a methodology to predict short-term coal consumption

A METHODOLOGY TO PREDICT SHORT-TERM COAL CONSUMPTION

THOMAS GARVIN, MYRON OLSTEIN, R. BLAINE ROBERTS* and DAVID I. TOOF

* University of Florida, Department of Economics, Gainesville. Florida 32607. LJ.S.A. (904) 392-0470

Abstract -This paper is the result of an eighteen month effort to develop a short-term demand forecasting model for bituminous coal and lignite. The work reported in this paper was developed under contract from the Federal Energy Administration by a team from Arthur Young & Com- pany and the University of Florida. However, the opinions expressed in this paper are those of the authors and do not represent any official opinion of any agency of the Federal Government or Arthur Young & Company.

I. INTRODUCTION

MANY of the events surrounding the developing energy crisis of the past few years have met with increasing public skepticism. Our recent past has shown the importance of accurate information in public policy debates. Additionally, the complex relationships

among the various energy forms dictate that future national energy policies recognize these interrelationships. Thus, sound policy analysis requires accurate data and forecasts which recognize and incorporate the many complexities in our existing energy systems.

Recognizing this, the Federal Energy Administration contracted approximately one year ago, with Arthur Young & Company to develop an automated seasonalized short term demand model for bituminous coal and lignite. The preferred level of detail was

to be the state level. The forecasting horizon was to be quarterly for a two year period and annually for five years. The model was to be econometrically based.

Every forecasting model is unique in some respects. There proved to be many limitations and considerations that had to be incorporated into the methodology to develop an accurate, quarterly, state level forecasting model. While one would prefer to develop a model that was descriptive and forecasted well, a forecasting model differs markedly from a descriptive model or policy analysis model. To be useful, a forecasting model must have exogenous variables that are more easily and accurately forecasted than the endogenous variables. In other words, the emphasis for a forecasting model is on the accuracy of the forecasts that the model generates and if the variables exogenous to the model can not be forecasted accurately, the model is not going to forecast accurately.

A policy analysis model, however, is intended to produce accurate estimates of the parameters of the model to provide a clear relationship between the exogenous and endogenous variables. In an ideal world the two approaches might be identical. In practice, however, there proved to be a substantial difference.

An optimal forecasting model must balance the marginal benefits of greater detail with the marginal costs of generating that detail. The costs include both development costs and future operating costs. The benefits accrue chiefly from the forecasting accuracy. Of course, for a given level of forecasting accuracy, the more the parameters of the model reflect true structural conditions, the better the model is. Generally, however, there is a trade-off between better structural detail and cost effective forecasting.

The development of good forecasting models is much more an art than is the development of analysis models. Experience with data and knowledge of the quality of the data are necessary for constructing accurate forecasting models. It is with these goals in mind and background that a theory must be developed. The theoretical development is essential to provide a foundation for confidence in the estimating equations (in addi-

53

54 THO~LAX G.NVIN. MYKON 01 srt I>. K. l3t.Ati-a Rotrr:~rs and D~\II) I. Tocw

tion to the usual statistical tests) and. more importantly, to indicate under what kinds of future conditions the forecasting equations might be in error.

Our initial approach was to recognize the difference in the quality and quantity of the available data for various demand sectors. Thus. demand was initially diffcrcntiatcd into four major components: (a) coking coal demand: (b) retail, manufacturing and other industrial coal demand: (c) coal demand by electric utilities: and (d) export demand for coal. Because of the detail available within the utility sector and the recognition that there might be a demand for coal not related to electricity generation. we rccognired both an inventory demand and an electric generation-related coal demand.

Thus. the total demand for coal in a state for a quarter was rcpresentcd as:

D,, = D, + D&,,,, + n,, + n,;,

where Dp = total demand for State P

D, = electric generation demand

D,,,,, = coking coal demand

D,, = other industrial demand

DE, = utility inventory demand.

Thus. the total quarterly demand for coal in the United States (D coal) would be:

D,<,,,t = x D, + D,,Y

Where D,, is total export demand. The following sections describe our approach to the development of these submodels

and our results with the selected equations.

II. ELECTRIC UTILITY DEMAND FOR COAL

The electrical utility sector is, by far, the largest coal demand sector, appraoching 70”,, of total demand for bituminous coal. Accurate modeling of the sector is therefore crucial for forecasting the total quarterly demand for coal on a State-by-State basis. However, the problems of developing a usable. accurate model of electric utility demand are severe, requiring allowance for data limitations and many structural shifts.

2. Methoriolo~g~~ ,for- rlczvlopir~~~ ccorzmwtric cqucltiorls

The consumption of coal by electric utilities is directly derived from the production of electricity. However. there are many limitations involved in the attempt to estimate coal consumption equations for State aggregates of utilities. including:

(1) The Clean Air Act resulted in air quality standards that forced. at least in the immediate term, a shift away from sulfur-laden coal to low sulfur oil and low sulfur coal. Consequently, the value of a particular type of steam coal became dependent upon a number of factors besides BTU content.

(2) The consumption of coal is limited by the capacity to burn coal. Given the variable lead time between an investment decision and the operation of an electric utility plant. attempts to relate a particular fuel capacity to relevant economic decision variables by an econometric model was beyond the scope of this effort.

(3) The OPEC oil embargo and the associated energy crisis, with its effect on capital markets. abruptly changed many forecasts that had been generated under the above conditions. Many parameters that had been generated from past structural conditions were altered by the events that preceded the recent recession, the worst since the Great Depression of the 1930s.

(4) The data necessary to analyze the effects of the above structural changes are limited. For example, prices paid for particular types of fuels, contract conditions for captive and semi-captive mines. the spatial effects on supplies and demands. transportation

Methodology to predict short-term coal consumption 55

costs, and the like, have not been collected with the regularity and frequency that would be necessary.

In spite of the conceptual limitations discussed above, the quantitative effects are not obvious. That is, while the above considerations are important, it is not clear how large a structural shift was created. Furthermore, some of these effects can be dealt with noneconometrically.

For example, the use of coal, for a given level of generation, can only vary within certain limits. If total generation is greater than maximum coal generation capacity, then the maximum use of coal cannot be greater than installed capacity times the maximum generation from all units times the heat rate. If total generation is less than maximum coal generation capacity, then the consumption of coal cannot exceed total generation times the heat rate. On the down side, the consumption of coal cannot be negative. Further, if total generation is greater than the maximum generation capacity using other fuels, then the minimum use of coal will be equal to the kilowatt hours that must be generated by using coal times the fuel rate.

Among other factors. the relative price of coal to other fuels should determine the use of coal within the limits described above. Figure 1 illustrates a probable relationship between the relative price of coal, P,/P,, and the consumption of coal between the mini-

mum and maximum bounds. As the price of coal falls relative to other fuels, the consumption of coal should approach its maximum. As the price of coal rises relative to other fuels, the consumption of coal should approach its minimum.

The shape of the curve in Fig. I resembles an ogive and, consequently. between relative coal price and coal consumption may be approximated

(2):

(C”,,,, - c/c - C,,,,,,) = oa+h(P,:P,J - 1

where C = coal consumption; C 111.1 x = maximum coal consumption; C 1,111, = minimum coal consumption;

P, = price of coal to the utilities; P, = price of other fuels to the utilities;

e = natural number e; and a and b are parameters with a < 0, b > 0.

the relation by equation

(1)

In (1) as P,/P, approaches -u/b. the consumption of coal approaches its maximum. As P,/P, approaches higher and higher values, C approaches C,,,,,. Since the formulation of equation (1) is open ended as P, rises relative to P, and N and b are estimated parameters. it can be assumed that C,,,i,, is zero. This leaves two possible formulations

for C,,:,, :

C m,, Y = R x ET,,,, x F (1)

C,,,;,, = ET x F (2)

Coal consumption

PC ‘PO

Fig. I.

xl THOMAS GARVIN. MYRON OLSTFIN. R. BLAINI.. ROD~RTS and DALII) I. Toot

where R = relative installed capacity; ET = electrical generation:

E 7;,,.,, = maximum electrical generation; and F = Heat rate.

The heat rate is relatively constant with some downward trend over time. Thus, assuming that E = ejll’tfl”“” where .1;, > 0 and .I; < 0, for case 2. equation (1) can be solved to yield:

In(C) = ln(ET) + (f. - 0) + ,f, time - hP,..“Po. (2)

For case 1, it will be assumed that ET,,,, is proportional by a factor of k, to the actual generation ET In this case, (1) can be solved to yield (3):

In(C) = In(ET x R) + Ink, + (,fb - (1) +,j’, time - hl’,.~P(,

(2) and (3) imply an estimating equation as given by (4):

(3)

In(C) = ~1~~ + 11, ln(ET x R) + u2P,./Po + cl3 time (4)

where the second term on the right hand side could be replaced with In(ET). In either case, ur should be equal to 1.0; ~1~ be negative; and (f3 be negative if it is significant.

The above equation (4) has the advantage of handling the effects of many structural changes noneconometrically through the variable R, relative installed capacity. However, there are other problems that are ignored. For example, the relative use of coal generation capacity could depend upon factors other than relative price. such as coal strikes or clean air regulations. While the appropriate prices paid by utilities including sulfur content theoretically could be constructed. they would pose an enormous forecasting problem. These and other aspects are discussed in more detail in the following section.

The econometric equations for coal consumption by state electrical utilities fit between two other sets of equations, electric generation and stocks of coal. These two sets of equations are described in the latter part of this section.

Since price data are quite limited and have several problems. both with regard to different sulfur and BTU content and in terms of forecasting, it was decided to test a simpler more naive model first. The equation tested for each state is given in (5).

C-.X.u - C.us( -4) = (I + h(ETx.x - E~?Yx( -4)) + c(R.v.~ - Rxr( -4)) (5)

where CXS = coal consumption in state 9.x:

E’EYs = electrical generation in state .Y.Y: and Rsx = relative installed coal generation capacity in state S.Y.

(-4) = indicates a 1 year lag.

Upon testing the model it became readily apparent that data limitations and structural changes precluded the use of either Equation (4) or equation (5) for forecasting purposes. For example, data on relative coal capacity, current and historical alternate fuel capability, and conversion time and cost components are non-existent. Data for fuel prices paid by utilities prior to 1973 are available only annually. Moreover, available fuel price data includes transportation costs. Lastly. uncertainty with regard to fuel avail- ability, environmental regulations and national energy policy override the pure economic decision variables. After extensive testing, a simpler equation was chosen. Thus, the current estimating equation of this sector is given by Equation (6).

In(C.u.u) = ~1 + hln(ETss) + dTIME + rSQl + fSQ3 + gSQ4 (6)


where Csx is coal consumption in state XX;

ET& is electrical generation in state xx; TIME is a dummy variable equal to 1 in 1965:4, 2 in 1966:1,. etc; and

321, SQ2, and SQ4 are seasonal dummies for the first, second, and fourth quarters, respectively.

(1). Ocert+e~~. As discussed in Section 11.1, the key variable in electric utility coal demand is electric generation. Thus, for each state we estimated one equation that forecasts electrical generation for that state. Each equation contains independent variables that are easily and directly forecasted by the available large scale macroeconometric models. This approach naturally subsumes many structural realities of each state and the coefficients for each independent variable reflect a compounding of many structural parameters.

Total generation demand within a state may be viewed as the electricity generated for consumption by residential, commercial, and industrial users, both in state and out-of-state. Generally speaking, the demand for electricity by commercial and industrial users is a derived demand based on the demand for the goods and services they provide.

Similarly. the demand for electricity by residential users is a derived demand. derived from the demand for the output of the stock of goods (lamps, heaters, ovens, etc.)

that use electricity. (2) General ,fi)rf?l of tile ~~q~~f~~~~~. For the short run, we assumed that the electricity

demand by the residential, industrial, and commercial sectors is approximately a constant proportion of total electricity demand. Such influences on demand as seasonal factors. weather, holidays and other factors involved in going from demand to generation in a state were approximated by the addition of additive seasonal dummy variables.

For many states, notably the New England states and Western states such as Nevada, California, New Mexico, Arizona, Washington, and Oregon, significant quantities of electricity may be generated in one state and sold to another. Because of this substantial interstate selling, nine regions were constructed. Each region consists of two or more neighboring states where interstate selling occurs. A total demand for electricity is then estimated for the separate regions. For example, one demand for electricity equation was estimated for the six New England states as an aggregate rather than six separate demand equations for each state.

Total state demand for generation depends upon state and ‘neighboring’ state income, the quantities of goods and services produced by industrial and commercial consumers of electricity, and relative prices. Since a reduced form equation was estimated, National Disposable Income in 1972 doIIars was used to capture the effect of state income and production by commercial users on total state demand for electricity generation. For the purposes of this forecasting effort, forecasts of Real National Disposable Income were obtained from the available large macroeconometric models.

In order to forecast the effect of state ind~lstrial output on total state electricity generation demand, national industrial production indexes were used. Since each state has its own particular set of important industries, different production indexes including the overall index of manufacturing were used for each state. Forecasts of these indexes were obtained from Iarge macroeconometric models.

Many factors (i.e. prices of electrical equipment, mar.ginal and average relative price of electricity) affect total state demand for electricity. To facilitate the forecasting effort and to overcome a lack of data, a ratio of the national price index of the wholesale price of electric power to the wholesale price of fuel was inciuded as an exogenous variable.

For the relative price of appliances, the implicit deflator for other consumer durables, excluding automobiles, divided by the aggregate GNP deflator was used. For the relative ‘price’ of commercial enterprises. the implicit deflator for investment in private nonresi-

dential structures divided by the aggregate GNP deflator was used. t‘inally. the relative prices of electrical machinery is defined as the implicit deflator for nonresidential producer’s durable equipment over the aggregate GNP deflator.

The general form of the equation estimated for each state is:

ET\-\- = (I + h J YDL + c’ .I= + tl E7’m + (2 PER + ,/’ PERC; + g PCDR +

ItPQR + I PICK +,;SQl + /\SQ2 + I SQ3 + I’ where

ET= is total electrical generation for state or region S.Y LI I are constantx: JYD is national disposable income in 1972 dollars indcxcd so that in 1967

JYD = 1 (JYD = YD72,!669.83): JYDL is lagged or led JYD where L is a code for the number of quarters

led or lagged: Jm is a two digit industrial production index apropriatc for region u

with a lead or lag of _L quarters: PER is the WPI for power over the M’PI for fuel: PERG is PER(- I);

PCDR is the deflator for other consumer durables o\er the aggrcgatc GNP deflator:

PQR is the deflator for producer’s durable equipment over the aggregate GNP deflator;

PICR is the deflator for private investment in nonresidential structures OLCI- the aggregate GNP deflator;

SQl. SQ3. and SQ3 are seasonal dummy variables for the first, second. and third quarter, respectively; and

L: is a random clement with expected value of zero and uncorrelated with other errors.

(3) Sun~ntr~~,. Table I summarizes the results of the equations for each state or rcgion. The standard error expressed as a percentage of the mean of the dependent variable ranges between 2.X6 and 9.25”,,. Of the 33 equations. I3 are under Y,,. and three arc between 8 and 9.25”,,. For 23 of the equations, the coetficicnt of dctcrmination. R’. is over 0.90. Seven of the equations have an R ’ between 0.X5 and 0.90 and three ha\c an R2 less than 0.X5.

While these results indicate a good track record of explaining historical electrical generation. in no state was the full model significant for all indcpendcnt variables with the appropriate sign and size for all coefficients. In fact. in most of the equations oni) one income or production variable and one price variable would hale the correct sign. In several of the equations, the price variable was not signilicantly diRerent from Lero. reflecting a very low price elasticity of demand. In cases where the coefficient for prices had the correct sign and magnitude, they were retained even though they wcrc insignifi- cant. Because of the problems with these proxy variables. the WPI price of po~ci relative to the GNP deflator was used in some equations. The results were esscntiallq similar.

(1). Ot~~~l~ir\~. The econometric equations that relate the consumption of coal by electrical utilities to quarterly deliveries of coal by state were based on a model in which utilities attempt to minimize the cost of obtaining coal in an uncertain world subject to a minimum stock constraint. The price of coal in the future is uncertain, but is distributed around some expected price that depends upon economic conditions that affect the aggregate supply of and demand for coal. Since electric utilities are required to produce to meet demand, one would expect utilities to bc rish-avcrsc. Whcthcl or not this is true. the decision to hold invcntorics can be charactcrizcd as the maximir;t- tion of expected utility of cost. The optimal stock is a function of: (I) the cxpccted cost reduction from holding inventories (including expected price dilTerenccs and


Table 1. Electric generation equations--goodness of fit. Period of estimation: 1966:2-1975:2

Durbin--Watson Relative State statistics

Alabama 0.8942 1.63 0.0424 Colorado 0.9252 1.82 0.0590 Delaware 0.7797 1.88 0.0751 Florida 0.9853 I.91 0.0378 Georgia 0.9686 2.11 0.0527 Idaho 0.7649 I .95 0.085 1 Illinois 0.96 I8 1.93 0.0310 Indiana 0.8380 1.87 0.0455 Iowa 0.8914 2.10 0.0497 Kansas 0.9174 1.62 0.0492 Kentucky 0.8584 2.09 0.0829 Louisiana 0.9497 1.98 0.058X Michigan 0.9042 2.21 0.0373 Nebraska 0.9679 2.22 0.0524 New Jersey 0.7310 1.92 0.0791 New York 0.9417 1.83 0.0271 Ohio 0.9720 2.23 0.0296 Oklahoma 0.9696 2.07 0.0549 Pennsylvania 0.9758 1.52 0.0356 Tennessee 0.8607 2.14 0.0603 Texas 0.9845 2.69 0.0367 Virginia 0.8825 1.94 0.0541 West Virginia 0.9716 2.01 0.0578 Wisconsin 0.9678 1.99 0.0324

Regions: New England MD-DC ND SD-MN-MT CA-NV NM-AZ WY-UT AR -MS-MO NC- SC WA-OR

0.9830 2.18 0.0254 0.8892 1.95 0.0537 0.9209 2.14 0.0451 0.9357 1.11 0.0309 0.9650 1.54 0.0631 0.9379 1.52 0.0769 0.9615 2.51 0.0604 0.9862 2.01 0.0280 0.9423 1.78 0.0492

standard error

seasonal handling differences); (2) the future price level (representing uncertainty) relative

to the unit cost index, and (3) next period’s consumption.. (2). Gener~ll f&r of the equution. The exogenous variables are PX, expected price

change; K unit cost index; the appropriate one period interest rate; expected future consumption; and last period’s stocks. Last period’s stock is known and future consumption has been forecasted.

There are many alternative proxies for the expected future price. Utilities will be assumed to know the values of a vector of known economic indicators of aggregate coal supply and demand, and therefore, the appropriate value of the price of coal to the utilities in the state. However, prices paid by utilities by state are available only from 1973. Two alternatives were used that reduce the forecasting burden considerably: The Bureau of Labor Statistics Wholesale Price Index for Bituminous Coal (WPIOSlNS) for the expected price change or the assumption that virtually all coal is purchased under contract in a particular state so that the expected price change is no longer a relevant variable.

Since the development of a complete theoretical model of strikes and the effect of expected strikes on expected movements and supply availabilities was beyond the scope of this effort, the alternative used was to rely on ‘curve fitting’ by including dummies that make sense but have no formal explicit theoretical foundation. This gives some indication of what might be expected for forecasting over periods when strikes may occur.

The only basic rule to be followed in the use of strike dummies is that positive and negative variation around the strike period seems likely. That is, a typical scenario

60 TIIO\IAS C;AK\ IV. id\ K,IU 01 s,,.I\, R. BLAILI: ROHI.I<I:, and D.\\ II) I. TOOI

might be that during the quarter prior to the strike stocks are built up. stocks are drawn down during the strike quarter. and built up (drawn down) again after the strike because the strike was more severe (less severe) than expected.

For the interest rate variable in the model. the prime rate should be an adequate proxy.

The dependent variable, the desired, optimal stock. (S,). is the quarterly average end of the month stocks. in tons, held by electrical utilities and consumption of coal by electrical utilities: C. is the quarterly consumption, both as reported on Form 4 filed with the Federal Power Commission and compiled in the FPC’s publication entitled E/Ktric~ Po\~Yr. Sttrtist its.

The specific equations used for the state forecasts are: (a) where the wholesale price index was significant

where

P)c’, = t-‘,+JI + I’,,,, ,) - P,

PCDR, = P, + ,;( 1 + I’,., + ,) D, = I:1 + J’,,,, ,

D23, = SQ2. D, - SQ3; where SQ2 is a second quarter seasonal dummy and SQ3 a third quarter seasonal dummy

D41, = SQ4. D, - SQl; where SQ4 is a fourth quarter seasonal dummy and SQl is a first quarter seasonal dummy

Dl2, = SQI D, - SQ2; where SQI is a first quarter seasonal dummy and SQ2 is a second quarter seasonal dummy

STK, = dummy strike variables P, = WPI for bituminous coal and lignite

“I., + 1 = Prime interest rate/400: and (1” ~ c/9 constants.

(b) where it is assumed that all coal was purchased on long term contract, therefore.

PX, = 0.

S, = L/,DMI.NI, + tr,D?3 + rr,D4l + rr,D12 + OS,_, $- tr,C‘,+, + tr7STK,

where DMINI = I,( I + I’,,, + ,) - 1 :

(3)

023, 041. 012. and STK, are the same as in (I). (c) For the States of Nebraska and Florida a na’ive model exhibited a better fit and

is defined as

s, = 11,) + tr,S, - 1 + ClzC ‘[+, + trzSQl + uJQ2 + n,SQ3 + ri,STRIKE (3

where S, is the consumption of coal; SQI. SQL and SQ3 are seasonal dummy variables; and STRIKE is a strike dummy variable.

111. RETAIL 4ND OTHER DEMAND FOR COAL

As coal is an input material and not a final good, the usual approach dictated by microeconomic theory for this sector would be to specify a derived demand function based upon relative prices of coal, other factors of production, and output prices. How- ever, this is not feasible because too little is known about the exact distribution of coal on a State-by-State basis. Moreover. the appropriate prices would have to include transportation costs. be adjusted for the quality of the coal (ash & sulfur content). and several other factors. In addition. while there is ample evidence that substitution among coal and other energy sources is possible, these structural shifts require some time to take effect. Consequently, such an approach would probably require a number of lags and is beyond the range of a short-term forecasting model.


2. General form of the equation

The approach used relates the deliveries of retail and other coal by State to Federal Reserve Board Indexes of Production (for the industries that use coal in each state). Since many of the coal-using industries have been able to greatly reduce the amount of coal needed per unit of output, a time trend was also used in each state equation to capture these increases in output per ton of coal. Such trend variables will unavoid- ably capture other factors correlated with time such as regional industrial shifts.

As with the equation for the demand for coking coal deliveries, seasonal factors, strike expectation variables, and other dummies for specific disasters were included. Unfortunately, while we do know of various disasters that crippled industrial production in particular states, we do not know the states that experienced increased production because of the disaster. Furthermore, the increase may be spread among many states and not be statistically significant.

The general equation which was estimated is given in Equation (1).

LOG(ROCOAL(a STATE) = a + h LOG(FRBINDEXES) + c SEA-

SONALS + rl STRIKE + e OTHER +,f TIME

where u - ,f’= Constants

ROCOAL(crmSTATE = the retail and other deliveries of coal by state;

FRBlNDEXES = the appropriate major coal using industries in the state:

SEASONALS = the appropriate seasonal dummies for each state;

STRIKE = strike expectation dummies; OTHER = dummies for particular state disasters; and

TIME = a time trend.

3. Linking equation jar cement production

An integral variable in this sector is cement production. Since cement production (J324) is not forecasted by any large macro-models we have developed our own estimating equation.

The selected equation for cement production is analogous to that of coke detailed

in Section IV and is (t - statistics in parentheses)

LOG(J324) = - 2.648 + 0.2628 LOG(0.6667 HS + 0.3333 HS (- 1)) (- 9.40) (16.78) + 0.8253 LOG(CER) - 0.0556 PC’ONTROLl

(9.31) (-2.13) - 0.0446 PCON TROLZ

(3.93)

R2 = 0.9212 D - CV = 1.67 SER = 0.0250.

where

5324 = Federal Reserve Index of Cement Production = 1.0, seasonally adjusted.

HS = Quarterly average of seasonally adjusted housing starts. CER = Investment in nonresidential construction in constant 1958

dollars PCONTROLI = Dumm variable for price-wage freeze of 1971 (1971:3

PCONTROLl = 1; 0 elsewhere) PCONTROL2 = Dumm variable for 1972-73 period of price controls (1972: 1,

PCONTROL2 = 1; 1972:2. PCONTROL2 = I: 1973: 1, PCONTROL2 = 1: 0 elsewhere.

67 THOMAS GAKVIN. MYRON OLSTEI\I, R. BLA~N~ ROLERI.S and DALII) I. Toot

Table 2. Industrial indexes of production used ln each state equation for manufxturing, retail nnd other deliveries of coal

Ohio Pennsylvania Indiana Alabama Mississippi West Virginia New York Delaware Maryland-District

of Columbia Michigan Illinoi; Californla~Washin_t[~n

Oregon Utah Kentuckq Virginia Colorxdo Iowa Minnesota Arkansas-Texas Louisiana Missouri Wisconsin Tennessee New England Nea Jrrsq North and South Dakota Nebraska-Kansas North Carolina South Carolina Georgia Florida Montana Idaho Arizona Nevada New Mexico None AluSk:l Paper Wyoming All manufxturing

Equation (3) indicates that if all construction were to increase by I”,, (residential and nonresidential) the output of cement would increase by 1.0881”,,, which is reason- able. Two dummies, for the 1971 price-wage freeze, Phase I, and the period of price controls, Phases 2 and 3. were used. The values of the price control dummies are consis-

tent with the reported shortages and effects of Phases 1, 2, and 3.

4. SummarJ

Table 2 summarizes the industrial indexes that were used in each state. It was not always possible to include the major user of coal as given in Table 2 since, as noted previously, there are reporting problems with those data. In three cases. the index of manufacturing was the only way an acceptable equation could be obtained. In Arizona Nevada-New Mexico no industrial production indexes were significant. For Texas-~ Arkansas--Louisiana, the data exist for one year only, 1974. Prior to that. Texas deliveries were not reported.

Table 3 summarizes the degree of fit for the retail and other coal equations. The mean average percentage error ranges from 3.0 20.6”,,. For the major retail and other coal consuming states, the mean average percentage error is from 3.0 to 7.7”,,. The largest absolute error is for Illinois, 181.7 thousand tons average per quarter. Foul

states: Pennsylvania, Ohio, Michigan, and Wisconsin, have absolute errors just over 100 thousand tons and for all other states the error is less than 100 thousand tons.

IV. COKING COAL DEMAND

1. Ocertlietc

The demand for coking coal is a derived demand based on the production of pig iron, which in turn depends upon the production of steel. The appropriate model

Primary iron and steel. basic chemicals Basic chemicals Primary iron and steel. basic chemlc&. cement Cement. basic chemicnls Basic chemicals Cement

Primary iron nnd steel. cement Cement. synthetic chemicals Basic chemical\

Primary aluminum Primary aluminum. cement Food processing, primary iron and steel Basic chemical? Food processing, other primary metals Food processing Food processing None Synthetic chermcals Paper, food proccssing Paper, basic chemicals All manufacturing All manufacturing Food processing Food proccssing Paper Basic chemical\ Paper AII manufrlcturing

THOMAS GAKVIN. MYRON OLSTEIN, R. BLAINE ROR~RTS and DAVID I. T~OF 63

Table 3. Demand for bttuminous coal by state in retail and all other degree of fit. Period of estimation: 1966-1974

State

Average quarterly demand

(thousands of tons) R2

Durbin~ Watson stattstic

Mean Mean average absolute

percentage error error (thousands

(“0) of tons)

Pennsylvania Indiana Ohio Alabama-Mississippi West Virginia New York MarylanddDelaware Michigan Illinois Caltfornia Washington~

Oregon Utah Kentucky Virginia Colorado Arkansas Texas-

Oklahoma-Louisiana IOWI

Minnesota Missouri Wisconsin Tennessee New England New Jersey North and South Dakota Nebraska- Kansas North Carolina South Carolina Georgia-Florida Montana-Idaho Arizona-New Mexico-

Nevada Alaska Wyomtng

2010.3 0.9393 1.53 5.2 104.9 1656.0 0.9225 2.08 4.9 81.1 3152.5 0.9724 1.72 3.0 113.6

543.7 0.8994 1.12 6.5 35.2 1281.0 0.X 167 I .62 5.x 74.3 1226.X 0.9746 1.36 5.5 70.6 240.9 0.8391 I.58 9.2 22.3

2208.7 0.9579 1.26 4.8 106.2 2361.1 0.9460 2.23 7.7 181.7

116.9 0.8963 1.73 11.1 13.0 168.0 0.7525 1.52 13.6 22.x 651.3 0.9242 1.72 5.0 32.4

1071.9 0.965 1 1.33 4.6 49.5 181.7 0.8X00 1.47 Il.4 20.8

647.5 463.9 438.6 460.2

1277.X 6X7.4 139.8 144.7 158.6 99.4

621.2 404.0 163.4 135.8

N.A. 0.8929 0.7155 0.8314 0.9 I90 0.X376 0.8950 0.9373 0.9269 0.9248 0.9372 0.5749 0.9444 0.7854

1.21 I.15 1.32 1.24 1.52 1.69 2.44 2.56 I .65 I.16 1.77 1.12

35.X 0.4955 1.58 138.4 0.8640 1.80 63.9 0.7350 1.30

N.A. 1.54

N.A. 8.7

14.0 9.3 x.7 7.2

20.6 13.4 11.1 14.4

5.9 11.5 7.5

15.2

11.1 14.5 15.5

N.A. 40.3 61.6 42.9

111.5 49.2 28.8 19.4 17.6 14.3 36.5 46.5 12.3 20.6

4.0 20.1

9.9

depends upon the exact nature of these interrelations. Due to data limitations, and to ensure that the model is consistent and responsive to alternative future economic conditions and policy simulations, our approach was to relate state deliveries of coking coal to aggregate steel production. From a strictly theoretical point of view, the model should be complete and simultaneous. That is, the demand for steel should be modeled and estimated simultaneously with the demand for pig iron, demand for coke, demand for coking coal, and the supply functions. This is not practical here. Furthermore, forecasts generated by macromodels typically have the recent errors added to the equation and ‘phased out’ over the forecast period. Therefore, the actual values of the FRB Index for primary iron and steel (sub-total of SIC 331) were used to explain the change in the FRB Index of Coke production.

2. General ,form of the equation

For a given level of steel production, the relative prices of coal, other energy, iron ore, scrap steel, and other inputs of the various processes should affect the demand for coke. The higher the price of coal relative to other energy sources, the less coal and coke would be used to make steel since many of the processes can be fired by natural gas, fuel oil, or electricity. Given the flexibility in the open hearth and the basic oxygen furnace for the mixing of scrap and molten iron, the lower the price of scrap relative to the cost of using pig iron, the more scrap should be used in a charge. The cost of using pig or molten iron depends upon the prices of coal, coke, iron ore, and other factors of production in blast furnace operation.

The observed prices of these components of steel production are the result of both supply~deln~lnd forces and ~~~vernmeI~t~t1 and instituti~~li~ll constrrtints. By- using steel production in the equation for the demand fc>r coke, these unobserved factor costs (factor prices less productivity) can be captured. However. the coetfcicnts of the prices that remain in the estimated equation cannot bc interpreted as the structural price elasticities of coal demand. The general form of the equation for .IC’OKE is:

LOG(JCOKE) = LI + h LOG(FRRSTEEL) + c LOG(STEELPRlCEJ:fO.lLPRlfE)

+ tlC0ALSTRfKE.S f li.ST~ELS’rRI~~S

Both coal strikes and steel strikes should atrect the relationship between steel production and coke production. During a coal strike. the coke production should be Icss than normal --perhaps, being higher than normal in quarters prior to ;I strike, depending upon the degree to which the strike was anticipated. While there are ;I number of separate coal strikes every year for many reasons. the major activity occurs at the time of new contract negotiations. Recently. these have occurred every three years: in the fourth quarter of 1968, 1971. and 1974. However. t hc (I /~~io~i effect of steel strikes on the timing of coke production is not clear.

3. Slart> tit~iir~cUic&s t$ c.ol<ir?gg CCiCii

As noted. the qLi~]itity of coal used per ton of coke varies within a relatively small band. There is virtually a fixed input-output relation between coke and coking coal.

Thus, without considering changes in regional capacity for I given level of aggregate capacity. seasonal factors. strike expectations. and other vagaries. the deliveries of coking coal at the state level should be proportionately related to the aggregate index of coke production.

To capture regional location changes oycr the past. the number of raw steel production plants in ;I State was also included. as shown in equation (I ):

LOG(COKEC‘OAL~tr STATE) = <I + h LOG(C’KHAT) + i’LOG(PLAh’TSru STATfi) + tl SE.4SONALS + i’STRIKES +,f’OTHER (1)

Where (I ,f’are constants. and CKHAT are the fitted val~~es from the equation for the FRB Index of Coke Production. Season& which are unique to individual states, ;I strike dummy and other dummy variables because of such occurrences as tturricanc Agnes which destroyed coking facilities in a few states were also included.

Because the errors in equation (1) would be expected to bc correlated with errors in the FRB Index of Coke Production. the technique that WIS used is two stage least squares. whcrc the fitted values from the equation for FRBCOKE are used in estinl~ti~i~ coke production for each state.

4. ,!.irlkir~g equilticms ./iv .sIuIe rrrd cotrl r/rrnum/ rqlrtrtiorls

The actual coke production equation as described in Section 1 is presented below.

( 1) cdir prf’rlttc’l im The equation for coke prod~ictiot~ is (7 --statistic in parcnthcscst:

(7) LOG(JCOKE) = -0.0064 + 0.262 LOG(J3il) + 0.150 LOG(JMl( - I)) (-0.79) (3.16) (1.01)

+0.164 LOG(f’S7‘EEL:f’C10,ilL( - 1)) - 0.1136 COALSTKI

(7.89) ( - 0.7.73)

-0.0751 COALSTKI! i 0.0799 STEELSTK ( - 3.35) (4.57) R’ = IXWJY I3 - !A’ = 1.37 SER = 0.0306

where JCOKE = Federal Reserve Board Index of Coke Production

(1967 = 1 .O), seasonally adjusted. 5331 = Federal Reserve Board Index of Primary Iron and Steel

Production, Subtotal (1967 = 1.0). seasonally adjusted.


PSTEEL = Wholesale Price Index for Steel (1967 = l.O), not sea-

sonally adjusted. PCOAL = Wholesale Price Index for Coal (1967 = 1 .O), not sea-

sonally adjusted. COALSTKI =

COALSTK2 =

Dummy variable for the 1971 coal strike (1971 :3-1971 :4, COALSTKl = 1; 0 elsewhere) Dummy variable for the 1968 and 1974 coal strikes (1968:4, COALSTK2 = 1; 1974:4, COALSTKZ = 1: 0 elsewhere)

STEELSTK = Dummy variable for the 1971 steel strike period (1971 :l--1971 :4. STEELSTK = 1 ; 0 elsewhere).

Equation (2) indicates that a l”,, increase in primary iron and steel production will cause a 0.412”,, (with some lag) increase in the production of coke. Since a price increase for coal would generally have some lag before increasing the price of coke, the current price of steel over the price of coal lagged one quarter was used. This equation indicates that a l”,, increase in the price of coal relative to the price of steel will reduce the production of coke by 0.164”, for a given level of iron and steel production. As expected. coal strikes and the unavailability of coal reduce the level of coke production. During steel strikes the level of coke production does not fall as low as would be indicated by the decline in the index of steel production.

5. SummurJs

Table 4 summarizes the goodness of fit of the equations for the States. The coefficient of determination, R2, ranges from 0.9704 to 0.4003. Most of the equations are quite good, especially for the major receivers of coking coal. A more appropriate indicator of the accuracy of the equation is the mean absolute percentage error. This statistic runs around 3--6?. per quarter for the major receivers of coking coal. A more appropriate indicator of the accuracy of the equation is the mean absolute percentage error. This statistic runs at around 3-6”,;, per quarter for the major States that receive coking coal. The largest average quarterly error in absolute terms is 228.2 thousand tons for Pennsylvania but that is only 3.7”,,, of the average quarterly deliveries of coking coal to the State. The only particular problems encountered in obtaining a forecasting equation were for those States that receive small amounts of coking coal.

Tahlc 4. Demand for coking coal by state, goodness of fit. Period of estimation: 1966-1974

State

Average quarterly demand

(thousands of tons) RZ

Durhin- Watson statistic

Mean Mean average absolute

percentage error error (thousands

(“,,I of tons)

Pennsylvania Indiana Ohio Alabama Mississippi New York West Virginia DelawareeMaryland Michigan Illinois California Utah Kentucky Colorado Arkansas Minnesota Missouri Wisconsin Tennessee

6204.0 0.9212 I .4x 3125.6 0.8844 2.09 3073.0 1910.3 1326.2 1245.9 1166.9 1200.9 839.0 509.6 465.7 411.3 265.1 22X.3 lXX.6

14.5 94.4 44.6

0.944 I 0.8331 0.9289 1.55 0.8669 1.52 0.93 II 1.63 0.8749 1.78 0.9248 I .50 0.9076 2.19 0.9096 1.53 0.7800 I .2x 0.7416 1.87 0.7303 1.51 0.9704 I .62 0.4023 2.48 0.6965 1.49 0.4003 2.50

1.31 1.14

3.7 3.x 3.7 4.5 5.1 3.7 5.3 7.6 3.1 5.7 3.0

10.0 x.3

13.9 32.1

9.8 27.6

9.2

228.2 117.6 112.6 X6.2 75.9 46. I 61.6 91.6 26.4 29.3 13.9 41.1 21.9 31.8 60.6

7.3 26.1

4.1

hh I-IIO\I.\S GAI<\I\. M\l<c)\ OI.CIIIN. K. BI AIUI KOIII~KI\ and D.\\ II) I. IOOI

C’ocfficients for the index of coke production arc listed in Table 5, One test of the potential accuracy of the model is the weighted average of these coefficients. The average

of I.16 is \cry close to one. This means that a I”,, increase in production will incrcasc

coking coal deliveries by I. I h”,,. However, one State group equation, Maryland Dcla- wart. contains a time trend with ;1 negative sign that will offset this slight o\t’rprcdiction.

All the strike expectation dummies used in the equations sutn to /cl-o cxccpt <nmc of 1966 and 1074. where the efi‘ccts of the strike extend beyond the period of estimation.

The final component of non-electric utility demand for U.S. coal is cxpor~cd co;tl. During the past ten years. bituminous exports have fluctuated between 49 and 71 million tons annually. or about ‘9 I?“,, of the total domestic production. 42 million tons ot- 79.4”,, of the 52.9 million tons of bituminous coal exported frotn the L7.S. in 197.3 were used for tnetallurpical purposes. In 1974. 51.7 million tons, or X6.2”,, of the 60 million exported tons, were used for metallurgical purposes.

In 1974. nearly 46”,, of total exports went to Japan, with Europe receiving 26.5”,, and C’anada 22.9”,, totalling 95”,, of total exports. As more detailed information ix not

availnblc. exports are related to indexes of industrial production for Europe. Japan.

and Canada. which are obtained from Bt~.si~tras Cort~/iliort.s Diqc,.sr. Depot-tmcttt of (‘on- tncrcc (\,arious issues). The relative price of coal in the United Stata to c)thcr coal

prices should affect exports. However. this would have required detailed c\:tntiltation of transportation costs. the collection of many data, and present it ditlicult forecasting

problem. Although. most of the coal exported is for metallurgical purposes. the i\tlc for export demand is, what is the driving force at the mat-pin. What relati\c pricch VCOLIIC~ GILISL exports of coal to vary’.’ Since there is no substitute for coking goal. the‘ metallurgical demand for export coal should be captured by industrial production iI)-

dcxcs for Japan and Europe. For the remainder of the exported coal. the relati\ c p”icc of steam coal to its substitute was included. Since world pctrolcum prices arc‘ Itirl? unifortn and petroleum is a substitute for stcatn coal. the relati\o price of coal to crude pc(roleum. as tneasured by the Wholesale Price Index, was LISXI. Also. strike \ ariablc\ were addcd for strikes in foreign countries. which increase quarterly csports.

The best quation for forecasting purposes is shown in equation (I):

Ill(C’E.Y/‘) = 9.45 - 0.41 In(PC’O.4L;PC’RC’L)E) + I.1 1 Ill(OE(‘lI) $ 0.12 Ill (./I’1 ~ 0.38 SQl + 0.03 SQ? + 0.04 SQ3 + 0.49 S7‘K C;S

+ 0.30 STKENGI + 0.38 STKENG’


where CEXP is quarterly U.S. exports PCOALis the WPI for bituminous coal PCRUDE is the WPI for crude petroleum OECD is the index of industrial production for OECD Europe JP is the index of industrial production for Japan SQl, SQ2, SQ3 are seasonal variables STKUS is a dummy for the 1971 U.S. coal strike with 1971:2-1971:3, STKUS = 0.333; 1971:4, STKUS = - 1, 1972:1, STKUS = 0.3333; other times

STKUS = 0. STKENGl is a dummy for the 1970 coal strike in England with 1970:1---1970:4. STKENGl = 1, other times STKENGl = 0. STKENG2 is a dummy for the 1974:4-1975:3 coal strike in England with 1974:4, STKENG2 = 0.3333; 1975:1, STKENG2 = 1; 1975:2, STKENG2, = 0.6666; other times. STKENG2 = 0

4. Analysis

Equation (1) indicates that an increase in the relative U.S. price of coal to crude petroleum by 1”” will reduce the demand for exports by 0.4:,. A 1”; increase in European industrial activity will increase exports by 1.191 while a 19; increase in industrial production in Japan will eventually lead to approximately a 0.12 0; increase in coal exports. Although the coefficient for European industrial production was not significantly different from zero, it was decided to keep the variable in the equation for forecasting pur-

poses.

VI. USE OF THE MODEL

1. Design

The short term coal demand model has been designed as an integrated set of functional procedures written in TSP and FORTRAN and implemented on FEA’s IBM-370 computer system. The operation of the model is facilitated by use of the WYLBUR software package for program modification and remote job entry from a conversational computer terminal.

The structure of the system is shown in the system flow chart, Fig. 2. Each function represents one executable procedure in the model. Due to the nature of econometric forecasting, proLision has been made to allow repetition of any functional procedure as many times as necessary to obtain desired results without adversely affecting any other portion of the model.

2. Mujor components

The system has been built from four major components: TSP programs, TSP databanks, FORTRAN programs, and an on-line dataset used as documentation for refer- ence during computer sessions. Each component is described below.

TSP programs. The majority of processing is performed by the Time Series Processor. This software package is designed for easy manipulation of time-series and related statistical procedures. The Coal Model uses TSP programs to estimate the demand forecasting equations, to store and update data, and to generate coal demand forecasts. Each program is stored as a WYLBUR dataset with all necessary job control language. To perform any of the functions described in the system flow chart, the user merely has to submit the appropriate data set for execution as a batch job. The output may then be fetched and inspected at a remote terminal, or printed on a high-speed printer.

TSP datahunks. All data utilized by the TSP programs are stored as timeseries in on-line datasets referred to as TSP databanks. These are standard IBM partitioned datasets. The file characteristics are determined by TSP and cannot be changed by the user. All databanks currently have sufficient primary and secondary extents allocated to allow at least five more years of data to be added before file re-allocation is necessary.

6X

UDdate Update RHSVAR demand

data bank data bank

I I

# Compute

llnk regressions

1 I

f 1 Compute Compute

retail.manufac. Compute

coking coa I and other export

regressions regresslons regresslons regressions

I f t

Compute utlllty coal CO”5Urn ptlon

c:tx;e stock

regresslons regresslons

I J t

1 Uodate I

f Forecast

non-electric coal

demand

t

Forecast electrlcal gyee;;;qn

t Forecast

$;I;\ Y

COflSU”?DtlOn

t Forecast

utility stock

demand

t Forecast electric utl ltty

coal demand

I b

0 Quarterly forecasts

0

Yearly forecasts

FORTRAN ~IJYX~~XH~.S. The report program is written in the FORTRAN programming language. This language was chosen because it is well known and it facilitates a number of mathematical procedures that are intended to be used as the reporting capabilities of the model are enhanced in the future. The input to the report program is created by a TSP program which translates the TSP databank into a sequential dataset access- ible by FORTRAN.

The report program produces tabulations of coal demand for each region and state on both a quarterly basis for two years. and on an annual basis for five years. U.S. totals are also provided. Since the model also forecasts electrical generation demand, this information is included in the report. The program was designed in a manner which allows for easy modification of the format and contents of the present reports.


On-line dataset. Because the sytem is designed for interactive use, an on-line documentation capability has been provided. It consists of an index of all exogenous variables. their definitions, sources, range of values, and usage of sector and state. By use of the appropriate WYLBUR search keys, it is possible to find any of the above information while the user is conducting a computer session without the need to refer to written documentation. The on-line format is also very useful for maintaining up-to-date documentation on the variables used in the model that are most subject to change.

A~~knowled~rmmr.s~~The authors wish to express their gratitude to Barry Cohen of the Federal Energy Admin- istration for his continued support, review and insightful suggestions with regard to development of this model. Professor Roberts wishes to thank Anne Morrall and Bob Trost for able and persistent assistance on the theoretical and econometric development associated with the model.

a methodology to predict short-term coal consumption

Documents