound by the standard is ðA i s Þ1=αi and energy per worker for firms not bound by the standard is ð1Àαi Þ=αi .Across all firms,E i L i ¼min ðA i s Þ1=αi ;1Àαi αi &':ð5Þ
We plot the results in Fig.2.Low-productivity firms have high energy-intensity abnt policy (the dotted line labeled “baline intensity ”).Intensity standards that t limits on energy per unit of output will bind on the low-productivity firms.In respon,the firms will shift their inputs towards l
abour,with lower-productivity firms disproportionately affected.
There are other types of intensity standards that t firm-specific limits s i .We refer to the as firm-specific intensity standards to distinguish them from the ctor-specific intensity standards where s is common to all firms within a ctor.Suppo the government requires firms that lower their energy intensity to x per cent of the firm's own baline.From Eq.(4),the standard would be s i ¼x ð1Àαi Þ=αi ÀÁαi =A i ,where x o 1reflects the required improvement.In this ca,all firms would find the standard binding and energy per worker would be x 1=αi ð1Àαi Þ=αi (identical for firms with similar αi ).Keep this in mind.We will e later that ctor-specific intensity standards misallocate resources both across firms and across ctors while firm-specific intensity standards misallocate resources only across ctors.
The next –and final –ction provides an equivalent way in which we can capture the effect of intensity standards.This approach cloly mirrors the misallocation literature in macroeconomics.It provides a powerful and tractable way in which full general equilibrium analysis policy may be done,both qualitatively and quantitatively.
Intensity standards as market distortions
A firm maximizing profits will make input choices such that the marginal revenue product of each input equals the marginal cost.For labour,producers will hire until αi P i Y i =L i ¼w ,where w is the wage.In all that follows,we treat labour as the numeraire and therefore normalize w ¼1.For energy inputs,the decision rule is similar:purcha energy until the marginal revenue product equals energy's price.If aggregate supply is perfectly elastic,we can define units such that energy's price is one,so ð1Àαi ÞP i Y i =E i ¼1.
Input market distortions,however,change the expressions.If producers face a distortion to the price of energy,
denoted τe i Z 1,then ð1Àαi ÞP i Y i =E i ¼τe i .Combined with the expression for optimal labour inputs,energy per worker is
E i i ¼1Àαi αi 1τe i :ð6Þ−4
−3−2
−101C O 2 E m i s s i o n s , L o g S c a l
e −4−3−2−101Emissions−Relevant Energy U, Log Scale
−4−2024
E n e r g y U s e , L o g S c a l e −4−3−2−101
Emissions−Relevant Energy U, Log Scale
Fig.1.Sectoral energy u and carbon emissions (WIOD 2009).Displays a strong relationship between ctoral emissions-relevant energy u and emissions.The correlation coefficient between the two is 0.998(0.975when in logs).Panel (b)illustrates emissions-relevant energy u and total energy u are nearly identical for most ctors,with construction,refining,and chemicals as the exceptions.The dotted line is the 45-degree line.Data is for the United States from the 2009environmental accounts of the World Input –Output Databa.
T.Tombe,J.Winter /Journal of Environmental Economics and Management 72(2015)137–163141
