Dynamic aspects of air quality control costs

1OUHYAI.

01;

I3VmONhfEN1’,~L

Dynamic

ECONOhllCS

Aspects

AND

XlANAG~~hlI’N’I

of Air Quality

WALTER DOLDE, DENNIS EPPLE, LESTER LAVE, AND SANUEL Carnegie-Mellon

University,

Received February

Pittsburgh,

4.

:i 1:3-:334 ( 1977 )

Control

Costs1

MILTON HARRIS, Imwr.4mT Pmnsylvan,ia

1521.1

6, 1976; revised April 21, 1977

Thii paper investigates aggregate cost differentials due to implementing environment a1 regulations over alternative time periods. These different,ials may be related i,o prematurcb obsolescence of the capital stock, technical advances in abatement, and perhaps ot,hrr factors. Our estimates, which are subject to a number of qualifications, indicAat,e fha~ t,hese differentials may be substantial. We conduct our investigat,ion within a simple but complete general equilibrium model and contrast ollr approarh with more conventional techniques of forecasting and policy assessment. Our model consists of :\ description of preferences, technology, and the interaction of economir agent.s which generates forecasts of economic variables for alternative srenarior. 1. INTRODUCTIOX

AS-D SUMMARY

This paper investigates aggregate cost differentials due to implementing environmental regulations over alternative time periods. A considerable literature exists on the relative costs and benefits of air quality controls in a static framework. Researchers have not, however, discussed t’he dynamic aspects of air qualit,) c*ontrol costs related to premature obsolescence of the capital stock, terhniaal advances in abatement, improved knowledge of the benefits and co&, ant I changing factors regarding air quality. Our preliminary estimates indicate th:kt implementing incremental air control standards in 1976 may well incur annual costs which are one-third higher than those that would be incurred if standards were deferred until 1985. In dollar terms, the cost of earlier implementation of the standards is approximately $5 billion annually. These estimates are subject to a number of qualifications, detailed below, and should not he regarded as more than indicative. We have constructed a simple general equilibrium model for our investigation ; it rests on a description of preferences and technology (including technicA progress) and assumptions about how households and firms interact in markets. Given information about exogenous factors, such as government policies, the model predicts the market equilibrium concerning the prices and quantities of various goods and services. This approach contrasts with conventional forecasting practice, which proceeds hy a combination of sheer extrapolation, parGal equilibrium analysis, and con1 An earlier version of this paper was presented at the 1975 winter meetings of the Econometric Society in Dallas under the title “An Economic Modeling Approach to Intermediate Term Policy Analysis with an Application to Air Quality Control.”

Copyri ht 6 1977 by Academic Pres. AU rig 2:ts of reproduction in any form

Inc. reserved.

ISSN

ooos-Oh96

314

DOLDE

ET AT,.

vcrted short run m:bcroeconomic models. In forecasts of pcrio& greater than :h few years, exogenous factors are changing; thus, extrapolation of price and quantity trends implies that preferences, technology, and the way that economic agents interact are changing in an accommodating way. Clearly this assumption will not obtain, making the forecast a crude approximation at best. Partial equilibrium models represent an improvement since price and quantity for one market are determined within the model. However, interactions with other markets are ignored or are represented by guesses of the forecaster. The short run macroeconomic models generally suffer from an inadequate treatment of the effects of capital accumulation and relative price changes. Most macroeconomic models, with their aggregate demand-inflation orientation, lack an explicit-and one suspects in the longer run, a robust-representation of technological possibilities. Section 2 of this paper outlines the theoretical framework for our discussion and critiques previous related research. Section 3 outlines our model, reports resultIs from a number of exercises, and attempts to place these results in perspective. The Appendix includes a mathematical representation of our model.

2. THEORETICAL

FRAMEWORK

14ND RELATED

RESEARCH

Clean air and water cannot be purchased or sold in organized markets by individuals acting in their own interests. An economic agent who pollutes the environment imposes a negative externality. The achievement of economic efficiency in the allocation of resources when such externalities are present requires a social program to internalize these costs to change the behavior of polluters and receptors. The Clean Air Act, as amended, the Federal Water Pollution Control Act, and various state and local laws comprise the basis for such a mechanism in the United States. They work by imposing emission standards ; if these standards are the result of careful analysis, they can lead to efficiency in resource allocation. The appropriate degree of environmental protection is that which maximizes the net benefit. Under the plausible assumptions that the cost of a marginal unit of environmental quality increases and that the benefit of a marginal unit declines as higher levels are contemplated, net benefit is maximized where marginal benefit equals marginal cost.2 Presumably environmental regulations are determined so that the actual level of environmental quality which results is equal to the optimal level. The acquisition of new information over time may change our estimates of the benefits and costs, in turn altering our estimate of the optimal level of pollution. In this situation a particular set of regulations may not still be justified; the associated benefit may not exceed the cost. Even where benefits exceed costs, the marginal benefit may exceed or fall short of the marginal cost, in which case the regulations are, respectively, too lax or too strict. With regard to currently propounded regulations, for example, Lave [6] indicates the benefits clearly exceed the costs for sulfur and particulate emissions into the air. The relationships between marginal costs and benefits are less clear. Because of the difficulty of obtaining evidence from which to infer benefits and costs, we doubt that much confidence 2 It is possible,of mental

quality,

course, that marginal in which case no resources

cost exceeds marginal should be allocated

benefit for every to environmental

level of environprotect,ion.

DYNAMIC

AIR CONTROL TABLE

-.~-

I

Project,ed Nat,ional Annual Benefits (Damage Cost Reduction) in Fiscal 1977 (1970 Dollars in Millions) Benefit class

,Sollrce class Healt,h (8)

:: I 5

COSTS

Residential cs)

Mobile Solid waste Stationary fuel combust,ion Industrial processes st,udied

-.-. c& 172 38126 1413

0 145 3267 1302

Total benefitc

.5397

4615

Materials and veget,ation (%) --.. !W ll!l 2366 7:-14 -.-4164

by Source Cl:rss Total benefit is)

!)4*?’ 4:ifi

9,445 :3,3.50 14,176

(:ont Id cosl (PI


Source: r3, Tables l-41. ClValue of benefits from reducing CO, NO,, and HC emissions not, available due to lack of data. h Healt,h damage cost due t,o NO,, from st,ationary fuel combllstion not, incl~tdd dlle 1.1,lack 01” data. c Benefit computation based on proport,ional reduction of damage costs excludes “miscellaneous” source damage co& since these are generally not, controllable and, t,herefnre, cannot home benefit~s.

can be attributed to attempts t.o evaluate regul:&on of other sourc’es of :ii~ pollution and of water pollution. Table I indicates estimates of costs and benefits of air qualit,y control prepared by the Environmental Protection Agency. Table II indicates EPA e&mates of t,he costs of water quality control. As indicated, a number of categories of costs and benefits are omitted due to lack of data. The air quality study was prepared for 1972 release and assumes current stationary and mobile source emission standards will be fully in force in 1977. The water quality estimates refer to 1981. Annualized costs consist of an imputed rental rate on capital-including interest, depreciation, and maintenance-and direct operating costs. Actual expenditures in early years will exceed these annualized costs, however, as investment is first put in place. For a critique and furt,her discussion of these estimates see I,R~Y~and Silverman [7]. A number of studies of the costs of pollution control at t)he individual industry level have been completed. One of the more recent and more comprehensive is t,he A. D. Little (ADL) study prepared for the American Iron and Steel Instituttl [l]. It is possible to make a rough comparison of the ADL and EPA estimates for the cost of air quality control in the iron and steel industry. The EPA [4] estimates the 1978 operating costs of air pollution cont’rol at $0.18 billion in 1970 prices, or about $0.19 billion in 1972 prices (using the implicit deflator for total (;iVP). ADL’s estimate of 1972 operating costs is $0.50 billion in 1972 prices. Since the ADL cost model makes operating costs very sensitive to current inT,estment rather than to steady-state investment, their estimates for 1978 operating costs would be lower. n’evertheless, the difference between t’he t,wo estimates is quite striking. Such EPA estimates for the future do include projections of economic growth and of t3echnological trends. The prices of resources used in emissions cont,rols arc

316

DOLDE

ET AI;.

TABLE National

11

Costs for Municipal and Industrial Water Treatment at Various Levels of RemovalWastes treated 86) 100 80

20

Level of removal (%I 100 !G-99

Annualized costs in 1981 (billions of $) 21.1 12.4

100 >

100

9ei-99

8.4

100

85-90~

4.1

.~ Source : [5]. p Excludes (potentially enormous) costs to control pollution from storm and combined sewers, agrigultural wastes, and other dispersed sources. h This is roughly bhe pre-1972 “uniform secondary treatment” standard.

not bid up. Firms do not or cannot substitute among labor, capital, and materials in producing output or abating pollution. Households’ supplies of factors of production and demands for output do not reflect the diversion of resources into abatement procedures. Rather, relative prices are assumed fixed at the levels that obtained at the time the estimates were made. Unlike guesses more than 5 years ahead about the position of the economy in the business cycle, consideration of the causes and results of relative price changes may constitute fruitful additions to forecasting exercises. Evans [2] goes a step beyond the EPA studies in assessing the costs of pollution by investigating the interactions between abatement and other economic activity. The EPA cost estimates described in the previous section are run through a general equilibrium model to examine relative price changes and producer and consumer responses. Evans uses his Chase Econometrics Macroeconomic Model (CEMM) and his Interindustry Forecasting System (IFS, an input-output model). The initial cost increases in each industry corresponding to abatement procedures are translated into initial output price increases through markup equations. The IFS model translates these initial price increases into tentative secondary price increases. The actual equilibrium changes in prices and outputs are determined simultaneously with aggregate demand determination in the CEMM. Table III lists Evans’ forecasts, made in late 1972, for constant dollar GNP with and without pollution control costs. While constant dollar GNP actually is higher in 1972-1975 with pollution control costs, part of the GNP differential is consumed by those control costs.3 Although the use of the CEMM-IFS appears to be an improvement over use of the nonequilibrium cost increases cqmputed by EPA, the CEMM-IFS results themselves must be regarded as rather ad hoc. Evans’ model, for example, does not include any production functions per se, nor does it need any for the short run 3 Evans does not report a year-by-year breakdown of- aggregate abat,ement, cost6 upon which his forecasts are baaed. The 1972-1980 grand total was $36 billion.

DYNAMIC

AIR CONTROL

317

COSTS

business cycle perspective for which it was designed. The model contains the usual combination of productivity, markup, and wage adjustment relationships, presumably selected for their ability to elucidate short run movements in wages and output per man hour. Thus it can hardly be expected to reflect accurately technological opportunities for pollution control to be implemented over a lo-yea?, horizon. The IFS is used with the CEMM, but only to transform individual industry cost increases into equilibrium industry price increases. ,4s with the EPA st,udies, firms are not assumed to undertake substitution among fact,ors of production in response to changes in relative factor prices. The discussion thus far deals only with the question of whether environmental controls may be justified ultimately. It ignores the issue of t,he optimal time pattern of implementation of those cont.rols for which net benefits are positive. Too long an implementation period cannot be optimal, since net benefits of COIItrols are foregone in each year until controls become effective. On the other hand, it is unlikely that instantaneous implementation is optimal either. Considerable ignorance and uncertainty still exist regarding the effects of and abatement possibilities for certain types of pollution. Further, portions of the current capital stock may suffer premature technological obsolescence which could be avoided with some lead time before controls take effect. Finally, some delay in implementation of controls might permit exploitation of technical advance in abatement procedures. One can, however, argue equally plausibly for early implementation of controls as a spur to technical progress in abatement. Further consideration of the timing of environmental controls clearly requires :I dynamic model which accounts explicitly for capital formation and depreciation, t’echnical progress in abatement, and the interactions between pollution control and other economic activity. In Section 3 we examine one such model and present some illustrat,ive calculations. However, t,he incenti\rr effects of early int,roduct,iorr of controls are not t,reated in the model. :3. Ol:li, 3. I. Overview

MODEI,

iiN

1CESIJI;I’S

oj the Model

We have constructed a dynamic model intended to mimic t,he evolution of t hc .1mericsn economy over time. The model is a full employment, model and does not, attempt, t,o account for business cycle phenomena related to fluctuations around the trend. Inflation is absent from the model: all relationships are stated in constant dollar terms. The costs of environmental controls are assessed in t,crm:: of the real output and real consumption sacrificed. TABLE Chwe

Econometrics

Forecast

III of GNP

in 19%

Ibllars,

1972

1972

1973

1974

1975

1976

1977

1978

1979

788.3 789.5 -1.2

840.9 843.9 -3.0

885.0 889.0 -4.0

917.5 919.6 -2.1

948.1 943.8 4.2

987.1 978.6 8,5

1029.8 1022.7

1073.0 1068.7 4.3

1980

_--Without control costs With control costs Difference -. source : [.a].

7.2

1111.9 llOS.T, 2.4

318

DOLDE ET AL.

In designing the structure of the model, we have insisted on consistency with historically observed trends in American economic growth. This is in sharp contrast to the work of Meadows and the Club of Rome group [8]. Our model contains potential for dramatic changes in economics events conditional on significant changes in exogenous factors. Unlike the Meadows model, however, our model does not assume the near future is discontinuously different from the recent past. The explicit equations of our model are indicated in the Appendix as are the numerical values of the parameters. In selecting parameter values we have sought guidance in the literature. In most cases, however, some modification has been necessary to overcome the imperfect correspondence between our model and estimates appearing there. In further work we intend to prepare our own statistical estimates of the parameters of our model. Until this task is completed, the quantitative results of our model should be regarded with even more than the usual healthy degree of skepticism appropriate for long range forecasts. Informal sensitivity testing indicates that the qualitative properties of our model are robust with respect to parameter values in plausible ranges. The model includes four distinct producing sectors: consumer tangibles, consumer services, investment goods, and energy. The latter constitutes an intermediate input into the other production processes. Capital, land, and labor services comprise the other factors of production. Both land and leisure are also used for final consumption. The model distinguishes among the behavior of three demographic groups differentiated by age. Technology in the producing sectors is characterized by production functions which permit substitution among capital, labor, land, and energy as inputs. Thus cost-minimizing firms can and will vary their input ratios in response to changes in relative factor prices. Neutral technical progress at a constant geometric rate is assumed in all four production sectors. The production of energy, however, is also subject to technical retrogression proportional to cumulative energy produced over time. This retrogression represents increasing costs of extraction of the raw energy resources. It is also consistent with rising prices for foreign sources of energy. It would not accurately represent the situation in which foreign energy prices remained constant or declined. Pollution emissions and abatement are defined relative to their levels in the cbarly 1970’s. Emissions beyond those levels are modeled to grow in proportion to the growth of production over levels experienced in the early 1970’s, in the absence of technical advances or the allocation of further resources to pollution abatement. The factors of proportionality for our four producing sectors are aggregated from EPA estimates for a finer industrial classification. Pollution abatement is subject to diminishing returns to scale. Only in the limit in which resources are allocated without bound to abatement is it possible for net emissions to approach zero. Thus as a practical matter, the model will not generate zero emission paths.4 The technology of emission abatement also permits substitution among the four inputs and enjoys neutral technical progress at a constant geometric rate. “As noted above, the current version of this model considers only emissionsinto the air and their abatement. Further, air emissions from sources not controlled, forest fires and the like, are not included here. Even were all pollution be pollution free.

from controlled

sources eliminated,

the air would not

DYNAMIC

AIR CONTROL

COSTS

31!)

Behaviorally, the production of pollutants, their abatement, and the relat’eti costs and benefits may be described as follows. Potential pollutants are joint products (“bads”) with the four produced “goods” in the model. Having determined the output levels of these four goods no independent control can 1~ exerted on the level of potential emissions. Abatement is another production activity to which resources may be committed, however, with cleansing of the ai1 the output of the production process. Environmental standards do not dict’ate how much abatement must be undertaken, per se. Rather they state t,he permissible level of net emissions. Given potential emissions, abatement must, be undertaken to the extent that net emissions do not exceed the prescribed standards. Resources used in controlling emissions are not available for producing othtbl goods. They represent the costs of abatement. In a static partial equilibrium framework we could value the cost of small changes in emissions directly, using the prices of the various resources. In a dynamic general equilibrium framework, however, relative prices and price changes may differ considerably between time paths corresponding to alternative levels of environmental standards. The cost, now must be measured as the consumption foregone using a fixed price index to control for price differences across paths. Thus we report differences bet,ween xggregate consumption on alternative pat,hs as measures of the cost of en\-it:onmental standards. Household demands for tangibles, services, investment (savingj, land, autl leisure depend on incomes, prices, and a tax levied to finance the use of resourrvs in abating pollution. Incomes are earned in the sale of capital, land, and label services. Demand for all goods responds positively to income and negatively t,o t,he tax. Demand for a particular good decreases when its own price rises and generally increases when the price of another good rises. An exception is leisure, viewed as complementary with consumer tangibles and household land WW. so that the demand for leisure declines when the prices of those goods rise. The population is divided into three age ranges, O-19, 20-64, and 6.5 and o\‘w. Only the middle group supplies labor, in amounts determined hy their demand fol leisure and firms’ demands for labor services. The two adult, groups behavtl :I,S separate decision-making groups. They have separate demands for the v:i.riolls olltputs, each related to their own income and t,:tx liability. The nonadult popul:~t’ion is not’ an independent decision unit. Provision for t.heir consumption ismath~ I)y the XL64 age group, the parameters of whose demand functions are posit’ivc, I’unctions of the ratio of the number of O-19 year olds to t,he numhcr of 20 64 yr:~r olds in the population. Given t’he equations embodying the behavior and technology described al)o\,c*, the assumpt’ion that firms minimize the costs of producing output, and the stocks of capital, land, and the population, we can determine the quantities of final outputs consumed by each age group, the quantities of each of the inputs into each of the processes, including abatement, and the relative prices of the various inputs and outputs. The solutions for successive periods are obtained in the same way. Current investment, net of depreciation, augments next period’s capital stock. Land area is assumed constant. The size of the population in each age group is exogenous, taken from Social Security Administration c>stim:btcs for th(b pop\ll:slion of t$ht: IJnited States in t,he fut,ure [!,I.

DOLDE

320 S.2. Indicative

ET AL.

Results

We have computed time paths for the model for six different scenarios. The six scenarios differ in (1) the rate at which environmental standards are enforced, (2) the rate of advance of technology in abatement processes, (3) the date and rate of premature obsolescence of the capital stock, (4) the rate of advance of technology in energy production, and (5) the rate of exogenous cost increase in energy production. The first factor requires the decrease of emissions to levels consistent with state and national standards under the Clean Air Act that are to be reached between 1975 and 1977. We examine cases in which these standards are first enforced starting in 1976, in 1980, and in 195.5. In all but one of our cases, we assume that technical progress increases the productivity of all resources used in pollution abatement at l.rj% per year. This 1.5% figure is already conservatively below the 2-3$!$ observed for most industrial processes over some decades in the United States. We nevertheless examine the pessimistic situation in which no technical advance occurs in the abatement process. With regard to the third factor, we examine two cases in which depreciation of the capital stock at triple the normal rate is suffered in the year in which stricter environmental standards are first applied in 1976 or 1980. Delay of the standards until 1985 presumably would permit sufficient planning time to preclude such excess depreciation. The amount of extra depreciation that results from early implementation of environmental standards is an arbitrary assumption on our part. We are not aware of any attempts to quantify this phenomenon explicitly. Because capital-land-la’borenergy input ratios and thus the marginal productivity of capital are fairly insensitive to a wide range of depreciation rates for a single year, the effects of alternative assumptions may be inferred by taking multiples of our results. In varying the fourth and fifth factors, we examine the additional costs that increased energy scarcity implies for environmental protection. In all but one of our simulations we assume technical progress in energy production will proceed at l.fiyo per year, but that costs of extraction and/or costs of foreign sources of raw fuels will rise by 0.001 of cumulative energy usage since 1972. The alternative pessimistic assumptions in case 5 include the absence of technical progress in TABLE

IV

Scenarios IXxaniiued

Characteristics 0

1 2

3 4 5

Maximum aggregate particulate emissions (F) Id million tons per year througll 1975, thereafter 3.6 million; rate of capital depreciation (6) 3% in every year; rate of technical progress in pollution abatement (7~) and energy production (TV)1.59, in every year; rate of exogenous cost increasein energy production _ as a fraction of cumulative production since 1972 (T) is 0.001 (base case) y is 15 through 1979, thereafter 3.6; otherwise identical to case0 Y is 15 through 1984, thereafter 3.6; otherwise identical to case 0 6 is Sci;, for 1973 only, 37, in all other years; 7p is zero in all years; otherwise identical to case0 P is 15 through 1979, thereafter 3.6; 6 is 6O’I0 for 1979 only, 37, in all other years ot,herwise identical to case 0 6 is By0 for 1975 only, 3’z in all other years ; up and TV are zero in all years; r is 0.003 iu all years; otherwise identical ljo case 0.

DYNAMIC

AIR CONTROL TABLE

Consumption

Year

_-. 0

V

on Path 2 Minus Consumption (Billions of 1975 Dollars) --

~--._ 1

:iL! I

COSTS

~__-..-~~~ 2

on the P:tt,h Indiraled

Scenario 3

4

.i

0 0 0 !) 24 24 24 2; 21; 2; 2i 2!) ‘,!I

0 0 0 0 0 0 0 .i Ii 17 Ii IS IS

0 :: 6 IX 2!l :Itl :;L’ :;.i :;I; ::S II 1-l I .-a

I !I72 197:i 1974 197.; 197ti I977 197x 197!) 19x0 19x1 19x2 IYX:: I9X4

0 0 0 0 14 14 14 14 14 1-l I.1 I4 I ‘1

0 0 0 0 0 0 0 0 12 I% 1% 12 12

0 0 0 0 0 0 0 0 0 0 0 0 (I

I !f%.i

2

2

0

IS

Ii

Xi

IY!Nl

2

2

0

21

ri

35

I99.i

2

2

0

‘Ai

ti

tie

energy production and a cost, increase factor three times as great as t,he other (asses. Table IV makes explicit the differences among the six cases. Table 5’ lists the differences between consumption (both private and public) on each path and the value of consumption for the corresponding year in case 2, t,he path with the largest deferral of environmental controls and the most optimistic assumptions about other variables. These consumption gaps comprise the appropriate measure of air quality costs in our model. They measure the sacrifice of goods and services available for final consumption. The use of GNP differentials would be misleading because an increase in investment’ in pollution controls ma] cause GKI to rise. Thus discussion of our cost estimates refers to consllmption gaps. All figures reported are measured in constant 1975 dollars. Prices in the model are stated relative to the price of human t#ime, which is fixed at unity. Technical progress causes labor productivity to rise, other things equal. As a result other prices decline when measured relat’ive to labor at a fixed price. Table VI shows for case 2 the change in price for each good, relative to thtx price of labor, between 1972 and 2000. More detailed time paths of prices. GSl’. and ronsumption are available from the authors on request. We first discuss some general results before turning t,o specific comparisons among scenarios. First, although it is generally thought that a concern with pollution and energy will influence economic growth t(o a greater ext’ent in the future than in the past,, future growt,h rates generated by the model are consistent with t,hose typical of the United States in recent decades. For the period before environmental controls are implemented (1975-1984) in pase 2, the model econom: exhibits an average annual growth rate of 3.0 ${1.5 In the base case the corrrspond5 Trend growth for the United States since 1960 has averaged about 4.0:;. The lower growth rate in the model is attributable to our conservative assumption that technical progress will prwecd ai, onl\- 1.5’“, .m the futllre, as compared to the Z.5,’ ; recorded in the ret-ent, pas1

322

DOLDE TABLE

ET AL. VI

Price Changes 1972-2000 for Case 2

Price (2000) / Good 1 2 3 4 5 6 7

Energy Consumer and government Consumer and government Investment Capital stock Land stock Human time

tangibles services

Price (1972)

Price (2000)

Price (1972)

0.0459 0.0295 0.0637 0.0637 0.0030 0.0042 1.0000

0.1000 0.0200 0.0415 0.0425 0.0024 0.0065 1.0000

2.19 0.68 0.65 0.67 0.80 1.55 1.00

ing growth rate is 2.8% while the lowest growth rate is 2.6% for case 5. For tl~c period 1975-1995, growth rates range between 2.6 and 2.9% for the various cases. The second general result relates to the division of GNP between investment on t,he one hand, and private and government consumption on the other. Consumption declines from about 79% of output in 1975 to about 64% in 1995. This retardation of consumption growth relative to GNP growth might be taken as a manifestation of the diversion of resources to use in environmental control. A comparison of the consumption to GNP ratios for 1984, however, shows this not to be the case. In case 2, for which environmental controls have not yet been tightened, the consumption share of GNP is 72%. The corresponding ratio for the base case is virtually the same, 73y0. Thus enviro nmental controls have approximately no first order effects on the composition of output. They cause diversion of resources approximately proportionately from consumption and investment. Demographic factors apparently account for the changing composition of output. Table VII indicates significant changes in the age distribution of the population between 1975-199L6 As life cycle considerations suggest, the aggregate saving rate rises as the proportion of the population in the working years increases. Third, from Table VI we observe considerable variation in the relative price changes experienced by different commodities. If all of the ratios in the last column of Table VI were approximately the same, disaggregation would be unnecessary. Clearly, however, capital, land, energy, and labor need to be distinguished as inputs in the production process. Similarly, land, time, and produced goods and services should be disaggregated from each other on the demand side. The three produced goods which are also components of final demandconsumer and government tangibles, consumer and government services, and investment goods-do not exhibit much price change relative to each other. Thus they might be treated as a single produced nonenergy good. Alternatively, further disaggregation into categories which are less good substitutes for one another, both in production and consumption, might result in more relative price variability. In the current model much of the interesting substitution may be taking place within one of our broad categories, having little effect on the price aggregate for that category. Details on the timing of the relative price movements are not shown, but occur fairly uniformly over the entire quarter century for most goods. The prices of 6 Demographic

factors are exogenous in the current [Q].

supplied by the Social Security Administration

model. Population

projections

are those

DYNAMIC

AIR CONTROI,

: ‘,2 . !

COSTS

Age L)istribution of the Populatioll (‘;:L)

1972 2000

o-19

20-64

36.8 29.0

53.4 59.6

-

6.5over 9.x 11.5

-

I_--_-__ Total --

.._

100.0 100.0

produced nonenergy goods (in terms of the price of human time) decline regularly over the period. The price of energy, because of the increasing extraction costs encountered, rises fairly smoothly through the period. The rental price of capital rises slightly for the first decade and a half. When the postwar baby boom clnters it,s prime saving years in the late 1980’s and 1990’s, capital formation increases, causing the rental price of capital t,o decline significantly.7 I,and is fixecl in cluantity. As the per capita amount declines, t)he price gets bid up relative to t,he price of t*ime. Finally, the tax rate on full income necessary t,o finance pol111t,ion abatement increases significantly in t’he year in which st,ricter contr& :II’C imposed. In other years its labor price declines smoothly. We t,urn now to six specific observations regarding the effects of the speed ot implement,at,ion of environmental standards under a10ernat8ive assumptions abollt premature capital depreciation, technical progress, and energy costs. 1. Deferring the initiation of environmental controls for 5 or 10 years woul(l permit consumpt,ion to be higher by $12-14 billion in 1975 prices in each year ol deferral and by about $2 billion in each year after controls are implemented, assuming no premature obsolescence of t’he capit’s st’ock. (Compare cases I and 2 with the base case of no deferral in Table Y.) The continuing differential even after cont,rols are implemented in 1980 or 1985 reflects the fact, that capit:ll format’ion for future growth also suffers when resources are allocat,ed to pollution caontrol rather than to producing GNP. The total GKP differentials (not shown) between cases 0 and 1 from case 2 are initially slightly more than twice as big as the consumption differentials themselves. 2. Should the implementation of environmental standards cause premature obsolescence of part of the capital stock, consumption and output foregone will be even greater. Case 4 assumes depreciation at triple the normal rate in 1979 before the implementation of controls in 1980. Comparison with case 1, which is identical except that no extra depreciation occurs, indicates consumption is lowel by $5-6 billion in each year as a result of the extra depreciat,ion. Even though this extra depreciation occurs once and for all in 1979 the loss is never regained. :IS difierentials of the same size exist even for 1995. 3. The absence of technical progress in pollution abatement would raise the cost of abatement significantly. Case 3 differs from the base case only in that pollution abatement is assumed not to be susceptible to technical progress and some extraordinary technological depreciation t,akes place in 1975 before environmental restrictions are tightened in 1976. The t)otal initial effect of these two factors is approximately to double the annual consumption cost of environmental controls (case 3 vs case 0 vs case 3) from about $14 billion to $29 billion. 7 The rental price of capital, measured aa it is in terms of the price of human time, is indicative of the wage-rent,al ratio faced in selecting capital-labor ratios in product,ion.

324

DOLDE

ET AL.

Allowing for the depreciation effects inferred in the previous paragraph, t,llcl absence of technical progress in abatement increases control costs initially by about 45y0 and by increasing amounts thereafter (65% by 1984). For purposes of policy evaluation, case 3 cannot be compared directly with case 2 in which environmental controls are deferred until 1985. Case 2 assumes technical progress in pollution abatement at rates typical of other production processes in the United States. In the unlikely event that no technical progress in abatement occurs, as case 3 assumes, consumption and GNP would be lower than in case 2 just to meet the environmental standards in effect prior to 1975-1977. Thus the consumption and GNP gaps due to nondeferral of stricter standards would be smaller than those reported in Table V. Table VIII indicates the proportion of the total consumption gaps between various cases and case 2 attributable to stricter environmental standards. 4. The absence of technical progress in energy production and the incurring of more rapidly increasing costs of raw materials and/or foreign energy sources would increase the costs of environmental controls significantly by 1984. By that, year the consumption different’ial between cases 5 and 3 is $17 billion. In 1975, however, the additional costs that would result under pessimistic assumptions about energy are $F; billion. As with the discussion of case 3, the consumption differential for case 5 over case 2 is not attributable totally to stricter environmental standards. 5. Given an interest rate, it is possible to compute the present values of the consumption differentials between case 2 and the other cases discussed in points l-4. Ignoring capital gains and losses, the interest rate implicit in the model is P6/P4 - 6, the rental price of capital relative to the purchase price of new investment goods, less depreciation. This interest rate averages about 2.25% for TABLE

Consumption Gaps, Total and Attributed Case

Descript,ion

to Nondeferral

Total consumption gap over case 2 1976

Standards deferred to 1985 Standards deferred to 1980 Base case Standards deferred to 1980, extra depreciation Extra depreciation, no technical progress in abatement Extra depreciation, no technical progress in abatement or energy, costly energy

VIII

1980

of Environmental

Standards

Consumption gap attributable to environmental controls

1984 1976

1980

1984

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.8

0.8

0.0

0.8

0.8

0.9 0.0

0.9 1.1

0.9 1.2

0.9 0.0

0.9 1.1

0.9 1.2

1.6

1.7

1.9

1.0

1.1

1.1

1.9

2.4

3.0

1.1

1.0

1.0

DYNAMIC

AIR

CONTROI,

'I'ABIX

Present

Values

of Cosls Case

---

----

-

1s

of Nondeferral

of l~nvironmental

P.V. at interest rate implicit in model*

Si,antlard~

P.V. at 6(;

__2 1 0 4 3 B

(’ 1’,/P4

‘,.).)-a)

COSTS

0.0 6.1 9.9 13.1 16.8 16.X

0.0 3.7

7.1 6.6 10.1 10.1

6.

t,he first 4 years, about 2.75(;l, for the next 5 years, and slight,ly lower therraftcr. Table IX lists these present, va111esusing both t#hc int,erest, rate in t,hr model and 6%. At, the interest rate from the model, the present vahle of the cost,s of nontlPfcrr:tl range between $92 hillion and $252 billion depending on assumptions ahollt, t,echnical progress, excess depreciation, cost increases for energy, :mtI implementation date. ITsing the 6% interest) rnt,c results in present V:&ICS ranging from $56 billion to $152 billion. 6. We have limited the number of scenarios examined t,o keep t#he results manageable and comprehensible. There is some interest,, however, in having further information about the cost curve for emission reduction. We have approximated this cost curve in the neighborhood of actual permit’ted emissions for 1985, t’he year in which stricter controls are effective in all scenarios. The natnrc of the approximation is that the prices of all goods and the level of potential emissions (Y,) are held const,ant. In that case the total cost of abat,ement bccaomes proport,ional to the square of the ratio of abatement to net emission+: Total cost of abatement

-

abatement __-__[ net emissions

2 .

1

The factor of proportionality differs for each scenario for each year, however, sincsta it depends on prices and on the state of technical progress in abatement. Table X presents approximate points on the cost curves in various cases. Thes:> c*ost curves and the underlying production function for abatement have asymptotes at zero emissions, hence the points indicat’ed represent more than a trivial range of variation. Bearing in mind the partial equilibrium nature of this result, we readily observe the increasing steepness of the rest curves. J.3 Our Results in Perspective Depending upon rates of technical progress in abatement and energy production, upon the rate of cost increase in energy sources, and the extent of premat,urc obsolescence of the capital stock, the annual costs of stricter air quality controls will range from $12 billion to $18 billion over the next decade according tjo out * This result, of course, is particular See the Appendix for details.

to our

modeling

of the pro&l&on

funct,ion

of ahaknenl.

326

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ET AL.

TABLE Total Costs of Abatement

s

for Different

Case

Levels of Net Emissions, 1985

Net emissions (P,)* 4.1

3.6

3.1

0

29.7

1 2 3 4 5

29.7 30.6 41.6 29.0 8.0

41.6 41.6 42.7 58.3 40.5 11.7

60.2 60.2 61.9 84.6 58.7 17.7

a Emissions measured in millions of tons of partiwlates.

model. These estimates are in line with EPA estimates for annualized costs by 1977 of $16.9 billion ($12.3 billion in 1970 dollars). About three-quarters of the $6 billion annual cost range between our more optimistic and pessimistic scenarios is explained by excess depreciation of the capital stock due to nondeferral of stricter environmental control. Smaller costs would persist even after 1986 due to a reduced rate of capital accumulation preceding that date. The extra costs of implementing environmental controls prior to 1985 have a present value of $56 to $252 billion, depending on the implementation date, the interest rate used, and the factors cited above. These cost measures abstract from business cycle fluctuations in the rate of capacity utilization in the economy. As of this writing, aggregate demand is more than $100 billion below the economy’s potential output at normal rates of capacity utilization. Government and private economists universally predict a period of lower than normal capacity utilization through the end of the decade. Thus the costs of implementing environmental controls at this time are likely somewhat smaller than the estimates which appear above. Finally, of course, policy decisions on the speed of implementation of environmental controls must be based on a comparison of the benefits with the costs. EPA has estimated the annual benefits of air pollution abatement at $14.2 billion 1970 dollars ($19.5 billion 1975 dollars). These benefits may also depend upon the timing of environmental controls. Earlier implementation, for example, may spur technological advances in abatement. Some individuals whose health is adversely affected by pollution may survive to gain the benefits of future medical advances if controls are initiated earlier. Given the uncertainties involved both with these benefit estimates and with our cost estimates, one should be cautious about advocating or critici.zing early tightening of air quality controls. Whatever the appropriate decision regarding immediate initiation of stricter controls, our work does indicate that a much stronger case can be made for implementation over a 5- or lo-year horizon. APPENDIX Al.

Introduction

Our model is a nonlinear general equilibrium model. There are three types of goods in the model : produced nondurables, produced durables, and fixed natural resources. Produced durables have two representations-as a flow of produced

DYNAMIC

AIR CONTROL

COSTS

32;

hoods :u~tl as :L stork consisting of the accumulated How, net, of esog~ous (It>preciation. IJse of the services of any durable or fixed natural resource (either as a factor of production or for direct consumption) is assumed not to deplete the stock. Energy is therefore treated as a produced nondurable. This means that no above-ground inventories of energy may be held, an assumption which appears to be innocuous. Except for pollution abatement,, all technology is Cobb-Doublas with Hicksneutral technical change. Production of energy is subject also to technical regress as a function of the cutilative amount of energy produced since the starting date. This reflects the assumption that progressively more resources are required t,o obtain energy of a given quality since, presumably, the least, expensively mined deposits are exploited first. Pollution abat’ement is assumed to be subject, to diminishing returns to scale. The fraction of hot,al potent,ial pollution emissions (i.e., the amount, which woulcl IW produced at current’ technology if no resources were used in abatement,) which (~1 be abated is assumed to approach 1.O as.ymptotirally :M all fnct,om used in :I,batrment. grow without, bound. The level of ,/jet emissions (t,otxl pot,cnti:kl emissions less abatement) is an exogenously set pollnt,ion standard whirh thtl caconomy is required to achieve. Total emissions is nssllmeci to br :i linear flmction of the output, of produced goods. The demands for all goods, except pollut,ion abatement, are linear in full income (which includes a negat,ive term corresponding t,o the cost, of pollution :d)atement,) and have constant price elasticities holding full income constant. :Zlthough demands for newly produced durables are investment, demands, t,heJ are assumed to depend only on current prices (this is equivalent to assuming that expected future prices depend only on current prices). The existing stock of tlurables cannot be bought or sold. Each demographic group is assumed to be composed of homogenous individuals. Demand functions for each group are specified and scaled to reflect the size of the group. Each group is assumed to own a proportion of the stock of each durable good which depends on the relative size of the group. The size of each demographic> group over time is assumed to be exogenous. The model is set up as a series of equat’ions whirh may he solved numerically by the Crauss4eidcl met,hod. -42.

Notntiou

There are r1goods, excluding pollution abatement. C;ood 1 is energy and good 11 is person years ; the subscript Q + 1 is used to refer to variables connected with pollution or its abatement. Good 1 to kl are produced nondurahles; kl + 1 to lzz are produced durables ; 6, + 1 t’o ks are the stocks of produced durables ; I;, + 1 Do n - 1 are the stocks of fixed natural resources. Kate bhnt X-3= 2k2 - ICI. There are G demographir

groups.

Let Xij(t)

= amount

of good i used to produce good j in period t for i E Cl,

n],

j E CL M U in + 11 and t 2 1 (not’e Xi,+1 is t,he amount of good i used in pollution

abatement)

;

328

DOLDE

ET AL.

J;(L) = output of good j in period t for j E Cl, &I; Ye(t) = total potential pollution emissions in period 2; 70 (1) = net pollution emission allowed in period t; Tilt) = state of Hicks-neutral technical progress in producing good j for j E Cl, Jd U (n + 1) (note T ,L+l is the state of technical progress in producing pollution abatement; T1 also includes technical regress as a function of the sum of all past output of good 1) ; iFi&) = stock of good i held by demographic group g in period t, i E [kz + 1, n + 11, g E [l, G], and t 2 0 (note, -k,+I,, is interpreted as the part of pollution abatement for which group g must pay) ;

xi(t) = 5 -L(O,

i E [k, + 1, n + 11

U=l

( -zTn+l is total pollution

abatement)

;

z;,,(t) = demand for good i by group g in period t, i E [I, nil g E [l, G], t 2 1 (note, for i E [k2 + 1, n], Zi, is the direct, demand for t,hr services of durable goods for consumption purposes) ; I’,@) = price of good i in period t, i c [l, n + 11, t 1 1.

Note that 70 and Tj are exogenous. Also, in any given period zi for i E [kz + 1, n] will be exogenous. (For i E [kz + 1, n - 11, zr; will depend on the previous period’s stock and output; for i = n, the population, gn, and the size of each demographic group, a,,, will be exogenous.) AS. Supply

The production

functions

for goods 1, . . ,, kp are

j E Cl, W,

for

Y,j(i) = Tj(t> fJ Xij(O‘Q

i-l

(1)

where Tj(t)

= T1(0)(1 + Qt-l

exp( -T[

t-1 C Yl(s>ll

for

j=1;tz1

for

j>l;tZl

8=0

= Tj(O)(l

+ Ij)t-l

(2)

where Y,(O) = 0. The parameters Aii are exogenous and we require 2 Aii = 1

i=I

for all

.i E- Cl, ~c21.

Note that Aij is the share of factor i in the total cost of producing equilibrium.

good j in

A4. Demand

The demand functions for demographic

group g are assumed to be given by

n+1

Z+(t)

= [Cig(t)

C .X20(t)PlCOl Ii Pj(QEii l-&+1 i=l

for

iECl,nl; i z kl + 1;

(3a)

DYNAMIC

AIR CONTROL

“I+t %k,,-1 = [ c Xt,(f)Pt(f) - f z=.ks+1

COSTS

f’,(1)Sj,(t)]f~~+,-l.

i=l i#kl+l

:iz!,

i3hj

Here Ci, is a11 exogenous scale factor, and Eij is ~1~0 exogenous. Sote that. the demand function is linear in nominal full income net of pollution t,axes ( C?2i2+ 1 8#t where - J?Tn+l,ois the amount of pollution abatement for which group g must pay). The parameter Ei, is the elasticity of demand for good i with respect to the price of good j holding full income constant. Sote that, because of t’he fact that, demands must he homogeneous of degree zero in a11 prices, we musl 11a\-c

$Eij=

-1

for

i E Cl, 111

j=l

(since Js’~,,~+~ is assumed to be zero). Equation (3b) makes the demand for the first residual. This enforces the budget constraint that come. In this full employment model, saving and equal ex ante. Thus the residual equation is writ,ten invest#ment goods.

I’otrntjial

pollution

emissions, Y 0, are linearly

type of produced durable ~1 total demand equals full ininvestment are automaticall) direct,ly in terms of one of the

related t,o output :

k?

Y,(t)= i=l c &Yi(O. Pollution abatement may be produced using other goods as factors of produrtion :tcnording t,o the following production function : -x’,,,

L(f) = Yo(t)(l

- [ ;I CX~)(--;2,,,+1X’;,,~l(l)~)]‘~l~tl(~)].

(5)

i=l

‘I’hc minus sign on the left-hand side of (3) is consistent with the interpretation of’ --~,+, as pollution abatement so that the cost of this abatement., -J~,,+18,, , Ir will be suht’racted from full income in the demand functions, (3). Not8t: that t,he production function for abatement has an asymptote at, I*,, as 1he inputs of all factors of production grow without bound. Thus, potent&t pollution emissions in this model refers only to those emissions which can bc :&tt,ed. To the extent that there are emissions which cannot be abated, this will not affect behavior and therefore not affect the solutions of the model. Such emissions may be incorporated in, say, an air quality index if desired. The parameters Ai,+ are productivity factors for the inputs. As mentioned in Section A2, TILfl is the state of factor-neut,ral technical progress in producing pollution abatement and is exogenous. Finally, we have that pollution abatement must make up t,he differenc~e l~et.wern t,he net pollut,ion standard, PO, and total emissions: X,,,,(f)

wlrc~rc~f,,(l)

is c~sogenous.

=

f,,(f)

-~

r-,,(f),

(ii I

330

DOLDE

ET AL.

A6. Demographics

The demographics in this model are exogenous and affect only the demand functions. All consumers are assumed to have the same full-income-held-constant price elasticities (the Eij) regardless of demographic group. Demographic effects on demand are incorporated in the constants Ci, for i E [l, n] and g E [l, G] and in the distribution of the stocks of durables across demographic groups. In particular, we assume xng(t) is exogenous for g E [l, G], Zig(t)

= k&)xi(t)

(7)

for i E [kz + 1, n - l] U (n + 11 and

g E Cl, ‘3, where h,(t)

= fig[Xng(t)/Zn

and fig is an exogenously specified function 5 fj, E 1, 0-I

for

(1)J

(8) (9)

with the property

that

i E [ii2 -I- 1, n - 11 u {n + 11.

A?‘. Dynamics

The dynamics of the model are very simple : stocks of produced durables decay exponentially at an exogenous rate and are augmented by the output of produced durables; fixed natural resource stocks are constant over time : .Qt>

= (1 - s,)Si(t ,- 1) + Yi-k*+k,(t - 1)

ai

= Xi(O)

for i E [k2 + ‘1, k31,

for i E [JCB+ 1, n - 1 J,

(10) (11)

where 6i is the exogenous depreciation rate for good i. Expectations of prices and quantities for future periods do not enter the model explicitly. Alternatively, expectations may be said to be static at current period levels; the current period is always viewed as being a long run equilibrium. Speaking rigorously, the interest rate reflecting opportunities for interperiod transfer of purchasing power, ought to include capital gains/losses as well as the net marginal productivity of capital. Capital gains/losses are not anticipated by investors in this model, given the expectations mechanism. Thus the interest rate here might be defined as P5/Pa - 6. In any event, it has no direct intertemporal substitution effect on capital formation. A8. Equilibrium

The equilibriurri‘ conditions Xi&)

= Ai,Pi(t)

Y&)/Pi(t)

for the model can be simply stated as for

iECl,n3,

jECl,kzl;

(12)

xi,,+](t) = ([X,+,(t) + Yo(t)1T,+l(t)P,+l(t)A~,,+~/2Pi(t>}2 for

i E Cl, nl;

(13) (14)

DYNAMIC

yi(t)

= ;

AIR CONTROL

Zig(t) + g xii(t)

g=l

for

COSTS

:I:3 1

i E Cl, hl;

(15)

j=l

xi(t) = 5 Zi,(t) + Z Xij(t> u=l

06)

j=l

Equations (12) and (13) are the marginal conditions for productive efficiency for all produced goods and for pollution abatement, respectively. Equation (14) states that the price of pollution abatement must equal the average cost. Equations (15) and (16) equate supply and demand for produced goods and services of the stocks of durables, respectively. By Walras’ law, one of the equilibrium conditions in (15) or (16) is redundant, and may be dropped. 11.9. Solution oj the Model The model is solved numerically for the endogenous variables by the Gauss-Seidel method. Given values for the parameters and exogenous variables, t#hc method requires an initial estimate of the solution and one equation for each endogenous variable in which that variable is expressed as a function of any of the other variables not including itself. In order to reduce the model to “Gauss-Seidel Form,” we require equations for PI(t), . . . , Pl,-l(t). These are constructed by MI)stit,uting Eqs. (12) into Eqs. (1) to obtain /‘j(t)

= [ ii pi(t)A’i,‘Tj(t) i=l

fi &j”i~]‘i(‘-“i~)

for

i=l

j E CLM,

(17)

i#J

and by substituting f’;(t)

(12) into (16) to get

= 2 iiijPj(t)Yj(t)/[Xi(t)

-

Then Eqs. (3), (4), (A), (12)-(18)

‘I’he numerical I)arameterization

5 ZiY(t)]

for

l/=1

j=l

exercises reported of the model :

form the required set.

in Section 3 are h:wed upon the following

0, potential pollution 0 = potential air pollution 1 to ICI produced nondurables 1 = energy 2 = consumer and government tangible goods 3 = consumer and government services k1 + 1 to kz, produced durables 4 = investment goods bz + 1 to li3, stocks of produced durables 5 = ca:tpit.:d st oak

DOLDE

332

ET AL.

k~ to n - 1, stocks of fixed natural resources 6 = stock of land n, population 7 = population (person years available for labor and leisure) n + 1, abatement 8 = pollution abated. Demographic

groups 1 to G: 1 = 20-65 years old, 2 = 65 and over.

Children aged O-19 own no land or capital, supply no labor, receive no income, and do not have independent demand functions. Their consumption is provided for by group 1. The Cil proportionality factors in the demand functions for group 1 are linear in the ratio of the child population (a,s) to the group 1 population (x71) :

CiI = CAiI + CKiI(2G3/m. It is not possible to account explicitly for the ownership of capital and land by We have instead assumed each owns a fraction kil groups 1 and 2 individually. and ki2, respectively, given by

Pollution

tax liabilities

\Vorking-Age

of the two groups are indicated

by analogous notation.

Adult Demand Coefficients (Cd;,), Chid Demand Coefficients and Retired Persons Demand Coefficients (C~Z) i

C-4,1

CKil

Ci2

2 3 6 7

0.675 0.276 0.021 0.5

0.18 0.068 0 0

1.44 0.595 0.0151

Demand Coefficients for Group 1 for Selected Years

t

CZl

C31

Cdl

CT1

1972 1975 1980 1985 1990 1995 2000

0.80 0.80 0.78 0.77 0.76 0.76 0.76

0.32 0.32 0.31 0.31 0.31 0.31 0.31

0.021 0.021 0.021 0.021 0.021 0.021 0.021

0.5 0.5 0.5 0.5 0.5 0.5 0.5

(CKil),

DYNAMIC

AIR CONTROL

COSTS

3x3

Elasticit,ies of Demand (Eij) (the i - jth Entry is the Elasticit~y of Demand for Good i with Respect to the Price of Good j) i

j I

2

3

4

.i

6 ~~-- -.__.

-___ 2

0

3 6 7

0 0 0

___~

-0.5 0.167 0.1 -0.1

0.15 -0.7 0.067.5 0.08

0 0 0 0

Share Parameters (01,) __---. 5 6

__-i

Distributive

0 0 0 0

Shares for Capital and Pollution

t

0.004 0.003 -0.8 -0.05

8

Tax by Demographic .-.. -~

Capital

IQ72 1975 1980 1Q85 1990 1995 2000

.-.

Groups for Selected Yearsa -~ Pollution tax

Group 1

Group 2

Group 1

0.63 0.63 0.625 0.62 0.61 0.61 0.615

0.37 0.37 0.375 0.38 0.39 0.39 0.385

0.88 0.88 0.s7.i 0.875 0.87 0.87 0.87

-..__

Group 2 0.12 0.12 0.12.1 0.12.5 0.13 0.13 0.13

cLShares for land are t,he same as those for capit,al.

Population,

-

1972 1975 1980 1983 1990 1995 2000

111a 118 130 141.5 147.3 152 157

Capital Sock, and Land

20.5a 21.9 24.3 26.7 28.8 30 30.2

a Millions of people. b Capital stock for 1973-2000 is endogenous.

76..>& 75.2 73 70.8 71.9 74.3 76.3

208 215 227 239 248 237 263.5

3429* NA NA NA NA NA NA

844 844 844 844 844 844 844

DOLDE

334

ET AL.

Factor Share Matrix i

(Aii) j

1 5 6 7

1

2

3

4

8

0.21 0.35 0.14 0.30

0.06 0.21 0.06 0.67

0.03 0.33 0.09 0.55

0.06 0.32 0.09 0.53

0.0029 0.0082 0.0005 1 .oooo

Technical

Change Parameters

2 3 4

15.0 3.5 3.63

0.015 0.015 0.015

8

4.5

0.015

Pollution

Generation

r = 0.002 65 = 0.03

Coefficients

(di)

i

1

2

3

4

di

0.22

0.009

0.008

0.006

Net Emission Standards For 1972-1975 For 1976-2000

(8,) 15.0 3.6

REFERENCES 1. “Steel and the Environment: A Cost Impact Analysis,” Arthur D. Little, Inc., New York (1975). 2. M. K. Evans, A forecasting model applied to pollution control costs, Amer. Econ. Rev. 63, 244-252 (1973). 3. Environmental Protection Agency, “The Economics of Clean Air,” U. S. Government Printing Office, Washington, D. C. (1972). 4. Environmental Protection Agency, “The Cost of Clean Air,” U. S. Government Printing Office, Washington, D. C. (1973). 5. Environmental Protection Agency, “The Economics of Clean Water,” U. S. Government Printing Office, Washington, D. C. (1973). 6. L. B. Lave, “The Costs and Benefits of Air Pollution Abatement,” Statement Before the Committee on Science and Technology, processed (1975). 7. L. B. Lave and L. P. Silverman, Economic Costs of Environmental Pollution, processed (1975). 8. D. M. Meadows, D. L. Meadows, J. Randers, and W. W. Behrens, “The Limits to Growth,” Universe Books, New York (1972). 9. “1975 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds,” Social Security Administration, Baltimore (1975).