DOCTOR OF PHILOSOPHY IN ECONOMICS

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1 The External Costs of Air Pollution and the Environmental Impact of the Consumer in the U.S. Economy A Dissertation by H. Scott Matthews Master of Science, Economics, Carnegie Mellon University, Pittsburgh, 1996 Bachelor of Science, Computer Engineering and Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, 1992 Submitted in partial fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY IN ECONOMICS Graduate School of Industrial Administration Carnegie Mellon University Pittsburgh, PA March 1999 i

2 Abstract Despite many years of environmental regulation, significant levels of air pollution are generated by the provision of goods and services in the United States. In 1992, approximately $180 billion of such damages occurred in the U.S. To reduce environmental damage, analysis tools such as Life Cycle Assessment (LCA) have been developed to better understand the total impacts of products and processes. These tools consider the effects associated with raw materials extraction, component fabrication, assembly, delivery, use, and disposition. However, these methods are hindered by the boundary problems and circularities that exist. We propose a solution to the boundary problem, a Leontief input-output (IO) model augmented by environmental impact information to determine the direct and total supply chain effects resulting from the production of the 500 commodity sectors contained in the Department of Commerce's 1992 IO table. The model considers environmental impacts externally to the basic Leontief framework. Toward this effort, we have generated a substantial data set linking releases of criteria pollutants and greenhouse gases with manufacturing activities in each sector. The result is an assessment, rather than an inventory, of environmental effects. The total air pollution releases found for each commodity are combined with a range of environmental damage valuation studies to estimate the external costs of these activities. We consider both the most polluting commodity sectors per dollar of output, as well as the sectors generating the largest external costs. Our results include the consideration of indirect (supply chain) effects as opposed to simply the direct effects from producing commodities. The production of electricity generates 34 cents of external costs per dollar cost, but the average commodity generates less than 4 cents. The results are also combined with the Consumer and Producer Price Indices as well as the Consumer Expenditure Survey to determine the external costs associated with buying and selling commodities. The average dollar spent by consumers generates about 3 cents of external cost, while producers generate 5 to 9 cents. The results show that the average American household's spending generates roughly 40 tons of carbon dioxide equivalent releases per year. Finally, using our data set of current emissions, and the findings above, we consider the effects of various policies to reduce emissions, including command and control and market-based initiatives. Market-based initiatives are projected to save billions of dollars in expenditures if enacted for sulfur dioxide, nitrogen oxides, and volatile organic compounds. In addition, if new regulations were set to reduce external costs, significant improvements over current levels would result. i

3 Acknowledgements The work presented here is the result of input and encouragement from many people. First, the faculty associated with this thesis. Lester Lave filled my studies with strong words, practical advice, and reflective anecdotes that will serve me well in the future as an academic. Most importantly, he believed I could do this when many others, including myself, doubted it. Chris Hendrickson is the model researcher and administrator, and serving as his understudy for 2 years has taught me the costs and benefits of life itself. Francis McMichael shares my love of data, and constantly offered "what if"questions that kept me on track (the title of chapter 2 is a tribute to him). Dennis Epple was my original advisor as a Ph.D. student, and although our research paths diverged, he has always been there when I needed him most. Other people deserve special recognition as well. Noellette Conway-Schempf has been my big sister for 4 years, subtly nudging me in the right direction even when I did not realize I was off course. Arpad Horvath, Octavio Juarez, and Satish Joshi are the Gods of EIO-LCA, and none of my results would have been possible without their ongoing assistance. Bob Dalton of GSIA has been a guiding influence in my decision to teach economics, and teach it well and with all of my ability. Finally, I am grateful for support from the Environmental Protection Agency, National Science Foundation, and the Department of Energy. Equally important have been the people who have maintained my sanity over the last 5 years. They have been sources of friendship, relaxation, and inspiration. I specifically thank Andi Cangin, Pete and Terra Harllee, Greg Legowski, and John Lipinski. Last but not least, everyone associated with the perennial powerhouse GSIA Sand Gnats Softball Team. All of these people prove to me on a daily basis that no man is a failure who has friends. To Brother Pat Carney, who long ago opened my eyes to the mysteries of mathematics. I dedicate chapter 2 to him, and hope he recognizes that there is a necessary, but not sufficient, amount of math in all economics. Finally, to my family, who have made me proud with their support. Thank you to mom, dad, and Shawnna. And to Deanna, who by returning to school this year expedited my completion, and taught me all of the probability I ever needed-- by proving the odds that a guy like me would end up with someone as wonderful as her. ii

4 TABLE OF CONTENTS LIST OF TABLES AND FIGURES...IV CHAPTER 1: INTRODUCTION... 1 BASIS OF THE EIO-LCA MODEL... 2 CHAPTER 2: ON THE EQUIVALENCE OF ENVIRONMENTAL ANALYSIS VIA LEONTIEF AND EXTERNAL INPUT-OUTPUT METHODS... 7 CLASSIFICATION OF RESULTS IN AN INPUT-OUTPUT SYSTEM... 9 INCORPORATION OF ENVIRONMENTAL EFFECTS INTO INPUT-OUTPUT MODELS CHAPTER 3: AIR POLLUTION COSTS OF INDUSTRIAL ACTIVITY THE TOTAL COSTS OF MANUFACTURING: DIRECT AND INDIRECT EFFECTS DAMAGE VALUATION OF EMISSIONS EXTERNALITIES FROM COMMODITIES: THE US ECONOMY IN CHAPTER 4: GREEN INDICES AND THE ENVIRONMENTAL IMPACT OF THE AMERICAN CONSUMER A GREEN PRICE INDICATOR ENVIRONMENTAL IMPACTS OF THE AMERICAN CONSUMER CHAPTER 5: POLICIES TO REDUCE EXTERNAL COSTS OF AIR POLLUTION ALTERNATIVE EMISSIONS ABATEMENT POLICIES QUALITATIVE ANALYSIS OF POLICY OPTIONS CUMULATIVE COST COMPARISONS CHAPTER 6: CONCLUSIONS FURTHER WORK ON RELATED ISSUES SUMMARY AND CONTRIBUTIONS APPENDIX A: DETAILED DESCRIPTION OF THE CONSTRUCTION OF THE CONVENTIONAL POLLUTANTS DATA COMBINATION OF DATA SOURCES AND ADJUSTMENTS MADE APPENDIX B: A SUMMARY OF THE VALUATIONS DERIVED FROM THE 812 REPORT APPENDIX C: COMPLETE LISTING OF EXTERNAL COSTS AND PERCENTAGES APPENDIX D: DETAIL OF PRICE INDEX CALCULATIONS, CPI AND PPI iii

5 LIST OF TABLES AND FIGURES FIGURE 2-1: THE LAYOUT OF ADVANCED INPUT-OUTPUT MODELS... 7 TABLE 3-1: TOTAL U.S. EMISSIONS AND ESTIMATED EXTERNAL COSTS OF VARIOUS POLLUTANTS IN TABLE 3-2: TEN COMMODITY SECTORS WITH LARGEST PM EMISSIONS TABLE 3-3: SOCIAL DAMAGES PER METRIC TON OF SULFUR DIOXIDE AIR EMISSIONS TABLE 3-4: UNIT SOCIAL DAMAGE ESTIMATES FROM AIR EMISSIONS OF ENVIRONMENTAL EXTERNALITIES.. 25 TABLE 3-5: ESTIMATED EXTERNAL AIR POLLUTION DAMAGE FROM $100,000 OF PRODUCTION (IN DOLLARS) FROM 8 SAMPLE COMMODITY SECTORS (TOTALS MAY NOT SUM DUE TO ROUNDING) TABLE 3-6: THE TEN COMMODITY SECTORS WITH HIGHEST EXTERNAL AIR POLLUTION COST PERCENTAGES IN THE U.S. ECONOMY, TABLE 3-7: THE TEN COMMODITY SECTORS WITH HIGHEST TOTAL EXTERNAL AIR POLLUTION COSTS IN THE U.S. ECONOMY, TABLE 3-8: THE TOP PURCHASES ASSOCIATED WITH $100 MILLION OF DEMAND FOR EATING AND DRINKING ESTABLISHMENTS [ALL VALUES IN MILLIONS] TABLE 3-9: THE TOP CONTRIBUTING EXTERNAL COST SECTORS ASSOCIATED WITH $100 MILLION OF OUTPUT FROM EATING AND DRINKING ESTABLISHMENTS, IN MILLIONS OF DOLLARS (OR PERCENT) TABLE 4-1: SUMMARY OF RESULTS FROM INCORPORATING EXTERNAL COSTS INTO THE CONSUMER PRICE INDEX TABLE 4-2: SUMMARY OF RESULTS FROM INCORPORATING EXTERNAL COSTS INTO THE PRODUCER PRICE INDEX - CRUDE MATERIALS TABLE 4-3: SUMMARY OF RESULTS FROM INCORPORATING EXTERNAL COSTS INTO THE PRODUCER PRICE INDEX - FINISHED GOODS TABLE 4-4: SUMMARY OF ENVIRONMENTAL IMPACTS FOR EVERY $100 OF CONSUMER PURCHASES, BASED ON CONSUMER PRICE INDEX WEIGHTINGS TABLE 4-5: SUMMARY OF ENVIRONMENTAL IMPACTS PER HOUSEHOLD, 1992, BASED ON CONSUMER PRICE INDEX WEIGHTINGS TABLE 4-6: A COMPARISON OF GENERATED ESTIMATES OF HOUSEHOLD IMPACTS VERSUS GENERATED PER- HOUSEHOLD ESTIMATES TABLE 5-1: MARGINAL ABATEMENT COSTS PER TON FOR MANUFACTURING INDUSTRIES FIGURE 5-1: ABATEMENT COST FUNCTION FOR PETROLEUM REFINING TABLE 5-2: ADDITIONAL $/TON DATA USED IN ABATEMENT COST MODEL FIGURE 5-2: ABATEMENT COSTS PER TON FOR COMMAND AND MARKET-BASED SO2 POLICY FIGURE 5-3: ABATEMENT COSTS PER TON FOR COMMAND AND MARKET-BASED NOX POLICY FIGURE 5-4: ABATEMENT COSTS PER TON FOR COMMAND AND MARKET-BASED VOC POLICY TABLE 5-3: REDUCTION LEVELS NECESSARY TO REACH SOCIALLY OPTIMAL LEVELS TABLE 5-4: CUMULATIVE COST COMPARISON OF POLICY OPTIONS (MILLIONS) FIGURE 5-5: CUMULATIVE COSTS OF COMMAND AND MARKET-BASED VOC POLICIES TABLE A-1: AIRS REPORTING THRESHOLD REQUIREMENTS FOR FACILITIES, TABLE A-2: SIC CODE TO INPUT-OUTPUT CODES MAPPING TABLE A-3 - SUMMARY OF ADJUSTMENTS MADE BASED ON EMISSIONS TRENDS REPORT DATA TABLE A-4: FINAL ESTIMATES OF CARBON MONOXIDE (CO) EMISSIONS PER SECTOR, IN METRIC TONS TABLE A-5: FINAL ESTIMATES OF LEAD (PB) EMISSIONS PER SECTOR, IN METRIC TONS TABLE A-6: FINAL ESTIMATES OF NITROGEN DIOXIDE (NO 2 ) EMISSIONS PER SECTOR, IN METRIC TONS TABLE A-7: FINAL ESTIMATES OF PARTICULATE MATTER (PM10) EMISSIONS PER SECTOR, IN METRIC TONS TABLE A-8: FINAL ESTIMATES OF SULFUR DIOXIDE (SO 2 ) EMISSIONS PER SECTOR, IN METRIC TONS TABLE A-9: FINAL ESTIMATES OF VOLATILE ORGANIC COMPOUND (VOC) EMISSIONS PER SECTOR, IN METRIC TONS TABLE A-10: FINAL ESTIMATES OF GLOBAL WARMING POTENTIAL (GWP) EMISSIONS PER SECTOR, IN METRIC TONS TABLE B-1: PANEL REPRESENTATION OF SIMPLIFIED ESTIMATION OF HEALTH EFFECTS VALUATIONS FROM REDUCED FINE PARTICULATE MORTALITY, 1970 TO TABLE B-2: COMPARISON OF EPA 812 REPORT BENEFIT CATEGORY VALUATIONS AND SIMPLE ESTIMATES, IN 1990 DOLLARS iv

6 TABLE B-3: BREAKDOWN OF DAMAGES IN EPA 812 REPORT ($1990, SHORT TONS) TABLE B-4: EMISSION-FRACTION ADJUSTMENTS TO $/TON VALUES ($1990, SHORT TONS) TABLE C-1: EXTERNAL COST VALUES FOR 500 SECTORS, SORTED BY TOTAL DAMAGE (MEDIAN VALUATION) TABLE D-1: SUMMARY OF INCORPORATING EXTERNAL COSTS INTO THE CONSUMER PRICE INDEX TABLE D-2: SUMMARY OF INCORPORATING EXTERNAL COSTS INTO PPI - CRUDE MATERIALS TABLE D-3: SUMMARY OF INCORPORATING EXTERNAL COSTS INTO PPI - FINISHED GOODS v

7 Chapter 1: Introduction The Clean Air Act of 1970 and its amendments have sought to improve the quality of air in the United States by mandating reductions of major source pollutants. Even though this effort has made significant progress in meeting the goal of cleaner air, there are still significant emissions of air pollution in the United States. Aside from motor vehicle emissions, the primary source of emissions is industrial activity. At the same time, global initiatives to reduce greenhouse gases in the atmosphere have linked climatic effects with combustion of fossil fuels. The combination of national and global initiatives to reduce emissions has created an environment where pollution prevention has become a priority. Many businesses have accepted this fact and sought to reduce their environmental footprints. One of the results of such activities is the International Standards Organization (ISO) standards. ISO attempts to streamline corporate environmental management in the same way that ISO 9000 revolutionized quality management. In both cases, firms can improve their processes by systematically looking at the impacts generated by them. In undertaking this effort, they have examined their business practices to find places where there could be ecological improvements. One tool to support firm-level environmentally conscious decision-making is life cycle assessment (LCA). LCA is a systematic approach linking the product life cycle, from design to disposition, with the environmental impacts generated at each stage. This view of a product is intended to yield environmental improvement by revealing the complete environmental picture of a product, rather than just the emissions generated in the usual course of production by the manufacturer. LCA is useful beyond the scope of a manufacturer as well. Service providers, government agencies, and other interested parties can use such methods to consider the total impact of their global business activities. The primary drawback of LCA is the complexity of the problem in determining all of the impacts associated with a product over its life cycle. Further, boundaries need to be 1

8 drawn around the problem to limit the amount of time and effort spent quantifying the relevant impact measures. Although this detracts from the overall accuracy of the results, it is necessary to find any answer at all. Alternatives to standard LCA have surfaced that seek to change the ways problems are considered, and the results that are generated. One such alternative is presented here that solves the boundary problem. Basis of the EIO-LCA Model Leontief [36] proposed an input-output system where the transactions in an economy were represented as a matrix of demands between sectors. When inverted, the model could represent the total output of an economy as a function of the final demands from each of the sectors. Leontief saw the benefit of linking emissions to the sectoral outputs that result [70], but his vision included them as additional rows and columns to the model. In essence, "pollution production" became another commodity sector within the economy. Although no pollution was ever "demanded" as in other commodities, its outputs were now part of the model. However, one of the side-effects of Leontief's method appears to be that this endogenous inclusion of external effects makes the input-output framework more complicated. To solve the model with a range of additional effects required the inversion of a matrix with additional rows and columns. Until even recently, this computation would have been a complicating feature of such a method. Miller and Blair [85] proposed that a similar method could exist with external augmentation of the basic IO model, but offered no solution of its equivalence. Chapter 2 verifies that our proposed model of incorporating environmental effects externally yields results equivalent to Leontief's method. This external method, Economic Input-Output Life Cycle Assessment (EIO-LCA) has been developed at Carnegie Mellon to specify the expected environmental effects associated with production in the economy [Lave 95, 2

9 Cobas 96, Horvath 97, Joshi 97, Hendrickson 98]. This model has been made available on the internet at as a publicly available research tool. Once the equivalence of our theory has been shown, we develop the complete EIO-LCA model in Chapter 3 to determine a range of environmental effects in the U.S. economy using the Department of Commerce's 1992 input-output data [DOC 97]. This is the most recent version of such data. Specifically, we link industrial activities to the outputs of conventional pollutants and greenhouse gases. The pollutant emissions considered are carbon monoxide, sulfur dioxide, nitrogen oxides, particulate matter, volatile organic compounds, and global warming potential (in CO 2 mass equivalents). The determination of the external costs based on pollutants generated requires a significant amount of data, disaggregated by commodity sector. We use a 3-tiered set of data to determine the conventional pollutant and greenhouse gas emissions from each of the 500 sectors. We first generate expected emissions using fuel consumption data from the Department of Commerce and EPA AP-42 emission factors. These data derive the expected amounts of each emission resulting from the combustion of fuels given particular technologies in each sector [EPA 95]. The second source takes data from EPA's Aerometric Information Retrieval System (AIRS) [EPA 98b]. This system collects and organizes emissions data from thousands of facilities that meet threshold reporting requirements for each of the conventional pollutants, and provides sufficient detail (including Standard Industrial Classification, or SIC, code) to use them with the input-output model. Note that this data system, although highly accurate in the data it does contain, represents an underestimation of total emissions of each pollutant since facilities that do not meet the reporting threshold are not in the data. Thus, the fuel consumption data and AIRS data are compared to get a more realistic estimate of emissions. Finally, data from the 1996 EPA Emissions Trends report are used as a baseline to check that pollutant data is fairly represented [EPA 96]. In general, this data is only needed 3

10 where sectors lack data in the other 2 methods. For example, construction and transportation sectors are problematic because they contain many mobile sources, and only have fuel consumption data. The Emissions Trends report provides estimates of emissions from these sectors. Overall, we analyze the results from each of these data sources to generate an estimate of emissions for each of the 6 pollutants for each of the 500 sectors (approximately 3,000 discrete points) in the U.S. economy. Applications of an Environmentally-Augmented Input-Output Model As noted above, EIO-LCA, with its roots as an IO model, yields the total economic impacts of a particular demand for a commodity (or without loss of generality, a range of commodities). As an example, instead of revealing only the direct impacts of producing steel - i.e. the emissions that result from operation of a blast furnace or steel mill, EIO- LCA yields the more complete "total supply chain" of effects such as the emissions from producing the electricity needed to produce the steel, etc. In Chapter 3, we use the total supply chain economic effects, and the resulting model solution, to determine the environmental effects associated with production for all of the 500 commodities in the 1992 IO table. We describe results both at the per dollar output and aggregate (per-dollar-output multiplied by actual 1992 output) levels. Since such results are in units of various species of emissions, we seek to normalize the environmental effects by using a range of economic valuation studies to convert the emissions into dollar damages. To this end, we summarize a series of "dollars per ton" studies that value the damage associated with environmental emissions. In general, these studies value the human health effects expected to arise from increased ambient air concentrations of the individual conventional pollutants, and put a price tag on the medical costs that arise from treating the respiratory and other illnesses that result. 4

11 The result of adding the range of valuations is a rank-ordering of the 500 commodity sectors by external costs generated per dollar of output, as well as an aggregate measure of the total external cost incurred by the production from each of these sectors. We note that these results are not completely external to the economy. The medical costs that would arise from pollution are partially captured by the demand of hospital and other medical sectors in the economy. However, the pollution-generating sectors that cause the external costs have no direct linkages to the medical sectors within the IO model. This model, then, represents the commodity sectors that generate these costs. Another benefit of the use of such valuation is that the EIO-LCA tool becomes more of an assessment mechanism. Investigating only data on the environmental impacts, it is at best a life cycle inventory tool. With valuation effects, it provides impact information that can be used for assessment purposes. Chapter 4 incorporates the external cost estimations within the context and framework of existing national price indices - the Consumer Price Index (CPI) and Producer Price Index (PPI). The results show that the damages caused by consumer purchases (using median external cost estimates) are about 3%, while producer purchases cause 5 to 9%. Further Use of Pollutant Data Using the large detailed pollutant data set, Chapter 5 considers the costs of policies to reduce emissions. Although policy issues are discussed periodically throughout the thesis, the primary emphasis is saved for this Chapter. We consider the effectiveness of several policies for improving environmental quality through mandated targets. This exercise is made possible by data from the Commerce Department's Pollution Abatement and Control Expenditures (PACE) survey. The PACE survey samples facilities in each of the sectors to determine the capital and operating costs arising yearly from the control of environmental emissions in their processes. 5

12 By combining data on the cost of control with the emissions generated by each sector, an analysis can be made that determines the average and marginal costs of abatement for each sector and emission. We then back-calculate the costs of compliance for various command and control and market-driven environmental policies. Economic and Policy Implications In summary, the results of this thesis provide a comparatively detailed analysis of the environmental impacts resulting from industrial activity in the United States. Further, it provides a measure of the relative damage coming from each of the sectors, and the effects associated with consumer and producer purchases. The costs of various policies to reduce the emissions and related damages associated with current levels of production are also estimated. These results are especially interesting considering the international efforts underway to reduce global greenhouse gas emissions. 6

13 Chapter 2: On the Equivalence of Environmental Analysis via Leontief and External Input-Output Methods Leontief [36] developed input-output models to relate the production inputs of goods and services in an economy to the production outputs of the other sectors, as well as to the provision of labor and other inputs. The most basic of these IO models describes an economy only by inter-sectoral transactions. One of the critical assumptions in an IO framework is that, generally speaking, firms in each sector purchase some amount of input from firms within the same sector (e.g. an agricultural sector where seeds are purchased to grow vegetables). In more advanced IO models, households are included. This expansion yields an additional row to represent the provision of the household product labor services, and an additional column to show the consumption of goods and services by households. Figure 2-1 shows the structure of such models, including the standard nomenclature for input-output matrices. In this thesis, matrices and vectors are in boldface type. Transactions (A): Purchases of goods and services between production sectors i: row index j: column index Economically-valued purchases: z ij Technical coefficients: a ij = z ij / X j Final Demand (Y): GDP Components (C+I+G+NX) Total Commodity Output (X): Output of each sector by summing across each row Value Added: Labor Services, etc. Total Industry Output: Column sums Figure 2-1: The layout of advanced input-output models Other sectors, representing the Gross Domestic Product (GDP) categories, are continually added to form more complicated models. Consumption (C), fixed investment (I), 7

14 government spending (G), and net exports (NX) are examples of these additions. In any IO model, total commodity output can be represented by the sum across each row's values. Thus for each of the n commodities indexed by i, X i = z i1 + z i z in + Y i (2-1) However, IO models are typically generalized by assuming inter-industry flows between sectors can instead be represented as a percentage of sectoral output. This flow is represented by dividing the economically-valued flow from sector i to sector j by the total output of sector j. Namely, a ij = z ij / X j (2-2) In such a system, the a ij term is a unitless technical (or input-output) coefficient. For example, if a flow of $250 of goods goes from sector 3 to sector 4 (z 34 ), and the total output of sector 4 (X 4 ) is $5000, then a 34 = This says that 5 cents worth of inputs from sector 3 is in every dollar s worth of output from sector 4. As a substitution, we can also see from Eq. (2-2) that z ij = a ij X j. This form is more often seen since the system of linear equations corresponding to Eq. (2-1) is typically represented as X i = a i1 X 1 + a i2 X a in X n + Y i. (2-3) It is straightforward to notice that each X i term on the left has a corresponding term on the right of (2-3). Thus all X terms are typically moved to the left hand side of the equation and the whole system written as 8

15 (1 - a 11 )X 1 -a 12 X a 1n X n = Y 1 -a 21 X 1 + (1 - a 22 )X a 2n X n = Y a i1 X 1 -a i2 X (1 - a ii )X i a in X n = Y i (2-4)... -a n1 X 1 -a n2 X (1 - a nn )X n = Y n If we let the matrix A contain all of the a ij terms, X all the X i terms, and Y the Y i terms, then system (2-4) can be written more compactly as (I - A)X = Y (2-5) where I is the n-by-n identity matrix. This representation takes advantage of the fact that only diagonal entries in the system are (1-a ii ) terms, and all others are (-a ij ) terms. Finally, we typically want to calculate the total output, X, of the economy for various exogenous final demands Y, taken as an input to the system. We can take the inverse of (I - A) and pre-multiply it to both sides of Eq. (2-5) to yield the familiar solution X = (I - A) -1 Y (2-6) where (I - A) -1 is the Leontief inverse. Classification of Results in an Input-Output System Before we proceed, it is important to distinguish between the various results inherent to an IO model. The results are the total outputs generated from an exogenous final demand. The structure and components of these outputs are worth noting. Due to the inter-sectoral transactions shown in the A matrix, any exogenous final demand will have "ripple" effects throughout the economy expressed in an IO model. For example, the brief numerical example shown above says that 5 cents of sector 3 product is in sector 4 output. Similarly, probably some amount of sector 4 product is required to make sector 3 9

16 output. At face value, this creates a circularity problem in determining results. However, this circularity is completely expressed in the Leontief inverse. The Leontief inverse can also be expressed as the power-series form X = IY + AY + A 2 Y +... = [I + A + A 2 + A ] Y (2-7) The successive terms of the power-series form represent the round-by-round requirements for producing total output X that are part of the circularity problem 1. Equation (2-7) shows that in the first round, IY is produced (the final demand). In the second round, AY is needed to produce the IY of final demand. In the third round, A 2 Y is needed to produce the AY from the second round, etc. The sum of these round-byround effects, including the final demand, is X. In this way, the input-output framework shows the "total supply chain effects" of producing goods and services in an economy. We can separate, however, these effects between the "direct" economic effects (i.e. the effects related to the pure production of the final demands) and the "indirect" economic effects - the effects related to producing all goods and services needed to produce the final demand. In our matrix terminology (consistent throughout this thesis), the direct effects are the [I + A]Y term in Eq. (2-7), and the indirect effects are the [A 2 + A ]Y terms. In all, we call the sum of the direct and indirect effects (X) the "total" economic supply chain effect of production. The magnitude of the direct, indirect, and total effects is completely dependent on the values of the A matrix. Thus, it is possible that the indirect effects will be larger than the direct effects. When we consider the environmental effects of this production, this same result holds. Since our ultimate goal here is to create a framework for analyzing relative environmental effects of production, the concepts of direct and indirect effects are central. 1 For a more detailed proof and explanation of the power-series form, see Miller and Blair [85]. Due to the computational complexity of generating large inverses, this alternate form is often used since successive terms can be calculated by multiplying the previous term by A. 10

17 Incorporation of Environmental Effects into Input-Output Models Leontief [70] first suggested the use of input-output (IO) models to perform environmental analysis, and it is from this point that two separate methods of incorporating environmental impacts can be generated. The first method is Leontief's published suggestion of endogenizing environmental effects by augmenting the A matrix with pollution product rows and columns. An example of this is CO 2 pollution from each sector. The suggestion of endogenizing environmental effects within the IO model was somewhat problematic at the time. Computational power and capacity were quite expensive, so adding even a single row and column for a particular emission created a problem in solving a larger system of equations. This is part of the rationale behind the second method, externally augmented IO models, and such a method is implemented later in this thesis. Externally augmented models keep the consideration of environmental effects external to the input-output model, but use the Leontief inverse and output calculations to generate these results. The use of such alternative methods is not itself novel. Miller and Blair [85] discuss that external methods if done correctly would yield computationally equal results, but they offer no proof of their equivalence. A theoretical exposition of each method is provided below, as well as a proof of their equivalence. Proposition: Given an n-by-n IO model with transactions matrix A and final demand vector Y, and a function H of environmental impacts per dollar output of each sector, the result of endogenizing environmental impact by adding a row and column yields the same result as externally creating a unit-environmental impact function. Proof: We begin with a sketch of the details of the externally-augmented method. In this method, the total supply chain economic output is found using the result of equation (2-6) above. Namely, the I-A matrix is inverted and then multiplied by the vector of final demands to find the overall economic output produced per sector. Such a method yields the total supply chain economic output previously discussed. Since X contains all 11

18 output produced (direct and indirect), we can use an external per-dollar-output emissions function to find the overall environmental impact for a given amount of output produced by summing across the impacts generated by each sector's production. In particular, we propose a function of the form H = e 1 X 1 + e 2 X e n X n = EX = E(I - A) -1 Y (2-8) where the function H multiplies a vector of per-dollar emissions from each sector, e i, by the total outputs of each sector calculated in (2-6). As seen above, this function effectively yields the total pollution generated. We now seek to prove that this external method of calculating emissions is equivalent to Leontief s method. The Leontief Method of Determining Environmental Impacts In this method, pollution is considered to be a product just like the other n commodities in the system. Some amount of pollution is "required" to produce each of the other n products. If sector 1 generates 50 pounds of pollutant, sector 2 generates 80 pounds, etc., then the pollution generated is also effectively considered as a flow resulting from production. Thus an nth+1 row and column is added to represent this production relationship. First, the additional row is added. To accomplish this, per-dollar pollution generation coefficients for a single pollutant are added to the system of equations endogenously, forming an additional equation as in (2-1). Pollution values per-dollar-output can be found as in Eq. (2-2) for each sector. To differentiate the pollution coefficients from the technical coefficients already used in Eq. (2-3), and to compare directly with the externally-augmented method, these pollution flows for each sector are denoted as e j. The total emissions produced could be found as X p = e 1 X 1 + e 2 X e n X n 12

19 where X p is total pollution produced as a function of per-dollar pollution generated and output for each sector. Note that there is also no final demand of pollution Y p, it is a negative externality and a by-product. To keep with the format of the input-output model, this pollution equation is rearranged as -e 1 X 1 - e 2 X e n X n + X p = 0 (2-9) Second, the nth+1 column is added representing "demand" for pollution. Again, no demand or purchase of pollution is made by any sector. The coefficient for pollution demand is zero in each equation of form (2-3), as in X i = a i1 X 1 + a i2 X a in X n + 0 X p + Y i. We can visualize the resulting new system of n+1 equations by using partitioned matrices that follow the format of Eq. (2-5). The system can be represented as e ( I 1 A)... e n 0 X 0 X 1 X 1 2 p Y 1 = Y 2 0 (2 10) Due to the additional row and column present in the left-hand matrix compared to the base model in Eq. (2-5), we call the augmented form above (I-A*). As in (2-6), we are looking for a solution yielding total outputs (including total pollutant releases) of the form X X X 1 2 p = e ( I 1 A)... e n Y 1 Y 2 0 (2 11) Thus, the first step of such a solution is to find the inverse of the (I-A * ) matrix. This can be done by a Gauss-Jordan reduction iterative procedure. The first step of such a procedure is to create a new partitioned matrix which contains the elements of the (I-A * ) matrix on the left and the n+1 by n+1 identity matrix on the right: 13

20 14 The Gauss-Jordan method uses linear combinations of rows to transform the matrix on the left of the partition into the inverse matrix. At the same time, this iterative procedure yields a matrix in the right partition which is actually the inverse of the original matrix on the left, i.e. (I-A * ) -1 is created on the right. The first step of the Gauss-Jordan method makes a pivot (the value 1) out of the element in row 1, column 1. This is done by dividing each element in row 1 by (1-a 11 ). Thus after this first step, the matrix would look as follows: Since the goal is to have an identity matrix on the left, all off-diagonal values need to be eliminated. This is done by linear combinations of partially-reduced rows. For example, we eliminate the -a 21 value from row 2 by multiplying row 1 by a 21 and adding the result to row 2. Such a process slowly transforms diagonal entries into 1's by dividing all elements in a row by the entry in the diagonal element and creates 0's by the linear combinations mentioned. This method is performed starting at the top left element and moves generally down and to the right. However, any subsequent row can always be transformed by using the partially-transformed rows above it to create the needed inverse matrix. Without loss of generality, we consider a nearly complete step along the way in transforming (2-12) into the necessary form. At this point, the matrix will have the general form ) ( ) ( ) (1 1 11) (1 1 11) (1 12 L L L L M M M M M M O M M L L L L pn p p nn n n n a a n a a a e e e a a a a a a (2-12) ) ( ) ( ) ( L L L L M M M M M M O M M L L L L n nn n n n n e e e a a a a a a a a a

21 0 0 I M L M e L en L (2-13) Effectively, this matrix has been almost completely reduced to the needed form to solve for the inverse. An n-by-n identity matrix has been created on the left, and the resulting partition L of the desired inverse has been prepared on the right. All that is left to do would be to continue the iterative reduction method on the final row. However, the reason the Gauss-Jordan method was used to find the inverse of the n+1 by n+1 system was to simplify the procedure. The system of equations is always still available for our use. Thus, if we have found the "solution" for the first n rows, we could necessarily use it and the "unreduced form" of the nth+1 row to find the needed output for the nth+1 row. In other words, we can plug in the n values already found into the inherent nth+1equation to find its output. This finding serves two purposes. First, it reduces to a small degree the computation needed to invert the augmented matrix. But more importantly, it shows that to a large extent, the inverse of the augmented matrix is nearly identical to the regular Leontief inverse used in the basic IO model. The appended column of zeroes and the 1 in the nth+1 row will not change in value at any step of the Gauss-Jordan procedure because we are multiplying constants by zero and adding to the value in that column (0 or 1). This realization of subset matrices to the answer hint at the complete solution needed. If we examine the values in the n-by-n system (2-13) above, they are equivalent to the solution needed for Equation (2-6), with each row's general result being X i = α i1 Y 1 + α i2 Y α in Y n, where the α values are the elements of (I - A) -1 and necessarily, (I - A * ) -1. We could continue the Gauss-Jordan method to explicitly determine the inverse of the entire n+1-square matrix, (I - A * ) -1. However, we can use a much more elegant method 15

22 to determine the elements of (I - A * ) -1. Post-multiplying the original (I-A * ) with the resulting (I - A * ) -1 by matrix will yield I by rule. To be more clear, we know that this multiplication has the partitioned form ( I A) E 0 P 1 R Q = I S 0 0 I where the right hand side of this equation is a partitioned n+1-square identity matrix. The first matrix on the left side comes from our representation in (2-10). The I-A partition is exactly equal to the original values in Eq. (2-4). We assume that E represents the (1x n) vector of per-dollar pollution terms from Eq. (2-9). Since we are multiplying a pair of n+1-square matrices, we know that the result will also be an n+1 square matrix. We assume that this inverse can also be partitioned into P, a n-by-n matrix, Q and R, vectors of size n by 1, and S, a single value. By matrix algebra, we know the following to be true of the partitions: (I-A)P + 0R = (I-A)P = I (I-A)Q + 0S = (I-A)Q = 0 -EP + R = 0 -EQ + S = I Based on this series of equations, we can quickly see that P = (I - A) -1. Similarly, since (I-A) cannot equal 0, Q = 0. It follows that R = EP = E(I - A) -1 and S = I + EQ = I. Thus, the inverse of the augmented Leontief system, (I - A * ) -1 has the form 1 ( I A) E ( I A) which is the expected result. When applied to the resulting final demands Y (i.e. from Eq. (2-11)), the resulting total output of pollution will be E(I - A) -1 Y, or EX. This result is precisely what we showed as the result in Eq. (2-8) above. Thus the external calculation method yields the same result as Leontief's method. 16

23 Application of the Theory Although computational power is now inexpensive, using an augmented Leontief matrix may not be the optimal method for dealing with environmental impact information in an IO model. One reason is the need for environmental data over a broad range of impacts, which would otherwise greatly expand the IO model. A model incorporating many distinct emissions could quickly become difficult to invert even with today's computational power. And inverting large matrices causes problems with numerical accuracy. The user of an environmentally-augmented IO model may be only concerned with a single emission - or a small set of all available emissions. In such a case, there would be little reason to solve the larger system of equations. In particular, for Internet-based tools the ability to deliver data quickly and as needed is paramount to any computational considerations. Thus delivering accurate data and solutions is needed without the computational burden of solving (through inversion) the augmented system. Without loss of generality, the previous equivalence proof can be extended to show that a set of m environmental impacts could be added to the model (as an m-by-n matrix of perdollar output values) to achieve an equivalent multi-dimensional analytic result. In the next chapter, we outline a method that uses this framework to provide environmental impact information for all commodity sectors in the 1992 U.S. IO model. 17

24 Chapter 3: Air Pollution Costs of Industrial Activity Introduction Current environmental regulation does not eliminate all pollution discharges or even all environmental damage from the discharges. Table 3-1 shows estimates for several pollutants. EPA estimated that 84 million metric tons of total criteria air pollutant emissions and 4.5 billion metric tons of carbon dioxide equivalent global warming potential were emitted as a result of industrial activity in The majority of emissions are a result of the manufacture and transport of goods. Species Emissions Estimated (metric tons) External Cost Carbon Monoxide 24 million $13 billion Nitrogen Oxides 17 million $18 billion Particulate Matter (PM 10) 11 million $31 billion Sulfur Dioxide 20 million $36 billion Volatile Organic Compounds 12 million $17 billion Global Warming Potential (in CO 2 equivalent) 4.5 billion $63 billion Total - $178 billion Source: [EPA 96, EPA 98a]. Table 3-1: Total U.S. emissions and estimated external costs of various pollutants in Since the 1970 Clean Air Act, opponents of environmental legislation have contended that air pollution abatement costs are large, costing jobs and disrupting the economy. However, EPA [1997] concluded that the social benefits of abating air pollutants since 1970 exceed costs by a large margin. The EPA analysis does not attempt to justify individual regulations. In particular, the majority of benefits come from eliminating lead 2 Note that the GWP value has been converted from 1.22 billion MMTCE, million metric tons of carbon equivalent, to metric tons of carbon dioxide equivalent, by multiplying by the weight fraction of carbon in carbon dioxide, 44/12. 18

25 from gasoline and reducing the concentration of small particles. Most costs come from reducing the emissions of pollutants causing urban smog (ozone). We estimate the air emissions and resulting external cost, both direct and indirect, from each of the 500 commodity sectors of the U.S. economy in The resulting estimates could be used to calculate an effluent fee to consumers for each commodity. They could also be used to estimate total costs for benefit/cost investment analyses. While these estimates give a rough approximation of the social costs from the principal six pollutants, they do not include other (toxic) air, water, or solid waste discharges. External Environmental Costs Market incentives motivate businesses to provide the desired goods and services at least cost, even if this means creating an externality by discharging pollution to the environment. More generally, an externality results whenever private costs (the costs to the firm) are different from social costs (the total costs to society). For example, banning tetraethyl lead from being added to gasoline created an estimated $2 trillion of social benefit [EPA 97a]. Isolating problem commodities and estimating their economy-wide environmental impacts will help make environmental regulation more effective and efficient. The environmental costs estimated here do not include the industrial expenditures for emissions control. These expenditures are private costs and already are embedded in the prices of goods and services. In particular, the 1990 Clean Air Act mandated almost a 50% reduction in sulfur dioxide emissions and allowed firms to trade emissions permits [Schmalensee 98]. Both the additional control costs and the costs for emissions permits are already included in the price of electricity and other goods. However, the damages resulting from such emissions in terms of human health and mortality are not included, and nothing explicitly makes decision makers consider these costs. 19

26 One way to internalize pollution externalities is to levy an effluent fee each time there are emissions. The effect would start by increasing the cost of extracting raw materials, which would raise the costs of making intermediate goods, along with the effluent fees for their emissions. By the time commodities were offered for consumption, their costs and prices would reflect their cumulative environmental discharges. Collecting these effluent fees would be administratively difficult. It would be far easier to collect the fee at the point of final sale, although incentives for miners, hazardous waste handlers, etc. are not so clear. Even if Congress mandated the correct quantity reduction in sulfur dioxide (and other pollutants), i.e., the quantity where the marginal social cost of abatement equals the marginal social benefit of abatement, there would still be externalities to be internalized. The producers have played their role by abating to the level where marginal private benefit equals marginal private cost. However, consumers still have to decide how much of each good or service to purchase. Only if consumers make consumption decisions on the basis of prices that reflect all the externalities will social efficiency be attained. The need to charge firms for the marginal social loss from emissions is discussed in Joskow [92] and Freeman et al [92a, 92b]. The Total Costs of Manufacturing: Direct and Indirect Effects We present estimates of the quantities of air pollutants and their social losses for 500 commodities. These estimates can be interpreted either as the amount that would have to be charged if effluent fees were levied at the point of sale for final use or as the cumulative impact of effluent fees charged at each step. In the latter interpretation, the estimate becomes an input into an analysis of the revenues to be raised and the disruption that would be caused by this fee. Our estimates are for the US economy in As historical estimates, they assume no adjustment in response to the fees. Clearly, the response to large fees would be improved 20

27 controls, switching materials and processes, and changing the demand mix, The estimates do provide an estimate of the external costs from economic activity that U.S. society actually paid in However, an IO model makes no explicit connection between economic purchases of inputs, production, and the external damages that result. For example, employee health effects may result from exposure to a particular substance or process, and companies may incur medical costs as a result. But there is nothing in an IO model that connects medical costs to the activity that causes them. So IO models themselves do not capture external costs. This analysis restricts attention to air emissions from commodity production. A full life cycle assessment for a product or a process would include liquid and solid waste discharges as well as the environmental discharges associated with use and end of life [Graedel 95]. For example, assessment of a standard automobile would include petroleum purchases during use. Examples of life cycle assessments using the EIO-LCA model appear in [Hendrickson 97, Horvath 98, and MacLean 98]. Emissions Data Sources Once economic outputs by sector are estimated, environmental emissions are estimated by multiplying the economic output by the average emission per dollar of output for each of the 498 commodity sectors. For the conventional air pollutants (carbon monoxide, nitrogen oxides, particulate matter, sulfur dioxide, lead, and volatile organic compounds) and carbon dioxide, data on direct emissions for stationary sources are available from the Environmental Protection Agency s AIRS database of reported emissions [EPA 98b]. For sectors not reporting to AIRS (especially those without fixed plants, e.g., trucking), a two-stage estimation is employed. First, fuel consumption is estimated based on the U.S. Department of Commerce data on fuel purchases used in the development of the inputoutput matrices themselves [DOC 97]. These are typically fossil fuels, and most air emissions come from the combustion of these fuels (e.g. coal, natural gas, petroleum, 21

28 gasoline, etc.). Next, air emissions are estimated based upon standard emission factors for industries and processes, as compiled by the U.S. Environmental Protection Agency [EPA 95]. Emissions of greenhouse gases are translated to equivalent releases of carbon dioxide based on a standard weighting method [IPCC 95, Wuebbles 95]. This method determines global warming potential (GWP), which was developed to compare the ability of each greenhouse gas to trap heat in the atmosphere, and thus to affect climate change. Note that the conventional pollutants are not part of the GWP methodology because their specific contribution to climate change is unclear. See Appendix A for details on the construction of the database for pollution emitted by sector, as well as a complete presentation of the total sectoral emissions data. Note that lead air emissions have been estimated but are not included in analytical results presented. Table 3-2 summarizes the total emissions of conventional pollutants for the top ten sectors (sorted by emissions of particulate matter). Total Air Pollutants Emitted (metric tons) Commodity Sector PM CO NO 2 SO 2 VOC Petroleum and natural gas well drilling 1,090, , ,000 12,000 14,000 Other new construction 710, , ,000 3,000 2,000 Other repair and maintenance 670, , , construction New residential 1 unit structures, 461, , ,000 1,900 1,500 nonfarm New office, industrial and commercial 335,000 75, , ,000 buildings construction Maintenance and repair of farm and 272,000 66,000 88,000 1, nonfarm residential structures Electric services (utilities) 233, ,000 5,170,000 11,300,000 40,000 Sand and gravel 169, New residential additions and 168,000 39,000 50, alterations, nonfarm Petroleum, natural gas, and solid mineral exploration 147,000 36,000 38, ,200 Table 3-2: Ten Commodity Sectors with Largest PM Emissions 22

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