Coal Pricing Methodology for the Annual Energy Outlook 1998

Coal Pricing Methodology
for the Annual Energy Outlook 1998

by
Michael Mellish

Coal supply curves, representing the relationships between the minemouth prices of coal and the corresponding quantities of annual production, are a necessary component of the Energy Information Administration’s (EIA) mid-term energy forecasting system. This paper discusses the revised coal pricing methodology used for the projections presented in the Annual Energy Outlook 1998 (AEO98). In previous EIA forecasts, coal prices were estimated through an approach that made use of both econometric and engineering methodologies. Econometric equations related minemouth coal prices to changes in capacity utilization, labor productivity, wages, and fuel costs. Additionally, engineering cost equations and data and assumptions regarding U.S. coal reserves were used to adjust minemouth coal prices for the impacts of reserve depletion on future mining costs and to determine the least-cost supplies of new mining capacity. The new econometric methodology relates minemouth prices for specific coal-producing regions and mine types to a set of independent variables that include coal production, labor productivity, wages, fuel costs, and the costs of capital equipment. The methodology avoids problems related to the limited availability of capacity utilization data, has a simpler functional form, and more accurately captures the regional relationships between prices and labor productivity. The discontinued use of engineering cost equations for estimating the impacts of reserve depletion on mining costs reflects EIA’s concerns about the substantial level of resources required for updating the equations and the inherent uncertainties in the projected cost estimates.

Background
Data and Trends: Coal Industry Prices, Production, Labor Productivity, and Factor Input Costs
Description of the Econometric-Based Coal Pricing Methodology
AEO98 Results
Appendix A: Regression Results and the AEO98 Coal Pricing Equation

Background

The Coal Market Module (CMM) of the National Energy Modeling System (NEMS) provides annual projections of U.S. coal production, distribution, and prices. In addition, the international component of the CMM provides projections of annual world coal trade flows from major supply to major demand regions, generating regional forecasts of U.S. coal exports. The core component of the CMM is the Coal Distribution Submodule (CDS), which determines the least-cost supplies of coal (minemouth price and transportation cost) to meet a given set of U.S. coal demands by sector and region. Minemouth coal prices are obtained from a set of regional supply curves generated by the CMM’s Coal Production Submodule (CPS). Domestic production and distribution of coal are projected for 11 supply regions and 13 demand regions.

This article focuses on the data and methodology used for estimating the econometric equation upon which the regional CPS supply curves are based. In general, the CPS produces annual econometric-based coal supply curves, representing the relationships between the minemouth prices of coal and the corresponding quantities of annual production. A separate supply curve is provided for all significant production by mine type (underground and surface), coal rank (bituminous, subbituminous, and lignite), coal grade (steam or metallurgical), and sulfur category in each of the 11 supply regions. Twelve coal types are represented in the CPS, reflecting unique combinations of coal rank, coal grade, sulfur content, and mine type. For the Annual Energy Outlook 1998 (AEO98), U.S. coal supply was represented with a total of 34 supply curves (Table 1). By region, Northern Appalachia was represented with eight supply curves, the most of any of the regions. The Western Interior, Dakota Lignite, and Northwest regions were represented with a single supply curve for each region.

The methodology for estimating coal supply curves for AEO98 reflects revisions from the one used for previous editions of the Annual Energy Outlook. The econometric methodology developed for AEO98 relates minemouth prices in each coal-producing region represented in the CPS to a set of independent variables that include coal production, labor productivity, wages, fuel costs, and the costs of capital equipment.

Previously, coal prices were estimated through an approach that incorporated both econometric and engineering methodologies. Econometric equations related minemouth coal prices to changes in capacity utilization, labor productivity, wages, and fuel costs. Additionally, mine engineering cost equations and data and assumptions about the quantities, distribution, accessibility, and recoverability of coal reserves were used to adjust minemouth coal prices for the impacts of reserve depletion on mining costs and to determine the least-cost supplies of new mining capacity.

Table 1. Number of Coal Supply Curves by CMM Region and Mine Type

CMM Supply Region			States	Deep	Surface	Total
1	NA	Northern Appalachia	PA, OH, MD, WV (north)	4	4	8
2	CA	Central Appalachia	WV (south), KY (east), VA	3	2	5
3	SA	Southern Appalachia	AL, TN	3	2	5
4	EI	Eastern Interior	IL, IN, KY (west)	2	2	4
5	WI	Western Interior	IA, MO, KS, AR, OK, TX (bituminous)	0	1	1
6	GL	Gulf Lignite	TX, LA	0	2	2
7	DL	Dakota Lignite	ND, MT (east)	0	1	1
8	PG	Powder and Green River Basins	WY, MT (west)	1	2	3
9	RM	Rocky Mountain	CO, UT	1	1	2
10	ZN	Southwest	AZ, NM	0	2	2
11	AW	Northwest	AK, WA	0	1	1
U.S. Total				14	20	34
Source: Energy Information Administration, Office of Integrated Analysis and Forecasting.

The revised econometric methodology differs from that used for the Annual Energy Outlook 1997 in that it incorporates production rather than capacity utilization as an independent variable, and it provides for regional variation in the coefficient for the labor productivity term. Also, the regression model for AEO98 was estimated using additional years of data. The effects of reserve depletion on mining costs are implicitly captured through the labor productivity variable, replacing the previous use of engineering cost equations for explicitly estimating these costs.

The new econometric approach represents an improvement over the previous methodology in several ways: (1) the substitution of production for capacity utilization as a variable allows the use of additional years of data (see below); (2) the regional variation in the coefficient for the labor productivity term provides a more accurate representation of the relationships between minemouth prices and productivity; and (3) the model has a simpler functional form, providing more stable forecasts of coal prices over time than the previous equation.¹

Use of Production in Place of Capacity Utilization as an Explanatory Regression Variable

The replacement of the capacity utilization term with production in the AEO98 coal pricing model reflects, in part, issues regarding the limited years of available data for capacity utilization. Capacity utilization data for U.S. coal mines, as collected on the Form EIA-7A, “Coal Production Report,” are available for 1979 through 1986 and for 1991 through 1996. These two sets of data, however, provide two distinctly different measures of capacity utilization. Capacity utilization data for 1979 through 1986 are based on estimates of daily productive capacity, whereas more recent capacity utilization data are based on estimates of annual productive capacity. For 1987 through 1990, estimates of daily productive capacity were collected, but, because the data were not to be published, they did not go through a complete data verification process.

For 1979 through 1986, EIA’s “Coal Production Report” survey questionnaire requested that mine operators “Report the maximum amount of coal that realistically could be/was produced on any day during the year.” EIA then calculated the annual productive capacity for each mine by multiplying reported daily productive capacity by the reported number of production days worked during the year.² The capacity utilization data reported in EIA publications are the ratios of reported annual production divided by the resultant estimates of annual productive capacity.

For 1991 through 1996, U.S. coal mines were requested to “Report the maximum amount of coal that your mining operation could have produced during the year with the existing mining equipment in place, assuming that the labor and materials sufficient to utilize the equipment were available, and that the market existed for the maximum production.” Annual capacity utilization was calculated directly as the ratio of reported coal production for the year divided by reported annual productive capacity.

As shown in Figure 1, capacity utilization at the national level differs considerably for the two time periods. In general, estimates of capacity utilization are substantially higher for 1979 through 1986. In part, the higher utilization rates for the earlier period can be attributed to the limitation that the reported number of days worked during the year represented the number of days used to calculate annual productive capacity. The capacity data collected for the years 1991 through 1996 do not incorporate this restriction. As a result, the previous coal pricing model incorporating capacity utilization as an independent variable was restricted to the 8 years (1979 through 1986) for which a consistent set of capacity utilization data was available. This limitation restricted the updating of the model with more recent data and raised issues about basing a forecast through 2020 on only a few years of data. In addition, short-run disequilibria in markets, which can lead to substantial changes in an industry’s capacity utilization, do not typically extend beyond a few years. Therefore, the inclusion of a capacity utilization term in a relatively long-term forecast, such as the AEO, is difficult to justify.

Figure 1. Capacity Utilization at U.S. Coal Mines, 1979-1996

These concerns led to the consideration of coal production data that are: (1) available for an extended time period and (2) consistent across all years. Also, there is solid economic rationale for the inclusion of production as an explanatory variable in a coal pricing model. In the economics literature, it is well established that supply curves for most products are upward sloping; thus, one should expect to observe a direct relationship between the quantity of a product supplied and its price, all other factors being held constant.

Estimating Cost Impacts of Reserve Depletion

The decision to discontinue the use of engineering cost equations for estimating the impacts of reserve depletion on future mining costs reflected EIA’s concerns about the substantial level of resources required for updating the equations, as well as the uncertainties inherent in the estimates. In essence, the engineering cost equations that had been developed by EIA represented an effort to estimate the incremental costs associated with the differences in geologic conditions of new mines versus existing mines, holding constant factor input costs, labor productivity, and technology. However, observed productivity data reported by mining operations over time reflect a combination of factors that include, but are not limited to: (1) technological change; (2) economies of scale; (3) more (or less) efficient use of personnel and equipment; (4) the overall skill level of the workforce; and (5) reserve depletion.

In the approach adopted for AEO98, the effects of reserve depletion on future mining costs are implicitly captured through the labor productivity assumptions. This approach recognizes that observed levels of labor productivity over time are a function of a variety of factors, which include changing geologic conditions. Projected levels of labor productivity by region and mine type are an exogenous input to the CPS. For AEO98, projected productivity growth rates by region and mine type vary in accordance with historical trends. In the previous methodology, projected increases in labor productivity primarily reflected technological improvements. Impacts on future levels of labor productivity and mining costs from reserve depletion were captured through the engineering cost equations.

Data and Trends: Coal Industry Prices, Production,
Labor Productivity, and Factor Input Costs

The econometric model of the U.S. coal industry developed for AEO98 relates historical trends in the average price of coal at mines to a set of supply-side factors that include production, labor productivity, wages, fuel costs, and the costs of capital equipment. All prices, price indices, and wages in nominal dollar terms were converted to constant 1992 dollars using the implicit gross domestic product (GDP) deflator. The model includes annual data for 10 CPS supply regions and 2 mine types (surface and underground) for the years 1978 through 1994.³ In all, the data set includes 255 observations, reflecting 17 years of data and 15 observations per year (10 surface and 5 underground).

The time period represented has seen substantial changes in factors affecting both the supply and demand for coal. While both supply- and demand-side factors are addressed in the coal pricing equation developed for AEO98, the discussion in this section focuses on the factors directly affecting the supply and costs of coal. The following sections provide information about the source and measure of each supply-side variable used in the coal pricing model, along with a brief review of the time trend for each variable.

Data

Data on the average price of coal at mines, production, and labor productivity are obtained from various issues of EIA’s Coal Production and Coal Industry Annual reports. To avoid disclosure of individual company data, coal price data for several States are not published, and those data are also excluded from the model.⁴ The States for which data were excluded were Maryland, Tennessee, Iowa, Missouri, Kansas, Arkansas, Louisiana, South Dakota, Arizona, Washington, and Alaska. Together, these States accounted for 2.7 percent of total production in 1996. In several other States (Indiana, Oklahoma, Montana, Wyoming, and New Mexico), data for underground mines were combined with data for surface mines. The combined data for these States were represented as surface-minable coal in the regression model.

The average price of coal at U.S. mines, in nominal dollars per ton,⁵ is calculated by dividing the total value of the coal produced at a mine by its total reported production. U.S. coal mines report their total production and the total free on board (f.o.b.) mine value⁶ of the coal produced. Reported coal production represents primarily the marketable product after preparation, which is either equal to or less than run-of-mine output. Calculated prices exclude data from mines producing less than 10,000 tons of coal during the year, which are not required to report information on the total mine value of coal produced. Data on U.S. coal production used in the coal pricing model, however, include production from mines producing less than 10,000 tons of coal during the year, as production quantities are not considered proprietary data.

Labor productivity (measured in tons of coal produced per miner hour) is calculated by dividing total reported production by the total direct labor hours by all employees engaged in production, preparation, processing, development, maintenance, repair, and shop or yard work at mining operations. Calculated productivity excludes data from mines producing less than 10,000 tons and preparation plants with less than 5,000 employee hours, which are not required to provide data on labor hours.

Data on the average annual wage for the U.S. coal industry are obtained from the U.S. Department of Labor, Bureau of Labor Statistics (BLS). The data are compiled and published by the BLS as part of its “Covered Employment and Wages,” or ES-202, program. The primary source of the statistics is the quarterly tax reports submitted to State employment security agencies by employers subject to State unemployment insurance laws. Unlike EIA’s “Coal Production Report,” which focuses on workers directly involved in the production and preparation of coal, ES-202 data also include coverage of corporate officials, executives, clerical workers, and other office workers. Annual average wages are calculated as the reported total annual wage bill submitted by a reporting economic unit divided by the reported number of employees. Coal industry data are available by State for 1975 through 1996, and by State and mine type (for a majority of States) for 1988 through 1996. State-level data were used for the AEO98 coal pricing equation, because of the need for a continuous data series for the entire period covered by the regression.

Fuel costs in the coal pricing equation are represented with a national-level price series for No. 2 diesel fuel. The specific series selected for the regression is the average annual refiner price of No. 2 diesel fuel to all users, as published in EIA’s Petroleum Marketing Annual. According to data published by the U.S. Department of Commerce, diesel fuel represented more than 40 percent of the fuel costs at U.S. surface mines in 1992 and an estimated 11 percent of the fuel costs at underground mines.⁷

The producer price index (PPI) for mining machinery and equipment is obtained from the BLS. The PPI targets the output of U.S. companies, excluding products produced by foreign manufacturers. Producers are selected for the survey through a systematic sampling from a listing of all firms that file with the Unemployment Insurance System.⁸ The PPI for mining machinery and equipment includes the manufacture of complete machines and component parts by establishments primarily engaged in the manufacture of heavy machinery and equipment for the mining industry. This price index, in conjunction with the yield on utility bonds, was used in constructing the regression variable representing the annualized user cost of mining equipment.

The variable PCAP, representing the annualized user cost of mining equipment,⁹ is calculated as follows:

where r is a proxy for the real rate of interest, equal to the yield on utility bonds minus the percentage change in the implicit GDP deflator; d is the rate of depreciation on mining equipment, assumed to equal 10 percent; and p_t is the PPI for coal mining equipment, adjusted to constant 1992 dollars using the GDP deflator. The three terms represented in the annual user cost of mining equipment are defined as follows: rp_t is the opportunity cost of having funds tied up in mine capital equipment; dp_t is the compensation to the mine owner for depreciation; and ((p_t - p_t-1)/p_t-1)p_t is the capital gain on mining equipment (in a period of declining capital prices, this term will take on a negative value, increasing the user cost of capital for year t).

Trends

Between 1978 and 1996, the average mine price of coal in the United States declined by 61 percent, in constant 1996 dollars, from $47.31 per ton in 1978 to $18.50 per ton in 1996 (Figure 2). During the same period, total U.S. coal production increased by 59 percent, from 680 million tons in 1978 to 1,064 million tons in 1996. The inverse relationship between the production of coal and its price over time is attributable to a host of factors, including gains in labor productivity and declines in factor input costs.

Figure 2. U.S. Coal Production and Prices, 1978-1996

Productivity has had a profound effect on competition in the U.S. coal industry. Between 1978 and 1996, labor productivity at U.S. mines rose from 1.77 tons per miner hour to 5.69 tons per miner hour, representing an increase of 6.7 percent per year. This growth contributed to a downward shift in costs over time, making additional quantities of coal available at lower prices. A graphical representation of labor productivity and the average price of coal at mines for the observations (unique combinations of region, mine type, and year) represented in the AEO98 coal pricing model indicates the strong historical correlation between prices and productivity (Figure 3). Figures 4 and 5 show the price and productivity data for two key coal-producing regions, Central Appalachia (underground mines) and the Powder River Basin. In 1996, these regions accounted for 16 percent and 30 percent of total U.S. coal production, respectively.

Figure 3. Minemouth Coal Prices and Labor Productivity for CMM Regions and Mine Types, 1978-1996

Figure 4. Average Mine Price of Coal for Selected CMM Supply Regions, 1978-1996

The large differences in productivity and price levels between regions reflect, to a large extent, the substantial geologic variation in mining conditions. Underground mines in Central Appalachia operate in relatively thin coal seams (average thickness of 4.7 feet in 1996) and generally employ continuous mining equipment to extract the coal. In the underground mines of Northern Appalachia and the Rocky Mountain region, thicker seams (5.8 and 10.7 feet, respectively, in 1996) are more amenable to the use of more efficient longwall mining equipment. In 1996, longwall mines accounted for only 18 percent of the coal produced from underground mines in Central Appalachia, as compared with 77 and 86 percent of the coal produced from underground mines in the Northern Appalachia and Rocky Mountain regions, respectively.

Figure 5. Average Coal Mine Labor Productivity for Selected CMM Supply Regions, 1978-1996

The surface mines of the Powder River Basin have large reserves of low-Btu, low-sulfur coal in very thick seams (average thickness of 61.2 feet in 1996) with low overburden ratios (cubic yards of overburden per ton of coal contained in the seam). Although production costs are very low, the region’s coal is situated far from the major coal markets and has only recently been able to compete with higher ranked coals from the Eastern Interior and Appalachian regions. Declining coal transportation rates and restrictions on emissions of sulfur dioxide at electric utility plants are other important factors that help to explain the rapid rise in the region’s share of total U.S. coal production, from 13 percent in 1978 to 30 percent in 1996.

Factor input costs follow a significantly different path over time from that of labor productivity (Figure 6). Diesel fuel prices and the user cost of mining equipment and machinery have declined considerably since the mid-1980s, but they have increased sharply in prior years of the decade. Annual coal industry wages in constant dollars have varied by only minor amounts since 1984. In 1996, average annual wages in the coal industry (in constant dollars) were only 13 percent above the 1978 level. Figure 7 compares national-level annual wage data with regional-level data for Central Appalachia and the Powder River Basin. This figure indicates that while mine wages vary substantially by region, the overall trends in wages follow a similar path over time (i.e., rising over the early years of the historical period but remaining constant during the later years).

Figure 6. Diesel Fuel Prices, Annual Coal Industry Wages, and User Cost of Mining Equipment, 1978-1996

Figure 7. Average Annual Wage in the U.S. Coal Industry for Selected CMM Supply Regions, 1978-1996

Description of the Econometric-Based Coal Pricing Methodology

The primary criteria guiding the development of the AEO98 coal pricing model were that the model should conform to economic theory and that parameter estimates should be unbiased and statistically significant.¹⁰ Following economic theory, an increase in output or factor input prices should result in higher minemouth prices, and increases in coal mining productivity should result in lower minemouth prices. In addition, the model should account for a substantial portion of the variation in minemouth prices over the historical period of study.

The model of the U.S. coal market developed for the CPS recognizes that prices in a competitive market are a function of factors that affect both the supply and demand for coal. The general form of the model is that a competitive market converges toward equilibrium, where the quantity supplied equals the quantity demanded:

In this equality, Q_i,j,t represents the long-run equilibrium between supply and demand in a competitive market.

The formal specification of the coal pricing model for AEO98 is as follows. For demand:

equ3.jpg (8119 bytes)

For supply:

The demand-side variables are as follows:

Q^D is the quantity of coal demanded from region i, mine type j, in year t in million tons.

TRAN is a producer price index for the cost of transporting coal in region i to the regions where it is consumed for each year t. The index is adjusted to constant 1992 dollars.

ELEC is an index of electricity generation requirements for each year t.

INDUSTRY is an index of industrial output for each year t.

OTHPROD is the total U.S. coal production in million tons minus coal production for region i and mine type j for each year t.

EXPORTS is the level of U.S. coal exports in million tons in year t-1.

PGAS is the delivered price of natural gas to the utility sector in constant 1992 dollars per thousand cubic feet.

WOP is the world oil price in constant 1992 dollars per barrel in year t.

STOCKS is the quantity of coal inventories held by U.S. electric utilities in million tons at the beginning of year t.

BTU_TON is the average heat content of coal receipts at electric utility plants in million Btu per ton for region i in year t.

CAA is a dummy variable representing the impact of the Clean Air Act Amendments of 1990, equal to 1 if year is greater than 1990, and zero otherwise.

e^D is a random error term corresponding to the demand function for region i and mine type j in year t.

The supply-side variables are as follows:

P is the minemouth price of coal in constant 1992 dollars for region i and mine type j in year t.

Q^S is the quantity of coal supplied from region i, mine type j, in year t in million tons.

TPH is the average annual labor productivity of coal mines in tons per miner hour for region i and mine type j in year t.

WAGE is the average annual coal industry wage in constant 1992 dollars for region i in year t.

PCAP is an index representing the annualized user cost of mining equipment in year t. The index is adjusted to constant 1992 dollars.

PFUEL is the average annual refiner price of No. 2 diesel fuel to end users in constant 1992 cents per gallon in year t.

e^S is a random error term corresponding to the supply function for region i and mine type j in year t.

In this model, the amount of coal demanded from region i and mine type j in year t is determined by the minemouth price of coal, the cost of transporting the coal to market, electricity generation, industrial output, coal exports, the total quantity of coal produced in other regions, the price of natural gas, the world oil price, the level of coal stocks, the heat content of the coal, and the regulatory regime as proxied by the passage of the Clean Air Act Amendments of 1990 (CAAA90). On the supply side of the market, the minemouth price is assumed to be determined by the quantity of coal produced, the level of labor productivity, the average level of wages, the annualized cost of mining equipment, and the cost of fuel used by mines.

Estimation Methodology

The supply function for coal cannot be evaluated in isolation when the relationship between quantity and price is being studied. The solution is to bring the demand function into the picture and estimate the demand and supply functions together. For the AEO98 coal pricing model, the two-stage least squares (2SLS) methodology was selected for estimating the set of simultaneous equations representing the supply and demand for coal.

The rationale for using 2SLS rather than ordinary least squares (OLS) results from the structure of equations (1) and (2). In equation (2), the error term in the supply equation (e^S) affects the minemouth price (P); however, in Equation (1), price influences the quantity demanded (Q^D). As a result, the quantity of coal supplied (Q^S) on the right-hand side of the supply equation is correlated with the error term in the same equation. This violates one of the fundamental assumptions underlying the use of OLS, namely, that the error term is independent from the regressors. As a result, the OLS estimator will not be consistent.

In addition, while WAGE, PCAP, and TPH are all hypothesized to affect the price of coal, they are also affected by the price of coal. For example, an increase in the price of coal resulting from increased demand for coal may affect the wages paid in the coal industry, as well as the cost of mining equipment. Prices may also influence the level of productivity. If prices decrease (increase), marginal mines are abandoned (opened), increasing (lowering) labor productivity. This violates the assumption underlying the use of OLS, making it an inappropriate method by which to estimate the supply function.

An accepted solution to the problem of biased least squares estimators is the use of 2SLS, where the objective is to make the explanatory endogenous variable uncorrelated with the error term.¹¹ This is accomplished in two stages. In the first stage of the estimation, the endogenous explanatory variables are regressed on the exogenous and predetermined variables. This stage produces predicted values of the endogenous explanatory variables that are uncorrelated with the error term. The predicted values are employed in the second stage of the technique to estimate the relationship between the dependent endogenous variable and the independent variables. The results from the second-stage (structural) equation represents the model implemented in the CMM for AEO98. The first stage (reduced form) equations are used only to obtain the predicted values for the endogenous explanatory variables included in the second stage, effectively purging the demand effects from the supply-side variables.

The structural equation for the coal pricing model was specified in log-linear form using the variables listed above. In this specification, the values for all variables (except the constant term) are transformed by taking their natural logarithm. All 255 observations were pooled into a single regression equation. In addition to the overall constant term for the model, intercept dummy variables were included for all regions except Central Appalachia. Regional slope dummy variables were included for the productivity and production variables to allow the coefficients for those terms to vary across regions and mine types. The Durbin-Watson test for first-order positive autocorrelation indicated that the hypothesis of no autocorrelation should be rejected. As a consequence, a correction for serial correlation was incorporated. The statistical results of the regression analysis and the equation used for predicting future levels of minemouth coal prices by region, mine type, and coal type are provided in the Appendix.

In general, the results satisfy the performance criteria specified for the model. Indicative of the high R² statistic, there is a close correspondence between the predicted and actual minemouth prices. Moreover, all parameter estimates have their predicted signs and, with the exception of the diesel fuel price term, are generally statistically significant. Some of the regional and mine type specific variables for the productivity term are insignificant, but in most cases the parameter estimates for these variables are relatively small.

Average annual seam thickness by region and mine type also was tested as a supply-side variable. The model results, however, did not support the hypothesis that decreases (increases) in seam thickness have exerted upward (downward) pressure on prices.

AEO98 Results

For AEO98, the econometric pricing equation together with projected levels of labor productivity, miner wages, capital costs, fuel prices, and lagged minemouth coal prices were used to estimate minemouth prices of coal by region, mine type, and coal type for different levels of production. Current and lagged (one-year) projections of the explanatory variables were obtained from other components of NEMS or were supplied as exogenous inputs. Projected values for coal production and the lagged minemouth coal price were obtained from the Coal Distribution Submodule, and diesel fuel prices were supplied by the Petroleum Market Module of NEMS. Projected values for the remaining factors (labor productivity, wages, and the user cost of capital) were supplied as exogenous inputs.

In the reference case, wages and the user cost of capital are assumed to remain unchanged in constant dollars. Productivity improvements are assumed to continue but to decline in magnitude over the forecast period. On a national basis, labor productivity increases at an average rate of 2.0 percent per year over the whole forecast, declining from an annual rate of 5.8 percent in 1996 to a rate of approximately 1.6 percent per year over the 2010 to 2020 period.

The forecasts of labor productivity (in short tons per miner hour) and the minemouth price of coal are shown in Figures 8 and 9. In the AEO98 reference case, the national-level minemouth coal price is projected to fall from $18.50 per ton in 1996 to $13.27 per ton by 2020, a decline of 1.4 percent per year. This price drop reflects both regional changes in production patterns and changes in factors affecting the costs of production, primarily increases in productivity. In the reference case, approximately 40 percent of the projected price decline is due to regional changes in production, and the remainder is accounted for by factors affecting the costs of production.

Figure 8. Average Labor Productivity at U.S. Coal Mines, 1978-2020

Figure 9. Average Price of Coal at U.S. Mines, 1978-2020

Figures 10 and 11 show price and productivity projections for two representative supply curves: medium-sulfur steam coal from underground mines in Central Appalachia, and low-sulfur subbituminous coal from surface mines in the Powder River Basin. These figures clearly demonstrate the inverse relationship between productivity and price as represented in the coal pricing equation.

Figure 10. Average Mine Price of Coal for Selected CMM Supply Curves, 1996-2020

Figure 11. Average Coal Mine Labor Productivity for Selected CMM Supply Curves, 1996-2020

For the Central Appalachia supply curve, prices are projected to decline by 0.7 percent per year, from $26.15 per ton in 1996 to $22.07 per ton in 2020. Productivity increases by 1.1 percent per year, from 3.16 tons per hour in 1996 to 4.09 tons per hour in 2020. Production remains relatively unchanged, increasing from 70 million tons in 1996 to 83 million tons in 2000, but returning to 70 million tons in 2020.

The regression coefficient for the labor productivity term for Central Appalachian underground mines is 0.728.¹² This coefficient indicates that a 1-percent increase in labor productivity will result in a 0.728-percent decline in the minemouth price of coal, all other factors held constant. In the AEO98 reference case, a 1-percent increase in labor productivity for the Central Appalachian supply curve corresponds to a somewhat lower price decline of 0.65 percent. The slightly reduced effect on prices reflects the additional impacts from changes in production and diesel fuel prices and the moderating effects of the lagged terms incorporated to correct for serial correlation.

For the Powder River Basin supply curve, prices are projected to decline by 0.7 percent per year, from $6.43 per ton in 1996 to $5.41 per ton in 2020. Productivity increases by 1.1 percent per year, from 31.11 tons per hour in 1996 to 40.29 tons per hour in 2020. Production more than doubles, increasing from 281 million tons in 1996 to 568 million tons in 2020.

The regression coefficient for the labor productivity term for Powder River Basin surface mines is -0.996.¹³ This coefficient indicates that a 1-percent increase in labor productivity will result in a 0.996-percent decline in the minemouth price of coal, all other factors held constant. For the Powder River Basin supply curve shown in Figures 10 and 11, a 1-percent increase in labor productivity corresponds to a decline in the minemouth coal price of 0.66 percent. A larger decline in the minemouth price of coal would have been projected for this region and coal type had not coal production for the supply curve doubled over the forecast period. Because the regression coefficient for the production term for Powder River Basin surface mines is 0.117, a 1-percent increase in production results in a 0.117-percent increase in the minemouth price of coal.

Post-AEO98 Updates and Revisions

Database Updates and Revisions

Following the completion of AEO98, work was initiated to improve the quality of the database that will be used to update the regression for AEO99. Data for 1995 and 1996 will be added as will additional data series for sulfur content, utility shipments by type of purchase (spot and contract), and electricity prices.

Data for coal minemouth prices, labor productivity, and production, originally entered from data published in various issues of Coal Production and the Coal Industry Annual, will be replaced with data obtained directly from the EIA-7A, “Coal Production Report,” database files. Likewise, data for utility receipts of coal (quantities and average quality) will be obtained directly from the Federal Energy Regulatory Commission (FERC) Form-423, “Monthly Report of Cost and Quality of Fuels for Electric Plants,” database files. This will provide a more precise measure of the data for Northern Appalachia, Central Appalachia, and the Eastern Interior regions, for which disaggregation of State-level data is required. Coal data for northern and southern West Virginia and for eastern and western Kentucky are not consistently available in EIA publications. In addition, coal quality data for receipts of coal at electric utility plants by State of origin are not published by mine type but are available from the FERC Form-423, “Monthly Report of Cost and Quality of Fuels for Electric Plants,” database files.

Future Work

Future work will include the examination and reestimation of the coal pricing equation using the additional years of data and the new and updated variables in the database. Data on electricity prices will be tested as a replacement for the price of diesel fuel, which was not statistically significant in the pricing equation developed for AEO98. According to data published by the U.S. Department of Commerce, electricity accounted for 84 percent of the fuel costs at U.S. underground mines in 1992 and an estimated 36 percent of the fuel costs at surface mines.¹⁴ Electric utility data on the average sulfur content of coal and receipts of coal by type of purchase will be tested as instruments in the first stage of the regression, as additional factors hypothesized to affect the demand for coal by region and mine type.

Appendix A
Regression Results and the AEO98 Coal Pricing Equation

The two-stage least squares regression equation for the Coal Production Submodule was estimated using the AR1 (first-order serial correlation) procedure in TSP 4.4 with the INST option. Based on the regression results shown in Table A1, the equation used for predicting future levels of minemouth coal prices by region, mine type and coal type for AEO98 is:

equ5.jpg (22524 bytes)

where y_i,j,k,t is a constant added to the regression equation for each supply region i, mine type j, and coal type k in each year t to calibrate the model to current price levels. For AEO98, prices were calibrated to the average annual mine prices for 1996:

equ6.jpg (4843 bytes)

where:

The first term ( ) is the intercept for the model. It includes the overall constant for the model (A) and the regional specific constants (b_i,1).

The second term ( ) is a required component of a feature added to the model. This feature provides the ability to adjust the overall coefficient for the labor productivity term for modeling runs of the Coal Market Module. Specifically, the term k is the parameter by which the adjustment is made. The SE term is the standard error of the parameter estimate (b₄) for the labor productivity term and is a constant. For AEO98, k was set equal to 2, reflecting the assumption that coal mine operators will not continue to pass along cost savings obtained through productivity improvements to the same extent that they have during the past 15 years. The basis for this assumption is that, as a result of strong competitive pressures, the coal industry has been realizing a lower rate of return than other comparative industries in recent years. Therefore, coal industry earnings need to improve somewhat in order to continue to attract sufficient amounts of investment.