Prices vs. quantities: What’s new? A perspective of input-output DSGE model with
directed technical change and uncertainty
Chin-Yoong Wong* and Yoke-Kee Eng
Universiti Tunku Abdul Rahman, Malaysia
Abstract
Disagreement over the optimal choice of environmental instrument can obstruct the determination of
regulators to reduce pollution emission. This paper revisits the long standing prices-vs.-quantities
debate with a dynamic stochastic general equilibrium model that features a feedback-loop upstreamdownstream structure and directed technical change in clean technology innovation. The welfare
evaluation criterion is a quadratic approximation to a household’s utility grounded upon a simple view
that a welfare-maximizing instrument should be emission-reducing without risking macroeconomic
stability. We find that an optimal instrument is no longer a choice between prices and quantities but
involves both. Downstream production should be taxed, and upstream production should have an
emission intensity cap imposed. The input-output structure transmits and propagates the emissionreducing effect of a downstream tax to upstream industries. Subsidizing clean technology innovation in
upstream clean industries shrinks dirty industries, fostering emission reduction. Moreover, an upstream
intensity cap creates a stable macroeconomic environment in which innovation is nurtured, as long as
the intensity constraint is not binding. These findings also help reconcile the debate on whether to
regulate upstream or downstream industries.
Keywords: Pollution emission tax; Emission intensity target; Directed technical change; Dynamic
stochastic general equilibrium model
JEL classification: E32, H23, Q52, Q55, Q58
* Ccorresponding author at: Department of Economics, Faculty of Business and Finance, Universiti Tunku Abdul Rahman,
Jalan Universiti, Bandar Barat, 31900 Kampar, Perak, Malaysia. Tel: 6054688888; Fax: .E-mail addresses:
[email protected] (C.-Y. Wong), [email protected] (Y.-K Eng)
1
1. Introduction
Given that production is one of the – if not the – main contributors to pollution emissions and
thus climate change, an effective green policy must be able to alter the way a production task is
accomplished. Though mandatory technology and performance-based standards, i.e., grams-of-CO2per-mile requirement for cars, have largely occupied the stage of environmental policy for decades,
market-based policies have often been found to be more cost-effective and innovation-spurring (Aldy
and Stavins, 2012).
Ever since the classic paper by Weitzman (1974), considerable efforts have been put into
identifying the circumstances under which a policy instrument is more effective and efficient. It is
generally agreed that the choice between price-based and quantity-based policy depends on the
elasticity of marginal benefit and cost of environmental regulation. When marginal benefit is more
elastic than marginal cost, erroneous price instruments, i.e., carbon tax, are less harmful and thus
preferred. Otherwise, quantity instruments, i.e., cap-and-trade and emission intensity target, are
preferable. Had uncertainty that affects both the marginal cost and benefit been positively correlated,
Stavins (1996), in extending Weitzman’s analysis, argues that quantity instruments are more likely to be
favored.
More recent contributions further broaden the dimensions for evaluation. Goulder and Schein
(2013), for instance, have highlighted the advantage of the carbon tax rate in having an exogenously
fixed emission price. Compared with a quantity instrument that fixes emission quantity but allows
emission prices to fluctuate, as the argument goes, a stable emission price minimizes policy errors in
the face of uncertainty in marginal benefits and costs of emission reduction. A price instrument naturally
becomes an optimal choice. This argument, however, ignores the likely welfare-improving interactions
between emission price and the economy in the sense of increasing firm’s output, which is only
possible when a quantity instrument is employed (see, for instance, Mansur, 2013).
2
Though the importance of these microeconomic dimensions is beyond doubt, the
macroeconomic implications of the policy options typically fall out of the area of concern. Fischer and
Heutel (2013) rightly reason that ignoring the interaction between environmental policy and
macroeconomic indicators risks misestimating the welfare implication of the policy options. Moreover,
how can a policy instrument be welfare superior if its implementation instigates economic instability,
retrogressing social material well-being and employment satisfaction? These problems motivate the
inquiry of this paper.
This paper revisits the “prices vs. quantities” debate by using a dynamic stochastic general
equilibrium (DSGE) model that features uncertainty in total factor productivity, preference, and
environmental policy. Welfare evaluation and comparison draw on the welfare criterion derived as the
second-order approximation to households’ utility, as in the tradition of the New Keynesian DSGE
model (see, for instance, Gali, 2008).
There are three important model properties that differentiate ours from those of Fischer and
Springborn (2011), Heutel (2012), and Angelopoulos et al. (2010). First, following Copeland and Taylor
(1994, 2003), pollution emission is simultaneously treated as if it were inputs into the production and a
by-product of production through the use an exogenous pollution abatement technology. As a
consequence, we are able to model explicitly the marginal benefit and cost of pollution. The former
reciprocally resembles the marginal cost of emission reduction, whereas the latter bears a resemblance
to the marginal benefit of emission reduction in the “prices vs. quantities” literature. This modelling
strategy enables us to provide a macroeconomic perspective that corresponds directly to the
microeconomic concerns of the debate.
Second, drawing upon Acemoglu et al. (2012), we incorporate directed technical change into
the clean technology innovation occurring in clean industries that compete for resources with dirty
industries. Acknowledging the fact that environmental policy creates obstacles and opportunities to the
clean technology innovation, which, in turn, can have an feedback effect on the efficiency of the policy
3
option itself (see, for instance, Wirl, 2013; Jaffee et. al., 2002), a DSGE model with directed technical
change enriches the interactions between environmental policy and the economy that may (and will as
found) alter the welfare performance of each policy option.
Last but not least, building also upon Acemoglu et al. (2012), we explicitly model an inputoutput economy with feedback loop, meaning that part of the downstream final output will be
transformed into materials for upstream processing. The main purpose of setting up an upstreamdownstream structure is to take stock of the welfare implications of implementing a new hybrid system
that calls for the use of different instruments across the value chains with different pollution intensity.
In doing so, this paper bridges three important strands of literature in environmental economics,
namely the “prices vs. quantities” debates, trade and environment as per Copeland and Taylor (2003),
and the environmental macroeconomics as surveyed in Fisher and Heutel (2013), with an input-output
macroeconomic model. The model is simple enough to allow a geometrical exposition for the core
lesson of the model, and yet, it is rich enough for more sophisticated general-equilibrium analysis.
Previewing the main findings elaborated in Sections 2 and 4, we argue that, with plausible range of
parameter values, taxing downstream activities during which upstream production is imposed an
emission intensity target is welfare superior to a pure emission tax or intensity cap. This finding is
especially robust when uncertainty in marginal benefit and damage are perfectly correlated and clean
technology innovation is subsidized by the tax revenue.
The intuition behind the result is simple. A pollution tax on consumer goods that decreases the
quantity demanded will lead to a decrease in demand for upstream inputs. At the same time,
subsidizing clean technology innovation in the upstream chain with the pollution tax revenue increases
the supply of clean inputs, tilting the relative prices of upstream outputs unfavorably against dirty inputs.
Thus, the decrease in downstream demand for upstream inputs is largely felt by the dirty industries.
Cleaner downstream outputs due to an environmentally favorable shift in input composition are then reprocessed in upstream production, contributing to further reduction in pollution emission.
4
Note also that expansion in upstream clean production implies a decline in the pollution
emission as a share of production, making the emission intensity target imposed on upstream activities
unbinding. In such circumstances, the shadow emission price will vary to accommodate rather than
offset the role of relative prices in resource allocation as a response to stochastic shocks. The intensity
target can therefore be further restricted to lower the cap for pollution without harming macroeconomic
responses to uncertainty as long as the constraint is not in effect. Closely related in spirit to this finding
is Bushnell and Mansur (2011) who promote downstream regulation and Driesen and Sinde (2009) who
suggest upstream regulation, which our model attempts to reconcile.
The rest of the paper is organized as follows. Section 2 lays out the model with a detailed
discussion. A partial equilibrium analysis is carried out with the assistance of geometrical exposition.
Section 3 discusses the calibration of model parameters. In Section 4, the welfare performances of four
policy options under different sources of uncertainty and circumstances are inspected. Section 5
concludes the paper.
2. The model
We consider a closed-economy model in which goods are produced through interconnected
upstream and downstream stages, and each stage generates pollution. In contrast to prevailing
macroeconomic models of pollution that feature single production stage with horizontally decoupled
sectors (see, for instance, Copeland and Taylor, 2003, for clean-versus-dirty good model, Fischer and
Newell, 2008, for emitting-versus-non-emitting sector model, and Levinson and Taylor, 2008, for Ngood model), or with one sector (Heutel, 2012; Angelopoulous et al. 2010), our model features
backward-forward linkages in the production processes with a feedback loop: Upstream industries
produce a continuum of differentiated “clean” and “dirty” outputs, which will be used as inputs for
downstream production of unique final goods, out of which a fraction will be re-sourced to upstream
industries as materials. In doing so, the model would be of great use to identify simultaneously how the
horizontal interactions between dirty and clean sectors in the upstream industry as well as the vertical
5
interactions between upstream and downstream industries may alter the level and characteristic of
pollution emissions. We hold the view that such horizontal-vertical interdependence is valuable in
distinguishing the circumstances wherein using one policy instrument is welfare-superior to others in
the face of different stochastic shocks.
Another important novelty of the model is to incorporate direct technical change a-la Acemoglu
et al. (2012) into an environmental macroeconomic model. We allow the direction and bias of
technological innovation and adoption endogenously determined by expected profitability, which, to
some extent, is conditional on the choice of environmental policy across value chains. As a result, the
choice of policy instrument not only produces immediate effects on the demand for polluting inputs, it
also indirectly affects the supply of clean inputs, thereby influencing the equilibrium level of pollution
emission.
Let us start with the description of the production environment.
2.1. Production structure
Downstream industry produces competitively a unique final good using a bundle of “clean” and
“dirty” inputs,
.
/ and
∫
.
/ according to the following production
∫
function:
(
where
)0
(
)⁄
(
)⁄
1
⁄(
)
(1)
is the first-order autoregressive exogenous total factor productivity (TFP) shock in
downstream industry, and
(
inputs are complements when
) is the elasticity of substitution between two inputs. The two
and substitutes when
. Following Copeland and Taylor
(2003), we model pollution emission in downstream production as
( √
(2)
)
6
where
indicates the pollution abatement cost (PAC), and
refers to the pollution intensity of final
good production. By definition, the PAC-adjusted output available for sales is
(
)
.
Together with Eqs. (1) and (2), the PAC-adjusted downstream output can be written as
(
(
)0
(
)⁄
(
)⁄
1
⁄(
)
(3)
)
Pollution is treated as if it were the input for production. Market clearing for final goods implies that
.∫
where
(4)
/
∫
refers to materials for upstream clean industry of type , whereas
are materials for
dirty industry of type .
As in Acemoglu et al. (2012), monopolistically competitive upstream firms purchase and
transform downstream outputs as materials for next-period production at a cost of
goods. The cost is normalized to
type-specific materials
for
units of the final
+. The upstream firms combine a continuum of
*
of varying qualities
and labor
according to Cobb-Douglas
production technology.
(
where
)
∫
(
(5)
)
is the common first-order autoregressive TFP shock for upstream production. When the
quality of materials improves, given the production on the one hand, less quantity of the materials is
needed. Given the cost budget on the other hand, better quality induces production expansion that
results in greater use of the materials. The assumption of decreasing marginal return implies that the
latter effect always dominates.
The average quality of material
.
according to the following difference equation
of average quality, and
/ for industry
∫
(
)
*
+ evolves over time
, where
indicates the growth
refers to the probability of successful innovation in sector at time . We
assume that the probability of successful innovation in clean technology
7
depends on the expected
profitability in clean sector
, which is, in turn, conditional on market price, demand, unit variable cost,
and fixed cost in wage unit. Only when the expected profit surpasses a critical threshold ̅ , it is
rewarding to invest in clean technology. In addition, the incentive for clean technology investment
and ̅ . The probability of a success in clean technology
increases with the difference between
innovation can thus be expressed as
̅ )
(
̅ )
(
,
(6)
If expected profit for clean technology investment falls short of the threshold level, it is worth
maintaining the use of dirty technology. This means that
̅ )
(
, which implies
. The difference equation can be rewritten as
.
̅ )
(
(
̅ )
(
(
(7)
)/
(8)
)
Identical to the situation of downstream production, upstream processing emits pollution according to
. √
where
and
(9)
/
, respectively, indicate the pollution intensity of upstream production and pollution
abatement cost in sector . We assume that
. PAC-adjusted upstream output
available for sales is given by
(
(
)
∫
(
)
)
(10)
Market clearing for labor market requires labor demand to be equal to total labor supply, which we
normalize to one, i.e.,
. In addition, market clearing for sector of a variety of in
upstream industry implies
(11)
∫
2.2. Pollution tax as instrument
8
.
We first consider the case of emission pollution tax
imposed identically across firms and
industries at -th stage of production. Together with the wage compensated to the labors hired
and unit price for material of type , upstream firms in industry minimize the cost of production
subject to the production function (10). Denoting
as the unit
variable cost, the first order conditions can be easily derived as what follows
(
)(
)
(
)
⁄
(12)
⁄
(13)
(14)
⁄
Inserting Eqs. (12) to (14) into (10) gives us the following expression of unit variable cost:
(
(
)
)
(
(
)
)
(
)
)(
.(
(
(∫
)/
)(
)
)
(
)(
(
(∫
)
(
)
)
)(
)
. (
)/
(
)
(15)
Unit pollution tax, wage compensation, and unit material prices constitute the unit variable cost. Holding
other factors constant, due to the assumption of
, the pollution tax is more costly for dirty
industries, and directed technical change of identical magnitude has a smaller cost-saving impact on
clean industries compared to dirty industries. Moreover, a reduction in unit material price will be more
cost-saving in the cleaner industries.
To shed more light on the mechanism, we insert the relative demand for laborers and materials,
.
/(
(
,
)
)(
)
and
the
relative
demand
for
materials
and
pollutions,
, into the cost function to derive the Marshallian demand for each input
as what follows:
(16)
⁄
(
)
(17)
⁄
9
(
)(
)
(18)
⁄
What we can infer from Eq. (17) is that when the price of downstream output (which becomes the
materials for upstream production) declines, its demand-raising effect is felt to a larger extent in cleaner
industries. The feedback loop of a directed technical change in clean technology is now evident: a
breakthrough in clean technology causes the unit variable cost of clean upstream outputs to fall,
inducing greater demand for clean upstream outputs in downstream processing. Cheaper input prices
drive down the unit variable cost (as will be derived momentarily) of downstream output and the
subsequent lower price of downstream output, which is re-sourced as materials for upstream
processing, will trigger resource reallocation toward clean industries and further reduce the unit variable
cost of clean upstream outputs. In short, the effect can be propagated throughout the value chains
mediated by the relative price changes.
Proceeding to downstream production, the firm’s problem is to minimize the cost of production,
subject to the production function (3). The first-order conditions are
derived as
(
(
)
⁄
(19)
)
(20)
⁄
where
(
denotes unit variable cost of downstream production, and
)⁄
1
⁄(
)
(
0
(
)⁄
) is the constant-elasticity-of-substitution bundle of clean and dirty inputs. From Eq.
(19), we can obtain the price ratio of clean and dirty inputs. Inserting the price ratio into
gives us the
following expression:
(
)
⁄(
)
Defining the producer price index (PPI) for dowstream production as
the optimal demand schedules for input
(
⁄
*
(
)
⁄(
)
,
+ is
(21)
)
10
Furthermore, by putting Eq. (19) for
(
)
+ into
*
, we can obtain the equilibrium condition for
(22)
⁄
which, together with (20) being put into (3), allows us to derive the unit variable cost in the form
(
)
(
)(
) (
)
(
)
(
)
(23)
consisting of pollution tax, material price, and TFP progress. Combining the equilibrium conditions for
(22) and
(20) and the cost of production
Marshallian demand for
(
and
)
(
, the
)
takes the form
(24)
⁄
(25)
⁄
Together with Eq. (19), the Marshallian demand for inputs (24) can be decomposed into
(
)
⁄
(
⁄
) ,
*
(26)
+
What makes (26) different from (17) is that price responsiveness of the demand for inputs in
downstream processing is of same magnitude over the types of inputs. This ensures that the feedback
loop is not explosive.
2.2.1 Aggregate demand for pollution
The indicator of interest throughout the study is certainly the aggregate demand for pollution
emission. By defining aggregate demand
as
∬
and taking the Marshallian demand for pollutions (16) and (25) into account,
(
is
)
(
(
)(
11
)
(
)(
)
)
(
(
)
(
[
).
/
]
(27)
)
The second equality is obtained by considering (26), whereas the last equality is derived with the use of
PPI. Note that the demand for pollution is increasing with the scale of production and is decreasing with
the price of pollution. This is largely in line with the standard conjecture (Copeland and Taylor, 2003).
2.2.2 Threshold profitability that induces successful clean technology innovation
The total cost of production for an upstream firm takes the form
where
,
denotes the fixed cost in industries , which may comprise R&D cost, technical barrier, etc.
For the sake of simplicity without implication, we assume that fixed cost in dirty cost is nil,
, and
the total cost is identical across firms . As price is a markup over the marginal cost,
( ⁄(
))
, Eq. (21) can be rewritten as
.( ⁄(
))
/ , which gives
us the total revenue
(.
/
(
)
)
(.
/(
))
The second equality is obtained in conjunction with Eq. (24). The expected profit for all firms in
industries is then given by
{∑
(
)}
(
)(
(
.
where
/(
)
)
(28)
)
denotes the subjective discount rate. To induce resource allocation toward clean technology,
the expected profit should be at least as large as the expected profit for using dirty technology. In other
words, ̅
, giving us
12
̅
(
) *
(
)
+
(29)
The probability of a successful innovation in clean technology can be increased when the “profit
premium” in clean industries rises or when
falls.
2.2.3 Can a rise in pollution tax reduce aggregate pollution emission?
The answer is supposed to be unambiguous: higher emission tax disincentivizes the use of
pollution-intensive materials to reduce pollution emission in production. The overall emission intensity
and hence pollution will decline. This is conventionally dubbed the technique effect (Grossman and
Krueger, 1995; Copeland and Taylor, 1994, 2003). However, in a model with directed technical change
that is adversely associated with pollution tax, the answer is no longer so straightforward. A higher
pollution tax that increases unit variable cost erodes the expected profitability of investing in clean
technology more than proportionally compared with dirty technology, directing resources away from
clean technology. With a decreasing supply of clean inputs, the resultant higher price of clean inputs
will induce a shift in inputs composition of downstream production toward the cheaper dirtier inputs. As
a consequence, the overall emission intensity and pollution now rise.
The question is which effect dominates?
PROPOSITION 1 (pollution tax, directed technical change, and emission)
(i)
An increase in pollution tax on upstream activities will produce a technique effect and
directed technical change (DTC) effect. The former reduces pollution through reducing the
demand for dirty inputs, whereas the latter increases pollution through reducing the supply
of clean inputs.
(ii)
When technical change is elastic to change in expected profitability, in which the pollution
tax has an influence, a DTC effect dominates the technique effect, meaning that an
increase in pollution tax on upstream activities increases aggregate pollution on net.
Proof. (i) Differentiate
(27) against
gives us
13
.
⏟
⏟
/.
(30)
/
where
(
)
(
[
(
̅ ))
(
(
(
since
(ii)
)(
)
)(
(32)
)
(33)
if and only if |(
)
(
)
̅ ))
(
(
(
((
).
)
/
) (
)|
)(
)|, indicating that the technique effect dominates the DTC effect, which
)(
only
(
(31)
]
.
⁄
can
(
/
)
)(
and
|(
).
be
true
)
if
(
̅ ))
((
̅ )) (
if
⁄
)
inelastic
(
(
holds true, and
is
change
in
,
)|
) (
|(
)(
that
is
. In other words, the reverse
)
is elastic to change in
)
)
to
)
in that |((
(
)(
(
)|.
The role of directed technical change in the relationship between pollution emission and tax
can be illustrated by a four-dimensional diagram (see Figure 1). The first dimension located at the
northwest of Figure 1 depicts the interaction between aggregate pollution emission and directed
technical change in clean technology (Eq. (33)), designated
curves. A faster growth in clean
technology driven by successful innovation will supply cheap clean inputs for downstream processing,
of which the cleaner outputs will be used as materials for upstream production. As a result, aggregate
pollution emission falls. The
curve thus slopes downward. In the absence of directed technical
14
change, the curve slopes vertically. Second, the downward-sloping
curve in the southwest of Figure
1 illustrates the conventional technique effect (Eq. (31)): a high pollution tax directs the demand for
resources toward cleaner industries. Third, southeast of Figure 1 simply illustrates Eq. (15), where
increasing pollution tax on upstream activities increases the upstream unit variable cost at a decreasing
rate.
Last but not least, the northeast dimension illustrates the equilibrium of
on the probabilities (7) and (8) and expected profit (28),
*
+. This relationship is indicated by the
proportional to
(
slopes steeper than
)(
)
without implication on the results, only the
. Based
is adversely proportional to
for
schedule. Meanwhile, based on (15),
. This relationship is represented by
schedule, whereas
and
slopes flatter than
is
schedule. Note that
1.
To keep the figure clean
curve is exihibited.
[INSERT FIGURE 1 HERE]
Suppose the government increases the pollution tax on upstream activities from
causing the unit variable cost to rise from
emission to fall from
remains at
to
to
to
,
on the one hand, and the aggregate pollution
on the other hand. In the absence of directed technical change, where
, this will be the end of narrative. Points
over four dimensions connected by the
rectangular grey dotted lines depict the equilibrium. However, in an environment with technical change
that is endogenous to the state of the economy, rising unit variable cost makes innovation in clean
technology less profitable and trickier. The growing pace of clean technology slows down from
to
along
curve.
curve, which has also increased unit variable cost in upstream production along
jumps to
, unit variable cost increases from
to
. The resulting price hike and fewer supply
of clean inputs redirect resources toward dirty inputs. The negating directed technical change effect
)
The proof is straightforward. Suppose
slopes flatter than
schedule. This means -(
(
)(
), which implies
).
)
(
)(
As
, then (
)(
, implying that is smaller
than 2 or a price markup that exceeds 200%, which cannot be true for a monopolistically competitive market. Only when
), which means a steeper
(
)(
schedule, the system exhibits stable dynamics. To prove the
* +. As
⁄
⁄
latter hypothesis, differentiate
against
for
,we obtain
.
1
15
dominates the positive technique effect of an increase in pollution tax, contributing to deterioration in
aggregate pollution emission to
.
Of course, this is true only when the technical change is elastic to the change in the expected
profitability. Figure 1 also depicts the case of state-inelastic technical change (the flatter, thinner
curve). It can be easily seen that the technique effect of
dominates the DTC effect
,
reviving the conventional wisdom that increasing tax reduces pollution emissions.
2.3. Emission intensity cap as instrument
Recall the pollution emission (2) and (9). Suppose now an emission intensity cap (cap
henceforth) is imposed in such a way that
assumed to be fixed at ̅
and
+ if
*
⁄̅
̅
̅
⁄
(
⁄̅
, where the cap is
identically across good , for
)
*
+
. For the sake of simplicity, we assume the same cap on both clean and dirty
upstream industries across good , ̅
̅ , without implications on the assumptions that pollution
intensity and abatement cost are higher in dirty industries,
and
. By not paying
explicitly for using “pollution services”, we have to rewrite upstream firm ’s cost minimization problem
as minimizing
Denoting
subject to the production function (10) and pollution emission (9).
as the unit variable cost and
as the effective shadow price of the cap (see
Fischer and Springborn, 2011), the first order conditions read
(
)
⁄
⁄
[(
⁄
(
[(
)(
)(
)
)
(
(
)(
)(
)
)
⁄
⁄
(34)
]
(35)
]
(36)
)
In conjunction with (10), (34) and (35) allow us to derive firm ’s unit variable cost in the form
(
)
(
)
(
)
(
)
.∫
/ .∫
16
/
(
)
(
)
̅
(37)
which gives us
(
)
(
)
(
)
(
)
By means of wage-material price ratio
price ratio
⁄
.
)⁄
(
.∫
⁄
(
/ .∫
.
⁄
(
/
)⁄ (
(
)
(
)
̅
(38)
)/ and wage-constraint
⁄
)/, as in the case of pollution tax, Marshallian
demand functions are derived as follows:
(39)
⁄
(
)
(40)
⁄
(41)
⁄
That makes Eq. (39) under a cap regime different from its counterpart (17) under a tax regime
in that the directed technical change in upstream activities that indirectly reduces unit variable cost and
thus the unit price of downstream output due to cheaper upstream input prices that do not instigate
demand reshuffling toward clean materials. In other words, changes in the relative prices of upstream
goods do not lead to the internal propagation of an “environmental cleaning” effect. Paradoxically, in
contrast, as will be proved shortly, a successful technical change in clean technology under a cap
regime may conditionally worsen the pollution emission.
Turning to downstream production, the firm’s problem is also reformulated as minimizing
subject to production function (3) and pollution emission (2). The optimal
conditions read
.
/
.
where
and
⁄
.
/
0(
).
/
(
)
⁄
1,
*
+
(42)
(43)
/
, respectively, denote shadow price of budget constraint (which gives us unit
variable cost) and of pollution emission constraint (which gives us price of pollution). By the same
17
procedure, we can derive downstream unit variable cost, the implied price of pollution, optimal demand
for clean and dirty inputs, and Marshallian demand for total inputs and pollution services as
⁄(
(
⁄(
(
⁄
(
(44)
) ̅ )
(45)
) ̅ )
(46)
)
(47)
⁄
(48)
⁄
Last but not least, we proceed to find out the revenue function that determines the probability of
a success in clean innovation under a cap regime according to (29). As price is a markup of unit
variable cost identically applied across the firms,
.
/
, together with Eqs. (46) and (47),
the revenue function for an upstream firm in clean industry can be rewritten as
0.
/.
/1
Likewise, by summing Eq. (47) for
*
(
.
/.
(49)
+ and (48), we can obtain total demand for pollution as
/
)
(50)
2.3.1. Can tightening emission intensity cap reduce total pollution emission?
Before addressing this question, we first take stock of the relationship between directed
technical change and pollution emission under an emission intensity cap regime.
PROPOSITION 2 (Directed technical change and pollution). A successful favorable technical
change in clean technology deteriorates total pollution emission if the clean inputs account for a small
fraction in downstream production and dirty industries are not too pollution-intensive compared with
clean industries, given the emission intensity cap and a reasonable price markup.
Proof. (i) By the use of Eqs. (37), (38) and (42), we rewrite Eq. (50) as
18
(
̅
.
/
)
.
(
(
)(
)
against
into
)
(51)
. /
/
As such, we can decompose the differentiation of
.
/.
/,
where
(
)
(
)(
(
(
(
)
)(
(
if
(52)
)
(53)
)
(54)
)
(
Eqs. (52) to (54) combined yield
⁄
)
(
).
/
)
(
(
(
).
⁄
)
and
condition holds true if and only if
. As
)(
, for a price markup of 20% or less (
and (
⁄
)
)) .
(
) , or
(
(
/
)
), this
.
The intuition is straightforward. Suppose there is a successful innovation in clean technologies
that contributes to industrial expansion and reduction in unit price of clean inputs and that emission
intensity is bounded at the cap constraint,
in that
̅ . Expansion in clean industry implies a fall in
̅ , allowing abundant capacity to pollute (in absolute term) from clean industry. Hence,
the substitution of clean inputs for dirty inputs in downstream production would contribute to pollution
emission if the pollution intensity of clean inputs is not too different from dirty inputs (
).
Such an effect would be intensified if the initial fraction of clean inputs in production is small
((
⁄
)
), which allows cost-minimizing downstream firms to increase the use of “not-so-
clean" clean inputs.
Turning to the relationship between cap and pollution, we propose that
19
PROPOSITION 3 (Emission intensity cap and pollution). A tightening emission intensity cap
always reduces total pollution emission.
Proof. Partially differentiating (54) against ̅ yields
̅
(
(
̅
.
̅
).
/
(55)
)
(56)
/
̅
which, together with Eqs. (52) and (54), gives us total differentiation of
̅
where
.
⏟
̅
⏟
̅
⁄
(
(
if and only if
̅
/.
this condition is always met, implying that
/.
).
/
(
̅
̅
/
)
).
⁄
against ̅ in the form
/
. As
and .
/
,
always holds true.
Figure 2 neatly illustrates the technique effect and directed technical change effect of a
decrease in intensity cap. Specifically, the northwest quadrant illustrates the effect of a directed
technical change in pollution emission as of Eq. (52), and the left lower quadrant illustrates technique
effect of a change in intensity cap as of Eq. (55). The lower right quadrant depicts Eq. (56) regarding
the relationship between unit variable cost and cap, and lastly, the northeast quadrant shows the
equilibrium of
and
.
[INSERT FIGURE 2 HERE]
Consider a reduction in the cap from ̅ to ̅ . Smaller polluting capacity increases the
(shadow) price of pollution and unit variable cost from
to
, forcing the cost-minimizing firms to
restrain the emission. Given the technology level, total emission drops from
to
, the technique
effect. We know what happens next. Rising cost makes innovation in the costly clean technology
unprofitable and less likely to succeed. The resulting slowdown in the clean technological growth rate
reduces its level from
to
along the
curve, which further increases unit the variable cost while
20
reducing the emission from
to
given the cap constraint ̅ . This reduction is thus attributed to
directed technical change effect.
2.4. Effective environmental policy instrument: a partial-equilibrium analysis
Back to the main question of this paper: is a pollution tax or emission intensity cap more effective in
reducing demand for pollution? We address this question by asking a slightly different question. That is,
to reduce an identical amount of total demand for pollution, which instrument requires the minimal
change?
PROPOSITION 4 (Tax on downstream, cap on upstream) A pollution emission tax on
downstream production is more effective as a tool than a tax on upstream production in reducing
aggregate pollution emission, given the level of clean technology, whereas an emission intensity cap on
upstream production is more effective than a cap on downstream production.
Proof. As
⁄
(
)[
(
).
/
and
]
⁄
, relative changes in tax on downstream and upstream production, reads
.
/ .
(
⁄
(
/(
).
)
and initial
if
and only if .
possible
(
).
/
that approaches
/
) . For the assumptions of
,
, given the same magnitude of
).
/
)
, which can always hold true if (
⁄
)
/(
(
, irrespective of the value of
, and
,
,
,
is
meaning
due to lower
.
By the same token, relative changes in intensity cap on downstream and upstream production,
given the magnitude of
̅
̅
,
̅ ⁄
̅
, can be obtained as
if and only if
̅
̅
(
21
̅
.̅
(
(
/(
).
).
/
)
/
). For
, which after
rearranging gives us
, which causes (
.
(
.
(
(
)
⁄
/(
⁄
clean and dirty industries. In short,
)
̅ ⁄
)
⁄
/(
⁄
)
). This condition cannot hold true when
and
)
̅
, which contradicts the definition of
holds true as long as
.
Because a smaller change in tax on downstream production can reduce total pollution
emissions to an extent achievable only by a larger change in tax on upstream production, we thus
argue that taxing the downstream activities is a more effective choice. The intuition is as follows. By
imposing a pollution tax on consumer goods that raises unit price, the quantity demanded falls. While
by itself a contraction in downstream production reduces the need for pollution services, more
importantly, based on the model, it indeed contributes to a more than proportional decrease in the
demand for pollution-intensive dirty upstream inputs. Cleaner downstream outputs that go back to
upstream processing as input further reduce pollution emission. An input-output structure thus
multiplies the demand shock of a small increase in pollution tax at downstream production through
backward linkages.
Suppose now a tax is imposed on the use of pollution services for upstream and not downstream
production. It is true to claim that the tax tilts the use of factors toward cleaner materials. However, this
favorable technique effect in the upstream production can be moderated or even offset by two defying
forces in the downstream. First, alongside the Cobb-Douglas production mode, one can reasonably
conjecture an incomplete pass-through of the rising cost of upstream production into the unit price of
downstream output. As a result of an incomplete pass-through, market demand for downstream output
remains largely unscratched, which, in turn, implies a sustaining demand for upstream materials,
including the dirty one. This is the vertical linkage effect. With the assumption of
, the
pollution-reducing effect of a tax on upstream pollution evaporates throughout the stages of production.
In other words, the input-output structure has muted the supply shock of an equivalent increase in the
pollution tax at upstream production through forward linkage.
22
Second, as aforementioned in Proposition 1, innovation in clean technology will slow down when
the expected profitability of this costly investment is eroded with rising tax burden. The resulting
reduction in the supply of clean inputs will cause its unit price to rise, directing downstream demand for
inputs toward the dirty industries. As a consequence, pollution emissions ironically deteriorate.
Turning to emission intensity cap, it works best by directly capping the most polluting industry. A
smaller cap simply implies reduction in demand for pollution. Imagine that a smaller cap is imposed on
downstream production. Given the assumption that downstream industry is not the most pollutionintensive, the cap has neither instigated significant contractionary impact on the aggregate demand for
pollution emission itself during the processing nor reduced downstream demand for the most pollutionintensive dirty inputs. Speaking differently, alongside the reasonable assumption that upstream industry
has the most polluting sector, the emission intensity cap on upstream use of pollution is the more
effective policy instrument.
In summary, in an input-output economy, an effective environmental policy mix requires a pricebased instrument for downstream activities and quantity-based instrument for upstream activities.
2.5. Marginal damage of pollution
To complete the analysis, we shift our attention to deriving the marginal damage of pollution.
Consider a representative household that offers laborer services to either upstream clean or dirty
industries. Let the probability of the household joining a clean industry be . The expected wage
compensation thus takes the form
(
)
. The household enjoys
satisfaction of spending and leisure but dislikes the suffer from environmental degradation. The
household’s utility function can be written as
{∑
where
(
(
)
)}
is the AR(1) preference shock; the parameter
the reciprocal wage elasticity of labor supply, and
23
denotes constant relative risk aversion;,
(57)
is
measures the magnitude of household’s
intolerance toward marginal disutility of pollution. The household works, receives a lump-sum
government transfer
financed by pollution tax income, and earns from past savings
to support
spending and saving. The household’s problem can thus be formulated as maximizing (57) subject to
the budget constraint. By deriving the first-order conditions and rearranging it, we obtain the relative
labor supply, the marginal rate of substitution between consumption and work, and the Euler
consumption function.
(
⁄
).
⁄
(58)
,
⁄
(
)
*
(
/
(59)
+
).
(60)
/
We make two assumptions to facilitate the computation of indirect utility function.
ASSUMPTION 1. Savings grow at the rate of interest rate,
.
ASSUMPTION 2. The household does not take a lump-sum tax transfer into account in utility
maximization.
With these assumptions, the budget constraint is simplified to
. Together with Eqs.
(58) and (59), we can obtain labor and consumption as a function of probability-based real wage index
⁄
(
(
where
)
* .
.
)
⁄
(
)
.
/.
/
(61)
/
/
(62)
(
).
/
.
+
Putting Eqs. (61) and (62) back into the utility function (57) with tedious simplifications gives us the
following indirect utility function:
(
(
)
0(
)(
1(
)
)(
)
)
. /
24
(63)
Following Copeland (2000) and Copeland and Taylor (2003), environmental policy is set at a
level that equates the marginal damage of pollution,
⁄
. Assume that the principle is applicable
identically across the stages of production. The equilibrium policy rule can then be written as
(
⁄
(
)
(64)
)
What Eq. (64) reminds us is that environmental quality is a normal good. Irrespective of household’s
attitude toward risk, a family growing wealthier becomes less willing to substitute pollution for income.
Upon greater demands for better environmental quality, a benevolent government has to increase the
pollution tax (or equivalently reduce targeted emission intensity cap) to reduce pollution emission.
Given the household’s income, the optimal policy response to a change in aggregate pollution
emission depends on . A household is indifferent to environmental degradation if
government does not respond to an increase in pollution emission,
⁄
, and the
. The household
becomes relatively uneasy with the worsening environmental quality when
, and the
government tightens the policy at a decreasing rate. However, once the household turns completely
intolerant with marginal disutility of pollution,
, the policy will be tightened at an increasing rate. In
short, conditional on the household’s tolerance toward marginal dissatisfaction with pollution, the policy
determines the supply of pollution.
With the conventional toolkits of marginal benefits and marginal damage of pollution, we can
now proceed to general equilibrium analysis of pollution emission when facing uncertainty in policy,
total factor productivity and taste.
3. Parameterization and calibration
Table 1 summarizes the values of parameters and shocks volatility used to quantify the model.
Overall, the values adopted are commonly found in the business cycle literature. For instance, in the
baseline calibration of the model’s parameters it is assumed that
, implying a subjective
discount rate of 4% per annum. It is also assumed that the household is risk averse (
25
) and has
decreasing marginal disutility of pollution (
). By assuming
, it provides a wage elasticity
of labor supply of 0.2 that falls in between the structural intensive margin estimates of 0.15-0.33 found
in Chetty (2011). The elasticity of substitution between varieties is set to equal 6 to give a price markup
of 20%. As for the shock persistence, it is assumed that all first-order autoregressive coefficients take a
value associated with a highly persistent shock. Following Fischer and Springborn (2011), pollution
emission as a share of production in the steady state is assumed equal to ̅
.
[INSERT TABLE 1 HERE]
4. In search of welfare-maximizing environmental policy
Through the partial equilibrium analysis, we learn qualitatively that a cap is more effective than
a tax as an instrument to curb upstream pollution over a reasonable range of parameters, whereas the
reverse holds true for reducing downstream pollution. Does this policy mix (price for downstream, cap
for upstream) hold in a stochastic environment? In this section, we probe deeper into the search of
optimal policy (mix) by quantifying the welfare implication of each choice in the face of supply, demand,
and policy uncertainty.
Instead of taking stock on the deadweight loss caused, we focus on the macroeconomic
implications of each policy choice. A welfare superior policy should be able to curb pollution emission
while not stirring macroeconomic volatilities. After all, how can an environmental policy claim to be
improving living standard if it comes at the expense of many ups and downs in material satisfaction and
employment? To address such welfare consideration, we derive a loss function that resembles the
second-order approximation to the utility function of the household in Eq. (57) when the economy is in
the neighborhood of an efficient steady state (see Gali, 2008). The derivation is detailed in the appendix.
By denoting ̂
. ̅ /, as the log deviation from steady state ̅ for a variable
, and ̂ as the
variability of deviation, losses in utility as a fraction of steady-state consumption can be expressed as
26
(
) ̂
,(
)(
(̅ )
)
,(
)̂
(
)̂ -
̅(
̅ ) ̂ (65)
where
denotes the polic regime. Based on this loss function (65), a welfare-maximizing policy
minimizes uncertainty in material consumptions, employments and suffers from environmental
degradation. In particular, we will consider four policy choices: a pure pollution emission tax, a pure
emission intensity cap (synchronized tax or cap on the production chains), a tax on downstream and a
cap on upstream, and last but not least, a tax on upstream with cap on downstream production.
The next step is to conduct a welfare comparison. By treating the pure pollution tax regime as
the baseline, we ask what is the welfare gain of adopting alternative regime? Let
welfare cost of adopting pure pollution tax regime instead of the alternative regimes
denote the
, which can be
defined as the fraction of consumption process in alternative regimes that a household is willing to give
up to be as well off when remaining under alternative policy regime as under pure tax regime, holding
the level of leisure and pollution constant,
can solve for
(
)
.(
)
/. Hence, we
in the spirit of Canzoneri et al. (2007).
(
)
.(
)
*(
)
+(
(
)
/
)
which can be rearranged as
(
)(
(
)
)
(
)
to give us
(66)
27
with the assumption that steady state consumption is identical across policy regimes. When losses of
utility of adopting alternative policy choice
(in absolute term) exceed losses under tax regime,
indicates welfare gain of adopting pollution tax. On the contrary,
indicates welfare
gain of choosing alternative policy choice over pollution tax.
4.1 Prices versus quantities or prices and quantities?
Table 2 reports the welfare performance under each policy choice in the face of different
stochastic environments. The values shown in the row of “Pure tax” are computed according to Eq. (65),
whereas the values shown in the rest of the rows are annualized welfare gain (in percentage) when
using alternative policy instruments compared with pollution emission tax according to Eq. (66). Based
on the findings of Table 2, we can now make four observations:
[INSERT TABLE 2 HERE]
1. Pure emission intensity cap is welfare superior to pure emission tax.
Interestingly, when a synchronized tax rate is applied throughout the vertical production linkage,
under no circumstances can this pure tax system be welfare dominant. The pure emission intensity cap,
however, is welfare superior if there are policy uncertainty and a large total factor productivity shock.
Why is an intensity cap better than a tax in terms of welfare performance? The answer can be found in
how these policies influence the relative prices and resource allocation. When an emission tax is
imposed, the relative prices between clean and dirty inputs and between inputs and labor services are
directly affected, triggering resource reallocations across sectors and factors, which, in turn, affects the
household’s decision on consumption, work, and pollution tolerance. An intensity cap, however, moves
the relative prices only when the cap is binding. Hence, whereas uncertainty in tax policy destabilizes
the relative prices immediately, varying the cap leaves no impact on the economy if the cap is not
binding. Despite the discrepancy in the underlying mechanism, our results echo the general findings in
the literature that a quantity-based instrument generates better welfare performance than a price-based
28
instrument (see for instance Mansur, 2013; Wirl, 2013; Karp and Zhang, 2012; Fischer and Springborn,
2011; and Angelopoulous et al., 2010).
2. Uncertainty in marginal benefit and damage of pollution matters for the welfare selection of
environmental policy.
The inverse demand functions of pollution of Eqs. (27) and (50), which take the form
), where
(
,
, and
denotes policy choice, policy shock, and a
vector of prices, respectively, can actually be viewed as the marginal benefit of pollution. It is obvious
that stochastic TFP, preference, and policy shocks create uncertainty in marginal benefit of pollution.
On
the
other
(
hand,
Eq.
(64)
captures
the
marginal
damage
of
pollution,
). It is evident that TFP and policy shocks are common sources of
disturbances for both marginal benefit and damage, whereas preference shock is unique to marginal
benefit of production.
The fourth and fifth vertical panels of Table 2 reveal that the choice of welfare-maximizing
policy depends on the source of uncertainty. An intensity cap is welfare superior to an emission tax
when policymakers are confronted with large TFP shock that creates uncertainty to both marginal
benefit and damage. Emission tax is ineffective simply because the persistent TFP progress neutralizes
the emission tax incentive in directing resources toward clean industries. At the same time, the
unfavorable price effect of tax mutes the favorable cost-saving effect of TFP shock toward households.
In contrast, opting for intensity cap is welfare-maximizing because the cap is unbinding when
TFP-driven expansion in clean outputs reduces the emission as a share of production and will remain
unbinding as long as the reduction in intensity cap does not outpace the decline in the share of pollution
emission. As a consequence, while intensity cap preserves the favorable changes in relative prices and
hence resource allocation effect of TFP progress, it also attains its goal in curbing pollution emission.
However, when the marginal benefit of pollution is highly uncertain because of large household
preference shocks, a pure intensity cap is potentially damaging, especially if household tolerance for
29
pollution is under-estimated. The binding intensity cap will cause high macro volatilities under such
circumstances without necessarily slowing down emission. According to Table 2, both pure emission
tax and hybrid instruments that call for intensity cap on downstream production and emission tax on
upstream activities seem equally warranted.
Here is the intuition. Whereas a pure cap constraint is welfare costly in the face of large
demand shock, an emission tax that instigates changes in relative prices becomes effective in directing
the increasing demand toward clean products, supporting clean technology innovation. On the other
hand, by also taxing upstream activities, resources are reallocated to clean industries, as a tax has a
greater cost impact on dirty than clean industries. This effort can be further facilitated by capping
pollution intensity of downstream production without provoking macroeconomic volatilities, as the
intensity cap turns unbinding under the circumstance of expanding downstream production.
This observation brings us to the classic Stavins (1996), which argues against the literature
then that only uncertainty in marginal cost of environmental protection (which means marginal benefit of
pollution in our context) matters. Stavins (1996) argues that uncertainty in benefit of environmental
protection (read: marginal damage of pollution in our context) also matters in the choice of optimal
instrument when the marginal benefit and cost are positively correlated. Such dependence tends to
favor the quantity instrument. Turning to our context, if only uncertainty in marginal benefit of pollution
due to stochastic preference shock is present, the findings are in line with the past literature since
Weitzman (1974) that a price instrument is preferred. However, in the presence of a common source of
uncertainty in both marginal benefit and damage, which resembles a complete positive correlation in
Stavins (1996), then a quantity instrument is clearly welfare dominant. It is less likely in our point of view
that the role of TFP will diminish in the future.
3. Public support of clean technology innovation improves the welfare performance of emission
tax but is not critical to the optimal choice of policy.
30
Recall the discussion in Proposition 1 that an emission tax may slow down innovation in clean
technologies, holding other factors constant, as a tax erodes the expected profitability of innovation,
which ends up ironically increasing pollution emission. What if the emission tax revenue collected is
used to support the innovation in clean technology in the sense of reducing the sunk cost of investment,
i.e., setting up a laboratory and purchase of expensive equipment?
As another experiment, it is assumed that a pollution tax revenue is channeled to funding
innovation instead of transfer to a household,
, so that private funded fixed cost in
investment is zero. The simulation shown in the last main column of Table 2 shows that a subsidy on
clean technology innovation does improve the welfare performance of emission tax policy, in the sense
that the welfare superiority of a non-pure tax policy shrinks from the range of 130 and 135 to 11 and 19.
Government financial support secures the expected profitability of innovation, enhancing the
likelihood of a successful innovation. The consequential increasing supply of clean inputs with lower
unit price shall direct downstream demand for inputs toward the clean one. As such, together with
subsidy emission tax, it will be more effective in reducing pollution emission and accommodating
resource allocations originated in TFP progress. This finding corroborates an earlier work of Carraro
and Siniscalco (1994), who argued for a joint implementation of tax policy and innovation subsidy to
attain an emission target without decreasing the output.
4. A hybrid instrument that caps on the upstream and taxes on downstream source of pollution
has the best welfare performance on average over a reasonable range of parameter values and
uncertainty.
Although by encompassing directed technical change in the model, one does not overturn the
finding that quantity-based instrument remains welfare superior when uncertainty in marginal benefit
and damage of pollution are correlated (due to the presence of TFP shock), there is a novel finding that
a significant reduction in pollution emission at no expense of macro volatilities can also be achieved by
capping the upstream while taxing the downstream productions.
31
The underpinning mechanism can be found in the discussion of Proposition 4. What is new
here is that, as Table 2 has shown, capping the downstream while taxing the upstream has the largest
welfare gain among the alternatives compared with pure emission tax choice when all but policy
uncertainty is present. It performs the best when innovation in clean technology is subsidized and only
the marginal damage of pollution is uncertain (due to preference shock), and it is almost as welfare
maximizing as the pure cap system in the presence of a correlated uncertainty in marginal benefit and
damage of pollution (due to TFP shock).
What would be more interesting is if this inference is robust against several important
qualifications. Recall that in Proposition 1, we suggest that an emission tax can be polluting if directed
technical change is very elastic to change in environmental policy, indicating that emission tax may not
be appropriate for production stage at which innovation takes place. Would the results be overturned if
directed technical change is inelastic? Thus, we first inspect to what extent our findings are subject to
the elasticity of technical change to environmental policy. The last major column in Table 3 conforms
the welfare dominance of a hybrid system over pure emission tax policy, irrespective of the elasticity of
clean technology innovation to the state of economy.
Another important consideration is household attitudes toward marginal disutility of pollution. If
a household is indifferent to or not so intolerant to environmental degradation,
, what concerns
the household is material well-being and employment, not the quality of environment. A pure tax system
that alters relative prices and creates macro volatilities is not preferred compared with an intensity cap
that matters for macroeconomic stability only when it binds. It is thus not surprising that intensity cap
welfare dominates pure emission tax and other policy choices that involve emission tax for the cases of
and
, as shown in Table 3. However, the welfare superiority of our preferred hybrid
system resurges once households are highly intolerant to marginal dissatisfaction of pollution,
[INSERT TABLE 3 HERE]
32
.
5. Conclusion
This paper revisits the long-standing debate on whether price or quantity instrument is welfare
superior through the lens of dynamic stochastic general equilibrium model that encompasses an
upstream-downstream linkage and endogenous technical change in clean technology innovation. The
welfare performance of environmental policy of interest is evaluated based on the welfare criteria
derived from the model that resembles a quadratic approximation to household’s utility that values
environmental quality alongside material well-being and employment. The advantage of doing so is
obvious: a welfare-maximizing environmental policy shall be reducing pollution emission without risking
macroeconomic stability that could dwarf the marginal benefits from emission reduction.
Overall, we argue that price and quantity instruments, not prices versus quantities, are needed
to clean the environment without trading off of macroeconomic stability. We also argue that upstream
and downstream regulations, not upstream versus downstream, are both needed. By taxing the
downstream final consumption, regulators can reduce the pollution emission in the upstream value
chains. Furthermore, the size of dirty industries can be reduced if the tax revenue collected is used to
subsidize clean technology innovation. At the same time, regulating upstream activities with an
emission intensity target, while fostering the effort of emission reduction, creates a stable
macroeconomic environment conducive for clean technology innovation.
Our results especially hold firm when policy uncertainty is absent, households are highly
intolerant to marginal disutility of pollution, and clean technology innovation is funded in the face of
large preference shock, irrespective of the responsiveness of innovation to the state of the economy. It
is certainly noteworthy to examine the robustness of the results in future work in an open-economy
model that allows for production fragmentation and foreign direct investment.
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34
Table 1
Parameters and shocks
Shock persistence
Upstream TFP
Downstream TFP
Preference
Policy
Parameters
Share of materials in upstream production
Subjective discount rate (quarterly)
Wage elasticity of labor supply
Risk aversion coefficient
Elasticity of substitution between varieties
Intolerance toward marginal disutility of pollution
Pollution intensity
Upstream clean industries
Upstream dirty industries
Downstream
Steady states
Directed technical change growth rate (quarterly)
Interest rate (quarterly)
Probability of working in clean industries
Probability of successful clean tech. innovation
Emission as a share of production
Pollution tax
Level of total factor productivity
Standard deviation of shocks
Upstream TFP
Downstream TFP
Preference
Policy
0.8
0.8
0.8
0.8
0.4
0.99
5
2
6
1.5
0.1
0.8
0.5
0.0125
0.015
0.5
0.5
0.0745
0.10
1
0.014
0.014
0.01
0.05
Table 2
Welfare evaluation of alternative policy choices
No policy uncertainty2
Pure emission
tax1
All shocks
-0.0256
Baseline
-0.0034
Large
TFP
shock3
-0.3576
Large
demand
shock4
-0.0069
Subsidy on R&D5
Large
TFP
shock
-0.0681
Welfare gain of adopting alternative policy choices (%)
1.20
134.36
-2.00
18.56
Large
demand
shock
-0.02
Pure intensity cap
8.88
Tax for downstream,
cap for upstream
7.28
1.24
133.48
-2.44
16.68
4.72
Tax for upstream,
cap for downstream
8.48
1.20
130.64
0.28
11.28
3.16
35
3.24
Notes: Welfare-dominant policy choice is bolded.
1The number indicates losses of utility as a fraction of steady-state consumption
2Standard deviation of policy shock is assumed equal to zero.
3Standard deviation of both upstream and downstream total factor productivity shock is assumed to be ten times larger than
the baseline calibration shown in Table 1.
4Standard deviation of household preference shock is assumed to be ten times larger than the baseline calibration shown in
Table 1.
5Pollution emission tax income is used to subsidize clean technology innovation in terms of reducing the fixed cost of clean
industries. For simplicy, it is assumed that private funded fixed cost becomes zero.
Table 3
Sensitivity analysis
Tolerance toward marginal disutility of pollution
Not too
Highly
Indifferent
intolerant
Intolerant
Pure emission tax
Baseline
-0.0065
Pure intensity cap
Policy elasticity of DTC
Inelastic
Elastic
-0.0014
-0.0012
-0.0031
-0.1586
Welfare gain of adopting alternative policy choices (%)
-0.0037
1.2
0.44
0.28
0.96
0.4
0.2
Tax for downstream,
cap for upstream
1.24
0.28
0.16
1.12
0.572
0.28
Tax for upstream,
cap for downstream
1.2
0.28
-10.84
0.76
0.52
-0.64
Notes: Welfare-dominant policy choice is bolded.
36
0
Figure 1. Higher pollution tax on upstream activities can increase aggregate pollution emission in the presence of elastic directed technical change
37
0
̅
̅
̅
Figure 2. Lower emission intensity cap on upstream activities decreases aggregate pollution emission
38
Appendix: Derivation of second-order approximation to utility
39