Prices vs. quantities: What s new? A perspective of input-output DSGE model with directed technical change and uncertainty

Transcription

1 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, Kampar, Perak, Malaysia. Tel: ; Fax:. addresses: wongcy@utar.edu.my (C.-Y. Wong), engyk@utar.edu.my (Y.-K Eng) 1

2 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-co2- per-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

3 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

4 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

5 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 N- good 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

6 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 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: ( ) 0 ( ) ( ) 1 ( ) (1) where is the first-order autoregressive exogenous total factor productivity (TFP) shock in downstream industry, and ( ) is the elasticity of substitution between two inputs. The two inputs are complements when and substitutes when. Following Copeland and Taylor (2003), we model pollution emission in downstream production as ( ) (2) 6

7 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. / (4) where 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 transform downstream outputs as materials for next-period production at a cost of purchase and units of the final goods. The cost is normalized to for * +. The upstream firms combine a continuum of type-specific materials of varying qualities and labor according to Cobb-Douglas production technology. ( ) ( ) (5) where 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. / for industry * + evolves over time according to the following difference equation ( ), where indicates the growth of average quality, and refers to the probability of successful innovation in sector at time. We assume that the probability of successful innovation in clean technology depends on the expected 7

8 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 increases with the difference between and. The probability of a success in clean technology 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. / (9) where and, 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

9 . 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

10 ( )( ) (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. derived as 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 ( ( ) ) (19) (20) where denotes unit variable cost of downstream production, and ( 0 ( ) ( ) ( ) 1 ) 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

11 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 ( ), the Marshallian demand for and 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 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

12 ( ( ) [ ( ). / ] ) (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) 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 { ( )} ( ) ( ( ) ). / ( ) (28) where 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

13 ( ) * ( ) + (29) The probability of a successful innovation in clean technology can be increased when the profit premium in clean industries rises or when falls 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

14 . /. / (30) where ( ) [ ( ). / ] (31) ( ( )) ( ) ( ) (32) ( )( )( )( ) (33) since and. (ii) if and only if ( ) ( ( ). / ) ( ) ( ( )) (( ) ) ( )( )( ), indicating that the technique effect dominates the DTC effect, which can only be true if is inelastic to change in, that is ( ) ( ( )) ( ). In other words, the reverse holds true, and if is elastic to change in 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

15 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 and. Based on the probabilities (7) and (8) and expected profit (28), is adversely proportional to for * +. This relationship is indicated by the schedule. Meanwhile, based on (15), is proportional to ( )( ). This relationship is represented by schedule. Note that slopes steeper than schedule, whereas slopes flatter than 1. To keep the figure clean without implication on the results, only the curve is exihibited. [INSERT FIGURE 1 HERE] Suppose the government increases the pollution tax on upstream activities from to, causing the unit variable cost to rise from to on the one hand, and the aggregate pollution emission to fall from to on the other hand. In the absence of directed technical change, where remains at, 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, which has also increased unit variable cost in upstream production along curve. 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 1 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 latter hypothesis, differentiate against for * +. As,we obtain. 15

16 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 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, where the cap is assumed to be fixed at ( ) identically across good, for * + and * + if. 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 subject to the production function (10) and pollution emission (9). Denoting 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 ( ) ( ) ( ) ( ). /. / ( ) ( ) (37) 16

17 which gives us ( ) ( ) ( ) ( ). /. / ( ) ( ) (38) By means of wage-material price ratio. ( ) ( )/ and wage-constraint price ratio. ( ) ( )/, 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. conditions read Turning to downstream production, the firm s problem is also reformulated as minimizing subject to production function (3) and pollution emission (2). The optimal. /. / 0( ). / ( ) 1, * + (42). / (43) where and, 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

18 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 (49) Likewise, by summing Eq. (47) for * + and (48), we can obtain total demand for pollution as (. /. / ) (50) 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

19 ( ). /. / ( ( ) ( ) ). / (51) As such, we can decompose the differentiation of against into. /. /, where ( ) ( ( ) ( ) ) (52) ( )( ) ( ) (53) ( ) (54) Eqs. (52) to (54) combined yield ( ) ( ( ). / ( )). if ( ). / ( ), or ( )( ). As ( ) and, for a price markup of 20% or less ( ), this condition holds true if and only if and ( ). 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,. Expansion in clean industry implies a fall in in that, 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-soclean" clean inputs. Turning to the relationship between cap and pollution, we propose that 19

20 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 against in the form. /. /. / ( ( ). / ) where if and only if ( ). /. As and. /, this condition is always met, implying that 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

21 reducing the emission from to given the cap constraint. This reduction is thus attributed to directed technical change effect 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. /. / ( ( ). / ). For the assumptions of,, ( ) and initial, given the same magnitude of, is possible if and only if. / ( ( ). / ), meaning ( ). /, which can always hold true if ( ) due to lower that approaches, irrespective of the value of, and. By the same token, relative changes in intensity cap on downstream and upstream production, given the magnitude of, can be obtained as. / ( ( ). / ). For, if and only if ( ( ). / ), which after 21

22 rearranging gives us (. /( ) ( ) ). This condition cannot hold true when, which causes (. /( ) ( ) ) and, which contradicts the definition of clean and dirty industries. In short, 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

23 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 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 { ( ( ) )} (57) where is the AR(1) preference shock; the parameter denotes constant relative risk aversion;, is the reciprocal wage elasticity of labor supply, and measures the magnitude of household s 23

24 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 ( ) ( ). /. / (61) ( ). / (62) where *. / ( ). / +. Putting Eqs. (61) and (62) back into the utility function (57) with tedious simplifications gives us the following indirect utility function: ( )( ) ( ) 0 ( )( ) 1 ( ). / (63) 24

25 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, and the government does not respond to an increase in pollution emission,. 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 ( ) and has 25

26 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 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

27 ,( ) ( )( ),( ) ( ) ( ) - ( ) - (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 denote the welfare cost of adopting pure pollution tax regime instead of the alternative regimes, 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, ( ).( ) /. Hence, we can solve for in the spirit of Canzoneri et al. (2007). ( ).( ) / *( ) + ( ( ) ) which can be rearranged as ( ) ( ( ) ) ( ) to give us (66) 27

28 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

29 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

30 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

31 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

32 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

33 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. References Acemoglu, D., Aghion, P., Bursztyn, L., Hemous, D. (2012). The environment and directed techical change. American Economic Review 102(1),

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35 Table 1 Parameters and shocks Shock persistence Upstream TFP 0.8 Downstream TFP 0.8 Preference 0.8 Policy 0.8 Parameters Share of materials in upstream production 0.4 Subjective discount rate (quarterly) 0.99 Wage elasticity of labor supply 5 Risk aversion coefficient 2 Elasticity of substitution between varieties 6 Intolerance toward marginal disutility of pollution 1.5 Pollution intensity Upstream clean industries 0.1 Upstream dirty industries 0.8 Downstream 0.5 Steady states Directed technical change growth rate (quarterly) Interest rate (quarterly) Probability of working in clean industries 0.5 Probability of successful clean tech. innovation 0.5 Emission as a share of production Pollution tax 0.10 Level of total factor productivity 1 Standard deviation of shocks Upstream TFP Downstream TFP Preference 0.01 Policy 0.05 Table 2 Welfare evaluation of alternative policy choices No policy uncertainty 2 Subsidy on R&D 5 Large TFP shock 3 35 Large demand shock 4 Large TFP shock Large demand shock All shocks Baseline Pure emission tax Welfare gain of adopting alternative policy choices (%) Pure intensity cap Tax for downstream, cap for upstream Tax for upstream, cap for downstream

36 Notes: Welfare-dominant policy choice is bolded. 1 The number indicates losses of utility as a fraction of steady-state consumption 2 Standard deviation of policy shock is assumed equal to zero. 3 Standard 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. 4 Standard deviation of household preference shock is assumed to be ten times larger than the baseline calibration shown in Table 1. 5 Pollution 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 Baseline Tolerance toward marginal disutility of pollution Policy elasticity of DTC Not too Highly Indifferent intolerant Intolerant Inelastic Elastic Pure emission tax Welfare gain of adopting alternative policy choices (%) Pure intensity cap Tax for downstream, cap for upstream Tax for upstream, cap for downstream Notes: Welfare-dominant policy choice is bolded

37 0 Figure 1. Higher pollution tax on upstream activities can increase aggregate pollution emission in the presence of elastic directed technical change 37