ML19296B059

Load Forecasting Sys Specs, Forwarded in Response to Question 350.3

ML19296B059
Person / Time
Site:	Grand Gulf
Issue date:	05/01/1979
From:	MIDDLE SOUTH UTILITIES, INC.
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NUDOCS 8002190792
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MIDDLE SCUTH UTILITIES LOAD FORECASTING SYSTEM SPECIFICATICHS Middle South eervices, Inc.

May 1, 1979 8002190 g

TABLE OF CONTENTS PAGE RESIDENTIAL SECTOR 1 INDUSTRIAL SECTOR 18 COMMERCIAL SECTOR 30 WHOLESALE SECTOR 38 STREETLIGHTING SECTOR 44 PEAK DEMAND SECTOR 53 ECONOMIC SECTOR 75

~

THE SPECIFICATION OF THE RESIDENTIAL SECTOR OF THE MIDDLE SOUTH FORECASTING MODEL 9

1

TABLE CF CONTENTS PAGE INTRODUCTION 3 I. CUSTOMER CONSUMPTION 3 A. Utilization of the Existing Stock of Electricity - Consuming Appliances 6

8. The Accumulation of Electricity - Consuming Appliance 8 C. The Per Customer XWH Consumption 10

!I. CUSTOMER GROWTH 11 A. Total Customers 11

8. Electrically Heated Homes 13 APPENDIX A: The Logit Model 16 O

2

INTRODUCTION This is the final specification of the residential sector of the Middle South Forecasting model. The methodology preserited here was applied to each of the five operating companies separately from which a system's forecast was made.

The analysis of residential consumption for each operating company had two distinct parts. First, the consumption for a typical customer was investigated.. When the effects of the factors which lead to his con-sumption were determined, the typical pattern of his future consumption was forecast using projected values of these factors. Second, the growth in the number of customers was forecast. By multiplying the projected customer consumption by the projected number of customers, the total consumption for an operating company was determined. The detailed speci-fication below follows this general outline - the determinants of customer consumption followed by determinants of customer growth.

I. CUSTOMER CONSUMPTION The use of electricity does not, of itself, yield benefit, or utility to the consumer. Rather, it serves as one input into a process which includes the stock of electrically-powered appliances 1 at the consumer's disposal. This can be distinguished from ordinary consumer expenditures on goods such as food from which benefit is derived directly. This points up one characteristic of the consumption of electricity. In -

any brief time period, the use of electricity is constrained by the current stock of electricity-consuming appliances. Over a longer period, the consumption of electricity depends on the rate of accumulation of these stocks. That is, the usage of a given stock depends on certain factors-weather, income, price - while the stock itself depends on other factors, sometimes not distinct - wealth, durable prices, availability of alternative energies.

1. We use the word " appliances" rather loosely here. Included are all electricty-consuming household goods, ranging from rei-ig-erators to light bulbs.

3

To arrive at an estimable equation for KWH usage per customer, we began with the following mathematical relationship:

n

1) KWF9C =yu.,*(K$t/ CUT.,)

t 3 1=;

Where:

KWH@C( = KWH sales per customer in perico t.

uj ., = KWH use of appliance i in period t.

K

$t = Stock of appliance i in period t.

CUT t

= Number of customers in period t.

In words, the KWH sales per customer in a given time period is the sum of KWH's used by any given appliance (ujt) times the average number of sucn appliances held by a typical customer (the number of such appliances held in the service area by customers divided by the number of customers).

Approacning our estimable ecuation, we noted a few relationships and made some simplifying assumptions. The expression K$t/ CUTt , the number .

of appliance i per customer, was approximated by the rate of saturation of appliance i. It underestimates K$t/ CUT t to the degree that a given appliance occurs more than once per customer-household. Nevertheless, we assumed,

2) S

$t

=K

$t / CUT t Where $tS is the saturation of ap-pliance i in period t Sacond, for appliances, other than weather-sensitive appliances, we attempted to measure average responses to income, prices and other f actors. --

We modeled separately air-conditioning response to cooling degree days and heating response to heating degree days. This simplification can be written, algebraicly 4

n Eu =a *I

3) 3t t i=1 G(3 wnere:

a g

= proportional response of usage to changes in economic factors 0

4t

= typical use of appliance i in period t Ojt, wnile abstracting away from weather, income, price and other f actors, varies with time due to technological changes.affecting usage levels.

Using equations (2) and (3), we were allowed to rewrite equation (1):2 n

4) KWH@C t

=a t * (I O jt *Sgt) i=1

2. The derivation of equation (1):

recall, n

KWH@C t

= I u jt * (K $t/ CUTt )

substituting from (2) yields:

n XWH@C t

= I u jt *S jt ,,

i=1 from (3) n KWH@Ct = a( * ( i=1I G jt *s)j 5

In words, we converted the problem of estimating the KWH usage per cus-txer into the framework described in our discussion of tne long-run and snort-run. KWH consumption in each period is a product of the usage rate ( ) and per ct.stomer stock of appliances, weignted by relative KWH utilization:

N (E Ujt ' Sjt) i=1 This latter sum expresses the typical customer's overall stock of ap-pliances per customer by weighting the actual stocks per customer by relative KWH usage.

Our discussion now proceeds along two paths. Firstly, we specify the determinants of 3t, the rate of KWH usage, applying what we have called short-run considerations. And, secondly, we consider the determinants of: N I u g*.*S i=1 9t' applying the long-run considerations. We subsequently, return to a synthesis of the two discussion with a description of the estimating procedure.

A. a-UTILIZATION OF THE EXISTING STOCK OF ELECTRICITY-

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CONSUMING APPLIANCES.

The rate of utilization of the existing stock was hypothesized to be a function of weather in the service area, the per capita income in ..

the area, the price of electricity, and " conservation" efforts. Weather conditions obviously detemine the level of heating and cooling appliance usage. To a lesser degree they also impact on usage by refrigerators or ranges. We used heating (cooling) degree days to quantify the effects of weather conditions. Given that the effect of weather affects a subset of all appliances, each of the weather variables were weighted by saturation level of the most weather-sensitive appliances. In this way, our specification allowed for the increasing influence of weather as the saturation of weather-sensitive appliances grew.

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The average customer in a service area shouid utilize more of a given stock of apoliances as ne is better able to afford the use of the stock's services. We proxy his economic condition by the per cacita inccme in the area. The level of usage and oer capita income were expected to be and were found to be positively related.

The real price of electricity was calculated frem the rate schedules of each operating company. The real price was a nominal price divided by the consumer price index for the southern U.S. Economic theory tells us that the price consumers use when making purchasing decisions is the marginal price, or the price for the last unit they buy. For this reason, we used only the cost per KWH in the last rate block electricity-consumers bought. Since customers were in different final blocks, a typical marginal price term was used, reflecting the block where the typical custcmer was most of ten found historically.

Finally, 4 proxy for conservation efforts was included. For a given level of the other variables, the urge to conserve, caused by peer pres-sure or advertising, led to lower usage levels.

We summarize the discussion of utilization by the general functional expression:

5) a( = a(WHDDt, WCDDt , RYP@Rt , RPEt , CONSt . . . )

Where: at = XWH usage rates of all N appliances in period t .

(as defined previously).

U(.) = The general function form.

WHDD t

= Weighted number of heating degree days in period t; WHDDt

= saturation of electrically heated homes times unweighted heating degree days.

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WCDD t

= Weighted CCD (Cooling Degree Days) in period t, WCDD = saturation of air conditioning units times CDDt .

RYP9P t

=Real disposable inccme per capita, period t.

RPEt

= Real electricity price per KWH, period t.

CONS = Conservation proxy Where exp (.) is the base of the natural logarithmic system to the power in brackets.

B. IG*S-THE ACCUMULATION OF ELECTRICITY-CONSUMING APPLIANCES -

The long run accumulation was specified by the overall saturation rate of electricity-consuming appliances. The saturation rate of each apoli-ance was weighted by the annual KWH usage.4 The second step in forecasting the KWH equivalent stock of appliances to model the saturation rates for the N appliances. Since no data was available for many smaller appliances, only major appliance saturations were modeled with the behavior of omitted appliances inferred from those analyzed. The data for the major appliances came from surveys by the operating companies and studies done by the Bureau of the Census in tne mid-south area. The applianc,es modeled were:

3. When the actual estimation was performed the deviations of WHDD t

and WCDD from their normal values were used. This was because the seasbnal adjustment of the data before estimation removed ~

the general, recurring, effects of weather. Our weather variables captured the changes in weather which were not normal.

4. The weighting scheme merges all the appliances into ene aggregate stock. It is as if we wanted to add apples and grapes. We could call it fruit, but a single grape is hardly equivalent to an apple.

So we convert each to ounces of fruit to form an aggregate.

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. REFRIGERATCRS

. FREEZERS

. AIR CCNDITIONERS (Wincow and Central)

. RANGES

. WATER HEATERS

. WASHERS

. DRYERS

. DISHWASHERS The saturation of appliance i was hypothesized to be a function of house-hold wealth, the real price of appliances, and the rate of growth in customer stock.

Household wealth, reflecting the household's ability to buy applian(.es, was proxied by an average of current and past per capita disposable income. The real price of appliances was a price index of appliances deflated by the consumer price index for the Southern U.S.

The last variable we used was the growth in the customer stock. This variable entered positively since new customers tend to have more ap-pliances than older ones.

6) SAPL jt = S(RW@P t ,RPAPLjt, CUT t

,...) .

Where: SAPL jg = Saturation rate of appliance i in period t. ,,

S(.) = The general functional form.

RW@P = Real wealth per capita, period t.

t RPAPL t

= Real price index for appliances, period t.

CUT = Customer stock period t.

t Escause room air conditioners are appliances for whicn the rate of sat-uration grossly underestimates the average stock per customer, a further adjustment correcting for the average number per household was performed.

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The explicit functional form used for the saturation estimation is much The explanation of the form is less intuitive than the form for a(.

oiscussed in appendix A.

C. THE PER CUSTOMER KWH CONSUMPTION Recall our specification for KWH@C t in equation (l')

n KWH@C g =a t * (I 6 9t *S9t) i=1 N

The variable: I d jt *S

$t i=1 was formed using the techniques discussed in (B) above. Since all N appliances were not included in the estimation in that section, we as-sumed that the omitted appliances d1d not affect the weighted appliance stock. That is:

N N K I 0 *S =K I O *S Where K = number of included appliances.

$t $t jt $t 1=1 i=1 N

We express this aggregate stock as S t

(= I Ggt*S$). Using "I

equation (5) yields:

9 h

7) KWH@C t

= A*RYP9P t D*RPEt c* CONS t exp(WHDD d t I + WCDDt)*5 The new parameter 'h' is introduced as the coefficient of Sg (tha es-timated appliance stock. The theory suggests h to be identically equal to 1, so by allowing it to be estimated freely, the strength of speci- ..

fication was tested. If the null hypothesis (h=1) was rejected, we must conclude that the long-short run dictomy is incorrect or the con-struction of the saturation rate has shortcomings. By taking natural logrithms of the left-and right-hand sides of our equation, a linear regression was performed. Thus, the estimated form was:

8) LOG (KWH@C t ) = a + b* LOG (RYP@P t ) + c* LOG (RPEt )

+ d* LOG (CONS t ) + f*WHDDt + g1CDDt

+ h* LOG (St )

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II. CUSTOMER GROWTH The growth in custcmer stock is essentially dictated by the grdwth in residential units in the service area. Consequently, those causal fac-tors typically ascribed to the formation of household units were used to mooel customer growth. The specification represents an applica-tion of a stock-adjustment model. That is, underlying factors deter-mine an equilibrium of customer stock which is adjusted to at a rate determined by short-run factors. The second step in modeling customer growth wEs to specify the determinants of electrically heated share of the total.

A. TOTAL CUSTOMERS The equilibrium stock was posited to be a function of the per capita wealth in the service area and the household-aged population of the area. The equilibriun stock is that stock of households where, given current determining factors, there is no incentive for the number of households to increase or decrease. The equilibrium stock seldom equals actual stock because the factors affecting equilibrium are changing faster than the stock is able to adjust. The adjustment mechanism will be made explicit later.

The first relationships may be expressed generally.

9) CUT * = C(RW@P , NR21& )

T t t Where: CUTt * = Equilibrium customer stock in period t.

RW@P t

= Real wealth per capita, period t.

NR21&

t

= Population, 21 years old and over, period t.

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At the beginning of each period the equilibrium stock determined by wealth and peculation dces not equal the stock of customers whicn al-reacy exists. Adjustment to the equilibrium takes place, but we exrect that the adjustment is not completed. Partial adjustment is a result of the increasing costs of moving from one stock to another. For example, to cause a home to be built within the quarter a household desires it aill require substantial overtime payments to the builder. Another factor causing only partial adjustment is the time required to finalize mortgage terms between the mortgagor and mortgagee. We hypothesize that the, change in customer stock is a fraction of the difference be-tween the equilibrium stock and the actual stock in existence. That is:

10) GCUT = A*(CUTt *-(1 -d) CUTt , j )

t Where: GCUT t

= Gross change in customer stock in period t.

(CUTT - (1-d) CUT t ,j)

A = The coefficient of adjustment (the fraction of the desired change actually occuring)

CUTt * = Equilibrium customer stock, as in equation (11).

CUT t

= Actual customer stock, period t.

d = Rate of stock depreciation (1-d) CUTt ,j is the stock of customers at the beginning of period t.

To estimate (10), we had to write the function in (9) explicitly. We -

said that (9) depended linearly on its independent variables. That is:

11) CUTt * = b + c*RWAPt + f*NR21&t By substituting for CUTt*from equation (11) into equation (10) we had:

(12) GCUTt= A*b + A*c*RW@Pt + A*f*NR21&t - A*(1-d)* CUT t ,j 12

Equation (12), however, could be estimated. We do not observe GCUTt ;

and it cannot be calculated because d, the rate of depreciation, is unknown. The net change in customer stock, the change frcm one period to the next, is observed. In fact, (13) NCUT t = CUT, - CUT (,)

is found as the difference between the number of customers from one period to the next. NCUT tis related to GCUT as t shown in equation (14).

(14) NCUT t = C'UT t - d* CUT t ,j - (1-d)* CUTt ,) = GCUTt - d* CUT t ,)

In words, the net change in customer stock equals the gross change less the replacement of depreciated customer stock.

By subtracting d* CUT t ,) from the left and right hand sides of (12) we have our estimabla equation.

(15) NCUT t = A*b + A*c*RWAPt + A*f*NR2164t - (A*(1-d) + d) CUT t ,)

B. ELECTRICALLY HEATED HOMES The share of electically heated homes is detennined by the number of new homes using electric heat and the net number of old homes switching ..

to electric heat. We began the derivation of an estimable form for this relation by noting an algebraic identity.

(16) CUERt= NDERt

• CDERt + CUER t ,j 13

Where: CUER t

= Customer stock, electrically heated, in period t.

NDER t

= New customers, adopting electric heat, period t.

CCER t

= 01c custcmers, acopting electric neat, period t.

We nypothesized tnat the number of both new and old customers acepting electric heat depended on the relative price of electricity to alterna-tive energy prices, non-price rationing characteristics of natural gas, and real per capita income. Each, old and new, however, depends on prices and natural gas availability in different ways since the cost for conversion to electric heat is much higher and, therefore, old cus-temers are less sensitive to relative price changes. We expressed these relationships in equations (17) and (18).

(17) NDER t/NCUTt = N(PE /PNG , PE /P0 ,ANG ,RYP@P )

t t t t t t (18) CDER t / CUT t ,) = C(PE t /PNG t , PEt /P0 t, ANG t, RYP@Pt )

Where: NCUT t

= Change in customer stock in period t.

CUT t

= Customer stock, in period t. ,

PE = Price of electricity, period t.

t PNG t

= Price of natural gas, period t.

P0 = Price of oil, period t.

t ANG t

= " Availability" natural gas, period t.

Data was not available on general service customers converting to elec-tric heat. As a result, the estimation was performed keeping in mind .

the underlying relationships summarized in equations (17) and (18) i.e.,

we could observe the change in all-electric customers from both sources.

This statement is written mathematically, (19) CUER t - CUERt.) = NDERt + CDERt For estimations, the general functional foms in equations (17) and (18) were assumed to be linear, i.e.,

(20) NDERt/NCUTt = a+b*PEt/PNGt + c*PE t/P0g + d*ANGt

+ e*RYP@P t

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(21) CDERt / CUT t ,) = f+g*PEt/PNG( + h*PEt /P0t

+ k*ANG t

+ m*RYP9P Substituting from (20) and (21) into (19) gave the estimable fom of tne ecuation.

(22) CUERt -CUER t ,j = a*NCUTt+b*(PE t/PNG t)*NCUT t+d*ANGt*NCUTt

+ e*RYPOP *NCUT t t

+ c*(PE t/P0 )*NCUTt t + d*ANG *NCUT.,

t

+ e*RYP@P *NCUT t t

+ f* CUTt ,) + g*(PE t/PNGt )

• CUTt ,)

+ h*(PEt /P0t )

• CUTt ,)

+ k *ANGt

• CUTt , j + m*RYP@Pt

• CUTt , j e

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APPENDIX A THE LOGIT MODEL By definition the variable SAPL must take on a value between 0 and it

1. A regression of SAPL on independent variables would not embody this constraint. For some values of the independent variable the forecasted-value of SAPL may be greater than 1 or negative. Writing the estimating equation with LOG (SAPL) would not cure the problem since forecasted values may still be greater than 1. Instead the dependent variable was specified as LOG (SAPL/(1-SAPL)) . The range of LOG (SAPL/(1-SAPL))

is uncontained, but conversion back to SAPL forced it to lie between 0 and 1.

To see tnat this is true, take the pneral expression 1

A) Z = LOG X/(1-X)

Z is of the form of the variable we estimated. It was unconstrained, allowed to take values from minus infinity to plus infinity. The solu-tion for X, the variable of interest in the forecasts, as a function of Z is:I B) X = exp(Z)/ 1 + exp(Z)

1. The :olution for X is found as follows:

Z = LOG X/(1-X) exp(Z) = exp(LOG X/(1-X) ) = X/(1-X)

Taking the inverse of both sides 1/exp(z)=(1-X)/X=h-1 so,f=1+1/exp(Z)

Finally, X = 1/(1 + 1/exp(I)) = exp(Z)/ 1 + exp(Z) 16

As Z tends to minus infinity, X goes to 0. As Z tends to plus infinity, X goes to 1. All intermediate values of Z cause X to lie between 0 and 1. Thus, our theoretical constraint is met.

This specification is known as LOGIT. It is the natural logarithm of tne " odds" that X will occur. In our content, it is the LOG of the odds that a customer will have appliance 1. By solving for SAPL, we have the forecasted saturation rate of appliance i.

For ease in estimation, the odds for the saturation of appliance i was hypothesired to be related to the independent variables multiplicatively.

That is:

C) LOG (SAPL$ g/( 1-SAPLit)) = a + D* LOG (RW@Pg ) + c* LOG (RPAPLt )

+ d* LOG (NR@ CUTg ) + f* LOG (CUT t) 17

THE SPECIFICATION OF THE INDUSTRIAL SECTOR OF THE MIDDLE SOUTH FORECASTING MODEL 18

TABLE OF CONTENTS PAGE I. INTRODUCTION 20 II. SPECIFICATION 20 A. Model Structure 20

8. Data Development 24 1

19

I. INTRODUCTION The operating companies' classification of customers into Industrial or Ccmmercial classes is often not done in the most economically mean-ingful way. A similar, but not identical, split is between manuf act-uring and non-manufacturing industries. Since this latter split was more meaningful economically, the data on the service area was avail-aole on this split, and the operating companies' data could be aggre-gated to fit this split, models were built on the basis of manufacturing /

non-manufacturing, not Industrial / Commercial. The specification which follows is that for manufacturing customers. The sp'ecification of the model for non-manufacturing energy is described in the section called Commercial which appears later in this volume.

II. SPECIFICATION The manuf acturing sector forecasted electric energy sales to each of the major manufacturing groups in each of the operating companies.

The classification of groups was done according to standard industrial classification (SIC). The majority of the breakdown was done at the 2-digit level with 3-and 4-digit groupings used for large sector (eg:

aluminum). Not all 2-digit breakdowns were modeled separately since the size of some was too small to allow confidence in the estimated parameters. An aggregate approach to these smaller groups was found to lead to better statistical results and forecasting accuracy.

A. MODEL STRUCTURE '~

In developing the manufacturing & mining model, four major factors were considered:

. Production Activity

. Factor Substitution

. Technological Change

. Conservation 20

Electricity is primarily a factor input to production, therefore its use is heavily tied to the levels.of production activity. However, tne relationship between production and consumption can and will change over time due to f actor substitution, technological advances and con-servation efforts. The model was developed to include each of these aspects and to test their relative impact on sales.

In arriving at tne estimated form, we began with the basic hypothesis that there was a proportional relationship between production and con-sumption of electricity, i.e.,

1) MWH gt = A*X it Where: MWH = Megawatt Hour--Sales Industry 1, period t.

it X

it

= Industrial Output--Industry 1, period t.

A q = Parameter This relationship is modified through time as we experience changes in the other detenninants, namely, input substitution, technology and conservation efforts. Th. coefficient A, therefore, is not constant but changes through time as each of these factors change.

The major sources of substitution is between alternative energy sources, namely, fuel oil, natural gas, coal and labor. The substitution was said to be a function of:

1) technological feasibility of substitution -

2) availability of alternative fuels

3) relative price of electricity to prices of other fuels and wages.

The first thing considered was the feasibility of substitution, given the production process. In most cases, the industry grouping was ag-gregate enougn such that viable alternatives do exist to the group as a whole. However, some understanding of the industrial group and their major substitution possibilities was developed.

21.

Secondly, once considered technologically feasible, to what extent was tne substitute available in the region? Availability is of two types:

1) never available or hardly used in the region of the country and 2) the supply was limited over a portion of the study period. In the former case, the inpact is minimal and can be dropped from further consideration during the estimation.1 However, in the latter case, some account had to be taken for the restricted supply as well as the economics of substitution.

For instance, we had to consider the curtailment of natural gas in our estimation to the extent it was a substitute fuel.

Finally, given the feasibility and availability, the choice of inputs was assumed to be a function of relative prices. The price term is included in distributed lag form to account for the fact that 1) it takes time for relative price changes to be perceived as permanent and

2) once changes are perceived, substitution takes time to occur.

Technological change was defined to include voluntary advanceme.'ts as well as government safety and health standards which required addttfonal/

less usage per unit of output produced. The most notable government legislation that has impacted sales growth was the Occupational Safety

& Health Act (OSHA) and the EPA's Air Pollution Control act. Every effort was made to identify these changes for each of the industrial groups investigated and to quantify them in order to include them in the estimation.

Finally, conservation efforts on the part of industrial users altered the steady relationship between output and consumption. Conservation

~

was considered to arise for two reasons: 1) the result of the oil embargo and resulting energy crisis of late 1973 and 2) the effort to minimize the impact of increasing energy costs. The first was consider either 1.) If the fuel source was considered a viable option in the fore-cast period, then the final forecast reflected that impact.

However, if not part of the historical picture, its full impact on sales could not be measured.

22

to be temporary or permanent depending on the extent of the programs enacted at the time of the crisis and the degree to which they have been maintained. While such efforts were difficult to quantify, an effort was made to obtain information on the major programs undertaken in the different industrial groups. Where explicit informatien was available on such programs, it was used; otherwise a conservation pattern was depicted over the interval allowing the statistics to measure the impact. The second reason, increased energy costs, was considered by including the real price of electricity. To account for the time span required to effect a significant change in usage, the price of elec-tricity was entered in distributed lag form. ,

Thus, the factor of proportionality, A, in equation (1) was considered to be not constant but rather a function of: 1) input substitution,

2) technological change and 3) conservation efforts.

Thus (1) was modified as follows:

2) MWH$t = A(Pjgg, Tit,CONSit,RPEgg)

• Xit where:

MWH gt = Megawatt Hour - Sales -- industry 1 - period t X4t = Industrial Output -- industry i - period t P

jjt = Relative Price of Electricity to Fuel or Wage j -- industry 1 - period t 9t = Vector of Technological Changes -- industry 1 -

T period t CONS gt

= Proxy for conservation efforts RPE gt = Real price of electricity -- industry 1 - period t We assumed, that the functional form of A was multiplicative, so we rewrote (2):

3) MWH

$t =a*P j$t d*T

• CONS dgg

• RPE ft *X jt k c jt An estimable fom was derived by taking the natural logarithm of both sides of (3):

23

4) LOG (MWHjt) = LOG (a) +...b j

• LOG (Pjit)+. .+C

• LOG (T4t)

+ d

• LOG (CONS $t) + f

• LOG (RPE4t) + k

• LOG (X,t)

The proportional relationship hypothesizeo between production and con-sumption suggests that the coefficient on output, k, should be close to one. In fact, k differed from one when estimated for a variety of reasons. The present specification assumed that the fixed level of consumption (i.e. independent of the level of production) was small in proportion to the variable usage. To the extent it was not, a per-centage increase in production will lead to less than 1% percent change in KWH use. Second, in the short run, as present plant capacity becomes fully utilized, the returns to scale diminish in some processes leading to a change in the proportional relationship. Finally, the inability to quantify the variables in A(.) may have caused severe bias in the estimation of k. Every attempt was made to gather as much information as possible that will impact A.

One crucial item that was not addressed in this specification is self-ganeration. To the extent customers generate their own power, a potential bias is created as sales do not reflect the electricity required to generate the estimated output.

3. DATA DEVELOPMENT In this section the development of the explanatory variables is outlined: ..

1) Industrial Outout The index of industrial output was developed for manufacturing and mining groups. It was obtained by combining national infor-mation on employee productivity with regional ta of the level of manufacturing employment activity. The loca. 3roduction index was constructed as follows:

4 24

s JQIND gt x

it , -

• E gast g

it where:

S X

t

= Index of Industrial Output -- Industry 1 - Region s JQIN0 it

= Federal Reserve Board index of Industrial Production

-- Industry i - U.S.

E it

= Total Employment -- Industry i - U.S.

E3 0st = Total Employment -- Industry i - Region s The term JQIN0gt/Egg is the average level of production per employee on a national basis, for each of the industrial groups.

We multiplied this ratio, as a proxy of production per employee in the individual industries by the number of employees in the area to arrive at an estimate of area production. The assumption made was that the gains in output per employee in the area could be proxied by those in that industry group on a national basis.

Given the level of disaggreystion at which estimation was done, this was probably reasonable.

2) Eneroy Substitution Two concepts had to be quantified here: 1) availability of natural gas and 2) energy and labor costs. The availability of natural gas was not easily quantified. Where availability was an issue a qualitative variable was developed.

Price tems for both electricity and alternative fuel sources had to be developed. The criterion used in developing all price estimates was that the term should reflect the change in prices that had occurred. Ir addition, in developing the price term for electricity, two criteria were followed: 1) the term was de-rived from the rate schedules, and if possible reflected the fact that customers fall into different blocks of a schedule and therefore face different prices and 2) the tem did not change simply because energy consumption levels changed, a problem known as simultaneous bias.

25

Two possibilities existed for constructing electreity prices, a) " typical bill" b) neighted marginal price A) " Typical Bill" The typical bill was constructed in the following steps:

1) define a " typical" or representable level of usage based on KWH consumption and KW demand for a billing period for each rate schedule,

11) hold the typical usage constant, calculate the cost of this level of use by applying the rates in effect (KWH and KW charges) as well as fuel adjustment and any tax surcharges, iii) weigh the average of the " typical bills" for the individual rates. The weights were based on the percent of the classes KWH sales that were billed under each rate.

Thus:

3 PETB 3 ajj

• TB /KWH$

where:

PET 83 = ' Typical bill" price of electricity (cents per KWH) agj = Proportion of KWH sales to industry j billed under rate i TBgj = " Typical Bill" - Rate i (cents) 26

KWH$ = " Typical" KWH usage - Rate i (fixed)

The typical bill approach avoided the simultaneity problem and was derived from the rate schedules, but it did require an as-sumption of " typical usage".

8) Weighted Marginal Price The weighted marginal price was a weighted ave' age of KWH charges, or consumption charges faced by the industrial user. The price term was constructed in the following steps:

i) A weighted marginal price for each applicable rate schedule was constructed. Each of the energy block prices was weighted by the proportion of custcmers whose end usage fell within each block. For example:

Rate Schedule - Large Power Service:

$5,000 for the 1st 1,500 KW or less of load

$ 2.75 per KW for the next 6,500 KW of load

$ 2.10 per KW for all additional KW l.354 per KWH for the 1st 360 KWH per KW of load 1.15c per KWH for all addition KWH The weighted marginal price for this rate schedule is WMP p-3 "3 1

• 1.354 +a 2

• 1.15c where:

aj ' ? 6i customers whose KWH per is et'een 0-360 a2 - f f customers whose KWH per KW is greal.er than 360 27

ii) The weighted marginal price for each industrial group was a second weighting of rate prices developed by the method in (1). This second weighting was based on the proportion of KWH billed in a given industrial group under each of the applicable rates. This second weighting took into account the relative importance of each rate to the industrial groups. Thus:

WMP 3=

aij

• N" i j=1 where:

WMP) = weighted marginal price -- industry j a9) = proportion of KWH sales to industry j billed under rate i WMP$ = weighted marginal price -- rate i Marginal price was based on KWH consumption and price per KWH. As such, it did not include the demand charges incurred under these rate schedules. The omission implicitly assumed that demand charges do not sig-

. ificantly affect total consumption but only the dis-tribution of consumption throughout the day. To the extent that this was not true, the exclusion of the demand charge was invalid.

Price terTns were included to reflect two phenomena:

1) conservation and 2) fcel substitution. The weighted ~'

marginal price, in that it reflects costs on the margin, was included to take into account conservation. For substitution of energy sources the entire cost structure was considered, by using the " typical bill" relative to alternative fuel costs and labor co_cs.

28

e

3) Technolooical Chances The exact form of variables to reflect technological change de-pended on the information available.

All major structural changes were noted along with their instal-lation date in order to account for shifts in energy during the equation estimations.

4) Conse rvation As mentioned, conservation of electricity was considered to be

, of two types. Reaction to increased energy costs was tested by including the real price of electricity. The price was deflated by the who'.esale price index for the relevant industrial group.

Conservation for " patriotic" purposes was also considered. A qualitative variable was constructed to depict a reasonable con-servation pattern.

e 29

THE SPECIFICATION OF THE COMMERCIAL SECTOR OF THE MIDDLE SOUTH FORECASTING MODEL 30

TABLE OF CONTENTS PAGE I. INTRODUCTION 32 II. MODEL STRUCTURE 32 III. SPECIFICATION OF THE ESTIMABLE FORM 35 e e 31

I. Introduction The Commercial sector presented a difficult forecasting problem.

The sector has shown substantial growth over the historical period both in employments and in energy. As a result, relating energy to employment effectively explains a great deal of the variation in energy. On the other hand, the causal betw7en employment and energy is complex. The growth of air conditior ing ard electric heat and the growth of. square footage of commarcial establishments are also known to be important detenninants in the growth of the sector's energy. The problem arises from the paucity of data for these significant causes. Thus it is possible to shcw good summary statistics, R-squares and so on, in the estimt. ion of the sector while little understanding of the behavioral charac-teristics of the sector are fonned.

In making our forecasts, we were careful to appreciate the historical relationship between energy and employments might not persist in the forecast period if the factors which we were unable to quantify changed radically.

II. Model Structure Consumption in the commercial /non-manufacturing sector was analyzed within, at most, seven ;najor classes: ,

1) Wholesale and Retail Trade

2) Finance, Insurance, and Real Estate

3) Personal Services

4) Construction

5) Communications, Transportation, and Public Utilities

6) Government 32

7) Mining The numoer of classes considered were reduced, when (1) the energy data from an operating company was not at the same detail, or (2) the employ-ment data for a class was not available. Estimating at the highest level of feasible detail was useful since the model was better able to analyze the particular growth patterns of each class.

In general, energy consumption of the commercial sector is dependent on:

1) growth of the sector of employments

2) consumption per employee - in particular, responses caused by:

a. th,_ saturations of heating and cooling equipment .

.b . voluntary conservation effort

c. the price of electricity

d. weather

e. technology

f. establishment size The growth of each class within the sector was proxied by the growth in the number of employees in the class. Using employees, rather than the number of establishments or commercial customers, measures the growth .

in the number, as well as growth in the size, of commercial establishments.

The growth of employment in each class was not estimated within the commercial block of the model since it was already considered within the service area economic models.

We specified that consumption per employee depended on a number of factors.

For some factors, it was a relatively easy task to identify variables which represented the history of the factors. For other factors, no time series were available. We began with the factors which could be easily modeled.

33

The price of electricity was modeled in much the same way as the price had been modeled in previous sectors. The price of electricity relative to the prices of alternative fuels and wages was included to capture .

the choice of technology. The less expensive electricity becomes rela-tive to other fuels, and labor, the greater the propensity for commercial estaolishments to -hoose electricity-based technology for heating, cooling, and other energy-cor.suming loads. The price of electricity used for this purpose is the typical price as described in the Industrial Speci-fication. It included KW, as well as KWH charges. Similarly, the real price of electricity was included to account for effects resulting from the increased or decreased cost of using electricity, the cost per kilo-watt-hour in the last block of consumption, deflated by the consumer price index for the the southern United States. The deflation was per-formed to correct for overall inflation in the sector and the economy.

A dummy variable was introduced to account for the voluntary, non-price related, conservation efforts which occurred in 1973 and 1974, in response to the oil embargo. The variable's impact was seen not to persist into the forecast.

Cooling-degree days and heating-degree days were included to reflect the impact of weather on commercial energy consumption. The effect of weather on energy will increase as the saturation of electricity-consuming heating and cooling equipment increases. However, time series were not available for the saturations of this equipment. Thus the weather variables were included without any modification. We were im- -

plicitly assuming that the saturations have been constant over the period of historical analysis. While this assumption may be appropriate for air-conditioning since the greatest penetration of air-conditioning occurred in the early 60's, it is not true for the saturati,ons of elec-tric-heating equipment. Since the growth of electric heating will increase with shortfalls in natural gas production, the assumption of constancy is a serious shortcoming of the specification as it now exists. Effort ought to be made in the future to measure the changes in commercial customers having electric heat load.

34

Technolocy affects electricity consumption in two ways. First, there are technological innovations which perform energy-consuming tasks more efficiently. These types of technology will reduce the consumption of electricity. Second, there are innovations which reduca the need for employees to perform the activities of the sector. These will, generally, increase the consumption of electricity per employee. The first type of technology was modeled by discerning important historical innovations which occurred and modeling them with qualitative, or dummy variables. The second type of technology might have been modeled by qualitative variables. However, since the impact of labor-saving tech-nology could not be readily quantified, the coefficient on the number of employees was estimated without constraints. An elasticity of more than one on employment is interpreted as increased load from labor-saving, electricity-consuming equipment.

The saturation, or stock, of electricity-consuming equipment in the sector was not available. B e hope was that the relative cost of elec-tricity to other fuels would pmxy the growth in the accumulation of these stocks.

III. Specification of the Estimable Form The consumption of electricity in the commercial /non-manufacturing sector was specified to be in multiplicative form, infact,

1) MWH g = A*(TPEL/Py ) bl * (TPEL/P2)b2 * . . . * (TPEL/ AHEM)Dn

• d

• (MPEL/CPIS)c CON

• TECH 8

• exp [f*0NCD03

• exp (g*0NHD03

• E 35

unere:

MWH 9

= megawatt-hours, commercial class i TPEL = typical price of electricity

= price of fuel j P)

AHEM = average hourly earnings MPEL = marginal price of electricity CPIS = consumer price index, Southern region CON = dummy for embargo induced voluntary conservation TECH = technology DNCDD = difference from nomal, cooling-degree days DNHDD = difference from normal, heating-degree days E, = employees commercial class i NOTE: exp ( . ) = e (.), i.e. the base of natural logarithms ~

to the power implied by the expression in parenthesis NOTE: The general " TECH" was replaced by the growth rate of employment data.

36

The actual estimation was performed linearly. Equation (1) was con-verted to linear form by taking the natural logarithm of each side.

2) log (MWH $

) = log (A) + yb

• log (TPEL/P1 ) + b 2 * ***

• b n

• 1 g(TPEL/ AHEM)

+ c

• log (MPEL/CPIS) + d * (CON)

+e

• log (TECH) + f

• DNCDD + g

• ONHDD + h

• log (Ej )

37

THE SPECIFICATI0F 0F THE WHOLESALE SECT 6R OF THE MIDDLE SOUTH FORECASTING MODEL 38

e TABLE OF CONTENTS PAGE I. SALES BY THE COOPERATIVES AND MUNICIPALS 40 A. Residential Sales 41

3. Comercial and Industrial Sales 42 II. SALES TO COOPERATIVES AND MUNICIPALS 43 39

Electricity sales to cooperatives and municipals result from their ultimate sales to their customers. In modeling this sector, we sougnt to capture tne benavior of tneir customers, as it relates to electricity consumption, from which the operating companies' sales could be derived.

I. SALES BY THE C0CPERATIVES AND MUNICIPALS Optimally, we hoped to model the sales of cooperatives and muni-cipals as the sales of the operating companies had been modeled.

This was, in fact, impossible. First, there were discrepancies in class definitions. There generally were classes, or combina-

• tions of classes, equivalent to the residential class. But, less likely were commercial and industrial classes. Even when they existed they tended to be very different from the manufacturing

- non-manufacturing dicotomy which is most meaningful economically.

Instead, non-resioatial customers were classified as large-power

'and small-power users. The distinction by cooperatives and muni-cipals is made on the basis uf KW demand, so that large-power include both manufacturing and large non-manufacturing like hospitals.

Small-power users are closer to commercial, or non-manufacturing, but some small industrial are also included.

Second, a more severe shortcoming was data availability. The sales by cooperatives and municipals were often not available or available on an annual basis only. Even when data from co-operatives and municipals were available, time series on casual factors in our models were not. For example, appliance saturations and employment data were not available for cooperatives and municipals.

The approach to forecasting the sales of the wholesale sector began by considering the ideal. But no analysis was done following the guidelines set forth for operating company sales. Although this was not possible, as few compromises as necessary were made.

This required the modeling effort to be tailored on a case by case basis. The following specification fits what was the case closee, to the ideal.

40

A. Residential Sales ne analysis of residential sales for the operating companies considered three major areas: 1. appliance saturations, 2. energy per customer, and 3. customer growth. For the wholesale sector, the analysis of appliance saturations could not be made; and energy per custcmer could not be considered in the same level of detail.

The causal variables for customers were available and the speci-fication for operating customers was followed.

I" Usage per customer - By assuming the munic pal and coogrera-tive customers are similar to those served by the operating companies, the history of saturation rates, income, prices, and weather was proxied by usage per customer of the operating companies.

That is,

1) MWH@CWS = f(MWH0C) where: MWH@CWS = usage per customer (residential) of cooperatives and municipals MWH@C = usage per customer (residential) of the operating company

2. Customer Growth - For the cooperative and municipal customer growth, the specification for the residential sector was applied.

Therefore,

2) CUT - CUT,1=a + b

• RW@P + c

• NR2164 - d

• CUT,1 41

where: CUT = custcmer stock (-1 subscript represents last periods stock)

RW@P = per capita wealth of the operating company service area NR2164 = population 21 to 64 years of age in the operating company service area S. Commercial and Industrial Sales The industrial sales for the wholesale sector are relatively in-significant. Most customers who are classified as manufacturing are small and serve a local market. Consequently, they are similar to commercial, or non-manufacturing, industries in their behavior.

No causal data, or size of firm data, was available on the wholesale level. Under these two constraints - 1. most non-residential energy is similar to the operating companies' commercial sector and 2. detailed industrial analysis is difficult - non-residential energy for cooperatives and municipals was related directly to operating company commercial sales.

3) MWHCIWS = f(MWHC) where: MWHCIWS = megawatt hour sales by cooperatives and municipals to non-residential '

customers MWHC = megawatt hour sales by operating company to commercial customers 42

II. SALES TO COOPERATIVES AND MUNICIPALS Discrepancies between sales by cooperatives and municipals and sales to cooperatives and municipals come from three major sources,

1. energy generated by the cooperatives and municipals, 2. energy purchased from other electric atilities, and 3. losses. The relation-ship between sales by and sales to cooperatives and municipals were considered on an econometric basis. In making the forecast, in an econometric mode, judgemental decisions had to be made and inputted. The possibilities to consider included:

I' would the cooperatives and municipals continue self-generation following the pattern demonstrated by history.

2, would they continue to buy power needs from vendors in the same historical percentages.

3. would technological innovation or service area changes lead to changes in loss factors.

Given historical relationships and qualitive assumptions in the forecast, sales to the cooperatives and municipals were made from forecasts of sales by cooperatives and municipals.

43

THE SPECIFICATION OF THE STREETLIGHTING SECTOR OF THE MIDDLE S0tJTH FORECASTING MODEL 44

TABLE OF CONTENTS PAGE I. INTRODUCTION 46 II. SECTOR DETAIL 46 A. Lamps 46 S. Wattage car Lamp 47 C. Streetlighting Energy 49 APPENDIX A: Streetlighting Specification and Estimable Form for Companies with Energy Data Only 51 e

t

• 45

I. INTRODUCTION ihe analysis of the streetlighting sector was divided into three parts. The growth in energy consumption was seen to depend on

1) the growth in the number of lamps and 2) the changing wattage requirements for the lamps. The first two sections of the fol-lowing discussion consider these two levels of detail separately.

Lamps and wattage per lamp were combined to form the total wat-tage in the sector. The third section relates the concept of sector wattage to total energy for streetlighting.

II. SECTOR DETAIL A. Lamps The number of lamps was considered to be dependent upon the growth in households. As more households have been formed, municipalities have extended streetlights into newly formed neighborhoods. To proxy the number of households in the service area, the number of residential customers was used. Of course, not all households formed were within the corporate limits of municipalities providing street-lights. Consequently, the correlation between customers and the number of lamps was modified to account for the degree of urbanization in the service area. As a proxy for this phenomenon, the number of non-manufacturing employees per capita was used. The rationale for this approach was that, as urbanization occurs, there is a coincidental growth in the number of persons engaged in sales and services.

That is, the growth in cities is paralleled by a similar growth in commercial establishments.

46

The general form of the relationship was specified:

1) LAMPS = F(CUT, ENM/NR) where:

LAMPS = number of streetlights CUT = number of residential customers ENM = number of employees in non-manufacturing -

industries in service area NR = population of service area The specific functional form was said to be multiplicative:

D

2) LAMPS = A* CUT *(ENM/NR)c The estimation was performed linearly on the natural log-arithms of each variable:

3) log (LAMPS) = log (A) + b* log (CUT) + c* log (ENM/NR)

8. Wattage Per Lamp The second concept considered in the sector was the wattage per lamp. Wattage per lamp depends on the relative growth of each type of lamp used within the service area. The first step in forming an understanding of the evolution of the wattage per lamp was to model the growth rates of the various types of lamps.

47

The specification of these growth rates considered the changes in the share of total streetlights held by each type of lamp. The share of each type was modeled by considering the long-tenn desired share of each type and the process of adjustment to that desired share. The specific form of the relationship used is known as a Gompertz function.

The Gompertz function assumes that the share depends on both the target, or equilibrium, level of the share, and the ratio between the target level and the actual level.

The relationship is said to be multiplicative. Letting S = actual market share S* = target market share The Gompertz function is written:

1) (S/S,j) = (S*/S,j)9 That is, the growth is the market share (S) from last period's share (S,j) is a proportion of the desired growth (S*/S,1) is a proportion of the desired growth (S*/S,j). g is the coefficient of adjustment. If, for example, g = 1, the actual share will adjust to the desired within the period.

If g = 0, S/S,j = 1 or no adjustment will take place. As ,

g goes from 0 to 1, the speed of adjust;nent increases.

Estimation for the market share equation was performed linearly by forming the natural logarithm of each side of the specified Gompertz equation and solving for S.

2) log (S) = g* log (S*) + (1-g)* log (S,j)

The concept of market share was related to wattage per lamp by cpnsidering the following identity:

48

3) WATTS @ LAMPS = WATTAGE *S + WATTAGE *3 * **

1 1 2 2 wnere:

WATTS @ LAMP = average wattage per lamp WATTAGE 9

= average wattage lamp type i S j = ratio of the number of lamps of' type i to the total number of lamps C. Streetlighting Energy The concepts of (A) and (B) were combined in the considera-tion of total energy sold to the streetlighting sector.

The first step was to form the total wattage for streetlignts in the service area. This was done by multiplying the number of lamps in the service area times the wattage per lamp.

LAMPS

• WATTS @ LAMP ,

Total energy for streetlighting was said to be proportional to the wattage in the sector.

1) MWHSL = A*(LAMPS

• WATTS @ LAMP) where:

MWHSL = total energy to the streetlighting sector Notice that A is the proportionality factor.

The actual estimation allowed the sector's energy to differ from exact proportionality. Instead, the sector's energy was allowed to grow at a rate differing from the growth rat e in sector wattage. This flexibility implied the fol-lowing functional form:

2) MWHSL = A*(LAMPS

• WATTS @ LAMP)b 49

I %

which was estimated linearly in the natural logarithms.

3) log (MWHSL) = log (A) e b* log (LAMPS

• WATTS @ LAMP) 50

APPENDIX A Streetlighting Specification and Estimable Form for Companies with Energy Data Only As described in Section C, total energy for streetlighting was saia

~

to be proportional to sector wattage

1) MWHSL = A*(LAMPS

• WATTS @ LAMP)

However, data on neither lamps nor wattage per lamp was available for s operating companies. Instead, we assumed that there is an adjust-me process toward a desired system wattage. This adjustment in total wattage has underlying it an adjustment in both lamps and wattage per lamp. We assume the adjustment process to be governed by the Gompertz function (see Section B).

Therefore,

2) WATTAGE / WATTAGE,) = (WATTAGE */ WATTAGE,j)9 where:

WATTAGE = Total streetlighting watts (LAMPS

• WATT 50 LAMP)

~

WATTAGE *= desired streetlighting wattage Solving for WATTAGE yields:

2') WATTAGE = WATTAGE,j f1'9)* WATTAGE *9 51

From equation (1) we derived

3) MWHSL = A* WATTAGE

4) WATTAGE,j = MWHSL,j/A and

5) WATTAGE * = LAMPS

• WATTS @ LAMPS

• Substituting (4) and (5) into (2') and the resulting identity into (3) yielded:

6) MWHSL =9 A *(MWHSL,z) II'9)*(LAMPS

• WATTS @ LAMP *)9 Using the specification for LAMPS in Section A, the final specification was derived b

7) MWHSL = a*MWHSL,z(I-9)*(CUT )g*((ENM/NR)c)g

• (WATTS @ LAMPS *)9 Notice that the constant (a ) is a combination of "A" and the constant in the LAMPS specification. WATTS @ LAMP

• is the desired wattage per lamp variable which was ignored or a qualitive variable was developed to account for the introduction of mercury vapor lamps.

The equation was estimated linearly in the natural logarithms of the variables; that is,

8) log (MWHSL) = log (a ) + (1-g)* log (MWHSL,j) + g*b* log (CUT)

+ g*c* LOG (ENM/NR) + g* log (WATTS 0 LAMP *)

52

THE SPECIFICATION OF THE PEAK DEMAND SECTOR OF THE MIDDLE SOUTH FORECASTING MODEL S

53

TABLE OF CONTENTS PAGE I. INTRODUCTION 55 II. ADDITIVE FORM 56 A. Sector Derivation 57 B. Estimation 68 APPENDIX A: Derivation of Weekly, Average Hourly Load Data 70 APPENDIX B: Estimation Implementation 72 e

54

I. INTRODUCTION Comaared to energy sales data, the information available on hourly demand was limited. Class of service data on an hourly basis w'as avail-able for only a few years and for only a few days of the year. The lack of detailed data on demands made the disaggregate energy data and models esser.tial for the development of tne Peak Cemand Model. The demand model was linked to the energy model in order to provide 1) con-sistency between models and 2) detailed information on customer and end-use mix. The consistency between models is important since hourly demands, e~ specially maximum hourly demands, are dependent on total con-sumption. Given the total energy sales, the peak of the consumption depends on the particular contributions of various customers and end-uses at the peak hour of consumption.

The model that was developed did not consider peak demand, per se.

In order to adequately sort out the contributions to demand from various sectors, analysis was done for a single hour of the day. This was done since the assumption was made that customer habits were fully consistent over time with respect to their daily usage pattern. Given the atsump-tion on habits at a disaggregate level, the actual load pattern for the utility system will change as customer mix and end-use mix change.

By selecting a single hour for analysis, the " habits" modeled were a problem.

The peak demand model was developed for a single hour of the day, the

" dominant" hour. The " dominant" hour was defined as the hour during the season (winter or summer) during which tne greatest percentage of seasonal peaks occured. This hour, then, is assumed at this stage of analysis as the hour at which system peak is most likely to occur in the future.

55

The estimable form developed for the peak demand model is called the

• additive" form. The additive forms views peaks demand as the sum of demands for major classes, sub-classes, and end-uses.

II. ADDITIVE FDRM The demand at a given hour is composed of the hourly demand of each of the classe:, i.e:

=

(1) MW k MWRk

• NNIk + MWCk

• MNN3k

• NW3'k, + MWC0 k

where:

MW, g

= Megawatt Demand - hour k MWR, = Megawatt Demand, Residential Sector, hour k MWI k

= Megawatt Demand, Industrial Sector, hour k MWC = Megawatt Demand, Commercial Sector, hour k k

MWWSj= Megawatt Demand, Wholesale Sector, hour k

=

MWSL g Megawatt Demand, Streetlighting, hour k MWC0k= Megawatt Demand, Company Use, hour k This summation of loads can be further disaggregated by breaking the sector demands into subclasses and end-uses. For example, the industrial demand can be broken down by major SIC category; the residential by

, major appliance use, etc. In 6ne limit, one would want to forecast the system demand by forecasting the demands of the individual classes.

The latter would be developed by accounting for the contribution of individual end-uses to the sector's demands. However, the current data set did not provide hourly demand by class of service, nor by major end-use. Thus a model was developed to forecast the aggregate hourly demand, MW '

k The detail provided by the economic and energy models was used to develop

~

the indicators of the sector contributions. In all cases the basic starting point was megawatt hour sales to the particular sector. If the sector load factor for the desired hour was constant then it would 56

be sufficient to include average megawatt hour sales over the period for each sector, allowing the coefficient to denote the share of energy consumed in the dominant hour, i.e:

MWJ kt

=a k

• MHU t

where:

MWJ kt = Megawatt Demand, Sector J - Hour k of period t a

k

= Fraction of MHJ tconsumed in Hour K MHJ t

= Average Megawatt Hour Consumption (or Demand),

Sector J - period t In fact the distribution of sector sales across the day changes as 1) the mix of end-uses changes and 2) the usage of those end-uses within the hour changes. Thus the key to this approach was the ability to break MHJ into components that allowed us to denote changes in end-use mix and in usage of these end-uses. The derivation of these component indicators are reviewed for each of the major sectors. These are then combined into an estimable form.

A) SECTOR DERIVATION RESIDENTIAL SECTOR The residential sector was composed of several major end-uses, identified, in part, in the appliance saturation model. A major breakdown for these end-uses was between base and weather sensidea appliances. The ' weather ,,

sensitive appliances, heating and air conditioning, represent a signifi-cant portion of the residential load and are highly sensitive to hourly weather patterns. The base appliances, while changing in mix, as a group represent a more consistent load. For these reasons, residential sales were split into base and weather sensitive components. The deriva-tion of each is developed below:

57

Base Comconent The base term was defined as the mecawatt hour sales a sociated with the use of non-neating and non-air conditioning appliances. It was derived from the available information and according to the following formula:

MHRi *

=

b RBASE j g b BAPPL j where:

RBASE j = MWH Residential Base, period i

=

MHRT b Average daily Megawatt-Hour Sales - Residential, period b 3

=

BAPPL j I XWH j

• SATj

• CURT j j=1 ie: Average annual KWH contribution of base

, appliances

=

KWH j Average annual KWH usage - base appliance j sal jj =

Saturation of base appliance j - period i CURT j =

Total residential customers - period i Period b was defined as the month in which the minimum ratio of energy per day to the base appliance stock occured. Daily Megawatt hour use was attributed to base appliance use in this period. In order to extend the base component over the course of the year this ratio was multiplied by BAPPL j which represented the growth in the base appliance stock over --

the year.

58

Weather Sensitive Comoonent The weither sensitive component was defined for the summer and winter periods. In both cases, weather sensitive for the period defined as the difference between total residential sales and the base component was derived, i.e.:

RWS j =

MHRT) - RSASEj wnere:

RWS 9

= Normalized Weather Sensitive component - Residential, period i MHRT j = Total Residential Sales, period i ,

RBASE j = Residential Base, Period i The weather sensitive component for the period was then corrected for weather conditions at the time of peak relative to weather conditions for the period. The weather sensitive component for the period was multiplied by a function of the ratio of cooling degrees at the peak to cooling degrees for the month. The function was chosen to best cap-ture non-linear responses of energy to weather (as represented by " good-ness of fit" for regression and estimated coefficient reasonableness.

See Appendix 8.)

CDD M RWS ik =

ik RWS where:

RWS ik

= Weather Sensitive component - Residential, period i, hour k .

RWS

= Weather Sensitive Component - Residential, period i CDD,

= Cooling Degree Days - period i CDD ik

= Cooling Degree Days - period i, hour k M = Parameter of non-linearity The winter component was analogously defined with heating degree days.

Thus residential sales were broken down into a base and weather sensitive component:

59

MHRik = RBASE9 + RWSik The base comocnent is constant within a period, varying across period due to growth in the appliance stock. The weather component differs from hour to hour due to changing weather conditions and from period to period due to the growth in the stock of weather sensitive appliances.

COMMERCIAL SECTOR As with the residential sector, the commercial sector was split into a base and weather sensitive component. In addition the contribution to peak demand of the major commercial establishments was deternined.

This latter effort was done through utilization of the detail MWH energy sales figures along with sample load shapes by type of establishment.

The derivation of the base and weather sensitive components are summarized for the general case.

Base Component The derivation of the base component is analogous to the residential sector. As with the residential, it is defined as megawatt hour sales associated with non-heating and non-cooling end-uses. Formally:

MHCT

• bs CBASE is ENM bs

""is where:

CBASE is

= Commercial Base, Sector s,: period i MHCT bs

= Average Daily Megawatt Hours - Commercial, period b, sector s ENM is

= Employment Sector s, period i

=

b Period during which the ratio MHCTis/ENMis is a minimum for the year 60

Consumption in period b is used to denote base usage. The average daily megawatt hours in that year were then extended over the seasons by monthly employment.

Weather Sensitive Comoonent The commercial weather component for the period was defined as follows:

CWS =

is MHCTis - CBASEis where:

CWS

$3

= Weather Sensitive Component - Commercial, period i, sector s MHCT is = Average Daily Megawatt hours - Commercial, period i, sector s CBASE is = Commercial Base, period i, sector s The weather component was' then corrected for weather at the dominant hour:

CDD ik M CWSiks = CWS$3 CDD j where:

CWS iks = Weather Sensitive Components - Commercial, period i, hour k, sector s For those sectors that had little if any sensitivity to weather conditions, ,,

total sales were considered base and treated as such.

Aqqrecation of Commercial Sectors The base and weather components were developed by commercial subsector according to the breakdown of megawatt sales in the MWH energy model.

Aggregate commercial base and weather components were derived by weighting the sector components. The weights were developed from the sample shapes; 61

a ratio of demand at the " dominant" hour to the average hourly load over the 24-hour period was developed for the base and weather sensi-tive components of each subsector. Thus the weights for sectors were derived as follows:

Wf,=MW 3

/AMW ahere:

'W k

= Demand weight base component, sector s, hour k MW = MW demand at hour k of base load sample, sector s AMW = Average MW hourly demand for base load sample, sector s The weights for the weather sensitive components were derived from weights for the base components (calculated from load shapes in the spring or fall) and weights for total demand (calculated from load shapes in the winter and summer). Explicitly, we definr:

Wsk

• NNks/AMW s where:

W sk = t tal demand weight - sector s, hour k MW ks

= MW demand at hour k, sector s AMW 3

= Average MW, hourly demand, sector s and, -

W{k*MW s /AMW" where:

W"k = Demand weight, weather sensitive component, sector s, hour k.

MW(3 = Weather sensitive demand at hour k, sector s AMW" = Average weather sensitive demand, sector s 62

W sk andWfk were calculated from sample load shapes for the non-weather sensitive and weather sensitive seasons of the year. W{, was then derived from these two weignts and an identity. In fact, CSASE CWS D* is ,g w ,

!s Wsk = Wsk MHCT sk is MHC'is That is, the total demand weignt is a weighted sum of the weights for base and weather sensitive loads.

W"k then was found by referring to the calculated base and weather sensi-tive energies and the weights for demands in the spring or fall and summer or winter, b CSASE CWS W k * (Wsk ~ Wsk MHCT 4 f The weather sensitive component for the commercial sector was derived as follows:

N CWS E W sk

• CWS is ik *s=1 where:

W = demand weight base component, sector s, hour k MWl k

= MW demand at hour k of base load sample, sector s D '

AMW = Average MW hourly demand for base load sample, sector s The base component for the commercial sector was derived as follows:

N CSASE ik

• E W sk

• CBASE is s=1 63

WHOLESALE SECTOR The wholesale sector is composed of municipal and cooperative customers.

For each, tne predominant end-users are residential and commercial.

As with these sectors, wholesale sales were split into a base and weather sensitive component. The base and weather sensitive components were derived for the municipal and cooperative customers separately. These components were combined with the residential and commercial terms to provide an aggregate term for these end-users. The last step was considered necessary given the strong collinearity between wholesale sales and those to the commercial and residential customers of the operating company.

The derivation for the municipals and cooperatives, components follows:

Base Comoonent It was derived along the lines of the residential and commercial base component; use was made of the residential and commercial bases to spread the base usage over the season.

WSXXBASE g = MHWSXX b * "r*RBASE9 %c

• CBASE$

ar*RBASE b

D c* CBASE b where:

WSXXBASE j = Wholesale group XX Base - period i (XX = --

cooperatives,muncipals)

MhWSXX b

= Megawatt Hours - Wholesale group as

= class sales (s) by the cooperative or municipal as a percentage of equivalent class sales by theoperatingcompany(Rggg9sidential, c = commercial; e.g. 7 = V5TXHHRT RBASE 4

= Residential base, period i CBASE j = Commercial base, period i 54

For those cooperatives where the residential and commercia; sales are provided independently the derivation is as follows:

R8ASE

= $

WSCORBASE j WSCUMHRT

• b RBASE b

CBASE

= $

WSC0CBASE j WSCOMHCTb

• C8ASE b where:

WSCORBASE j =

Cooperative Base - Residential sector, month i

=

WSCOCBASE j Cooperative Base - Commercial Sector, month i Weather Sensitive Comoonent The weather sensitive component was derived for the aggregate group.

In each case the derivation is shown for the summer season. The form was analagous for the winter season:

WSXXWS =

ik (MHWSXX$ - WSXX8ASE $ )

where:

WSXXWS j =

Weather Sensitive Component - Wholesale group XX, period For the cooperatives with separate sales to the residential and com-mercial sector a weather sensitive component was derived for each:

WSCORWS g =

MHCCMHRTg - WSCORBASE$

and WSCOCWS g =

MHCOMHCT$ - WSCOCBASE$

55

Given the nature of the wholesale load, components were combined with the residential and commercial components of the operating companies to arrive at total commercial and total residential components. That is, TP?ASE =

9 RSASE, + WSRBASE9 TCSASE =

ik C3ASEik + WSCSASE$ *WSWf TRWS =

$ RWS$ + WSRWS$

=

TCWS ik CWSik + WSCWSj

• WSW" where:

TRBASE 4

= Total, company plus wholesale, residential base, period i RBASE 4

= Company residential base, period i WSRSASE g = Wholesale residential base, period i TCBASE j = total, company plus wholesale, commercial base, period i CSASE

= Company commercial base, period i WSC8ASE j = (Unweighted) Whole commercial base, period i b

WSW k

= Weight for dominant hour relat" base load (see Commercial Sector)

TkWS 4

= Total, company plus wholesale, residential weather sensitive energy, period i RWS

=

Company residential weather sensitive energy, period i WSRWS

= Wholesale residential weather sensitive energy ,

period i TCWS

= Total, company plus wholesale, commercial weather sensitive energy, period i CWS j = Company commercial weather sensitive energy, period i WSCWS

= (Unweighted) wholesale commercial weather sensitive energy WSW' k

= Dominant hour weight for relative weather sensi-tive load (see commercial sector) 56

These aggregate terms were used to represent the commercial and resi-dential sectors.

INDUSTRIAL SECTOR The industrial sector provides the most stable load of all user classes.

It is the least sensitive to weather conditions, thereby eliminating the need to separate the sector's sales into base and weather sensi-tive components. The factor having the greatest impact on demand con-ditM" is the change in industrial mix. To account for changing mix, yet to avoio problems of multicollinearity, the average hourly loads for the various sectors were weighed by their contributions to peak and aggregated to be included as one term. That is, N

INDBASE E W sk

• MHJ ik *s=1 si where:

INDBASE ik = Total industrial (base), period i, hour k W

sk = Demand weight, sector s, hour k MHJ si = Average hourly load, sector s, period i As in the commercial sector.

W sk

• MNsk/AW 3 where: -

=

MW sk MW demand at hour k of load sample, sector s

=

AMW s Average MW hourly demand of load sample, sector s STelEETLIGHTING On the occasions where the " dominant" hour occured after sunset, street-lighting sales were also included. Otherwise, streetlighting sales were not in91uded since its load during the daylight hours is minimal.

67

COMPANY USE AND LOST AND UNACCOUNTED FOR The total system load differs from the sum of all the loads discussed above by tne demarias for company uses and losses. Since no consistent time series were available on these two sources of demand, their con-tributions were assumed to be fixed percentages of the other class con-tributions. Consequently, the coefficients estimated, as described in (8) following, must be ir.terpreted to include these uses contri-butions to peak.

B) ESTIMATION In arriving at an est'mable form, equation (1) was combined with the detailed megawatt hour information derived for each of the major sectors:

2) MW ik = a o* TRBASEj+aj *TRWSik + bo*TCBASE +

b,

• TCWSik + c*INDBASEik where:

MW ik

= Megawatt Demand - period i, hour k TRBASE j = MWH Total Residential Base - period i (includes wholesale)

TRWSjg = MWH Total Rasidential Weather Component -

i, hour k (includes wholesale)

TCBASEik= MWH Commercial Base - period i (includes whole-sale), weighted for hour k TCWS = MWH Commercial Weather Component - period i, hour k (includes wholesale)

INDBASEik= Industrial Component period i, weighted for hour k Equation (2) was estimated for both the summer and winter seasons.

The summer season was defined to be June 1 to September 15, the winter was defined to range between December and February. These definitions were based upon an analysis of the distribution of normal cooling and heating degree days over the year.

68

The equations were estimated on weekly data. The weekly frequency en-abled the mocel to pick up the impact 'of weather on demand. Thus, period i, used liberally in the text, should be interpreted in the context of estimation as weekly. For further discussion on the development of the weekly data, please see Appendix A. For discussion of estimation implementation, See Appendix B.

O e 69

APPENDIX A Derivation of Weekly, Average Hourly Load Data The derivation of the weekly data used for estimating the peak load model was done in two steps. The first step was to convert the monthly energy data into weekly data; the second to convert energy data into a meaningful average hourly load definition.

Demand data was available on a real-time basis. That is, observations on system loads were defined as the integrated demands for the hour at wnich they actually occurred. On the other hand, energy data from which our independent variables for regressions were derived, was avail-able monthly on a mixed, lagged basis due to the billing cycle. The first step in converting the energy data into the form necessary for regression was to correct, as much as possible for the billing cycle.

(Referring to the main text, when derivation of base, weather sensitive, and weighted class components were discussed, the period i is monthly, monthly on a billing cycle basis. Consequently, the data manipulation described in the main text was performed before the correction for the billing cycle was done. )

The first step for converting energies to an average hourly load mapped ..

onto the real-ti.'e demand data was to convert the monthly data onto hourly units. This was done by dividing the base, weather sensitive, and weighted class components by the number of hours in the billing month .

In the second step, the data had to be mapped to match as closely as possible the real-time demand data. This was done in two steps. First, veekly observations were created by linearly interpolating the available 70

monthly data. Thus, any given week's observation was a weighted sum of the current months energy data and the following month's energy data.

The second step was to correct for the lag in the energy data due to billing lags. The lag for each company differed but the approach was consistent across all five. If the company's billing was "n" days after the meter was read, the interpolated weekly data was pushed back to the week "n" days previous to the one in which the data originally re-sided. As a result, the energy data used as an independent variable was closely aligned with the corresponding demand data.

e 4

71

APPENDIX 3 Estimation Implementation In estimating the Peak Demand Model, two problems arose which had to be corrected for within the estimation phase of the project. They were:

1) Data on Company use and lost and unaccounted for were not avail-able or inconsistent with other energy data.

2) Either because of a statistical problem known as multicollinearity or due to shortcoming in the separation of energy into base and weather sensitive components, freely estimated coefficients differed from what we expected and, therefore, were not reliable for forecasting.

Our solutions to these problems are discussed in this appendix.

I. Incorporating company use and lost and unaccounted .r The fundamental problem with the data for these types of energy came from the unaccounted for category. It was essentially calculated by each company as the difference between energy generated and energy sold. ,

Because of the timing differences between the two series - the former on a real time basis, the latter on a billing basis - it corrupted the series so that it was meaningless for our use. In fact, the series could be, and was negative on occasion. The interpretation, that more was billed than generated, was, of course, false. It merely represented a month when billed energy was lower than generated energy. This could occur in any month when energy needs were significantly higher the previous months.

72

The solution to the problem was to allow the estimated coefficients to pick up the company use, lost and unaccounted for energies. This implicitly assumes the omitted energies are constant precortions of tne included energies. Thus, the coefficient on the industrial base tern, for example, is interpreted as that sector contribution to peak both from its own requi ements and its contribution to losses at the time of peak. To the e . tent that company use is also correlated with the energy from a given sector, that sector's contributions was also over estimate by capturing some of the operating company use's con-tribution.

II. Unreliability in estimated coefficients Because of the method by which the independent variables were created, de anticipated the estimated coefficients for some variables to lie within a certain range. Following is a short list.

1) The industrial base tenn had weighted sectoral cnntributions to peak. The weights reflected the percentage of the s2ctors' average hourly load occuring at the dor.inant hour. Therefore, the estimated coefficient was expected to be 1 plus a factor for losses (1.05

- 1.15).

2) The non-manufacturing base tenn was created following the same format as used for the industrial base. Therefore, we expeci.ed the same range in coefficients on this term.

3) The coefficient on the residential base term was to pick up the implied weight on the average hourly demand at the dominant hour.

Therefore, depending somewhat on the operating company under an-anlysis we expected the coefficient to range between 1.2 and 1.6.

When the equation was estimated freely, the coefficients generally did not fall witnin the anticipated range. Since our prior beliefs about the coefficients reflected the underlying behasioral nature of peak demand growth, more reasonable coefficients were necessary for developing a reliable forecasting tool.

73

The first step was to reconsider the weights used in developing our terms. In general, refinements of the weights improved our estimates but did not resolve the problem.

Finally, in order to overcome the problem the regressions were estimated imposing constraints on the estimated coefficients to reflect our prior celiefs. This was a reasonable approach because (1) constrained esti-mations reduce collinearity in the independent variables and, therefore, reduce the variance of the estimated coefficients and (2) constrained estimations may reduce bias in estimated coefficients due to shortcoming in data collection and manipulation.

The constraints were implemented in two steps. In most cases, the first step was sufficient to adequately correct the problem. The first step was to combine the non-manufacturing base tem and the industrial base term. Since both were expected to be 1 plus a loss factor, we could reasonably anticipate the constraint that they have identical coefficients would be meaningful. If that wasn't enough, we formed a prior on the dominant hour residential base weight and added a weighted residential base tem to the industrial and non-manufacturing base tems. This was less preferable since the prior weight developed for the residential base term had a weaker basis than for the other sectors.

Why was the resulting constrained estimation more reliable thari the unconstrained? First of all, we could feel more confident in the meas-uring the contributions of ir.fastr tal and non-manufacturing energies to peak in the forecast. But equally important, the reduction in the

variances of the estimated coefficists, resulting from the decre?se in multicollinearity, cave more reliable estimated coefficients on the weather sensitive tems for which we had no prior beliefs.

74

THE SPECIFICATION OF THE ECONOMIC SECTOR OF THE MIDDLE SOUTH FORECASTING MODEL 75

TABLE OF CONTENTS PAGE INTRODUCTICN 77 STATE MODEL I. OVERVIEW 79 II. SECTOR DETAIL 82 A. Employment 82

1. Manufacturing and Mining 32

2. Non-Manufacturing 84

a. Services 84

b. Construction 85

c. Government 87

8. Wages and Prices 87 C. Demographics 89

1. Population 89

2. Age Distribution of Population 91

3. Civilian Labor Force 91 D. Housing 92 E. Fiscal 92 F. Income 93

1. Wage and Salary Disbursements 93

2. Transfers 94

3. Other Labor Income 95

4. Property Income 95

5. Proprietors

• Income 95

6. Restdent Adjustment 96

7. Personal Contributions to Social Insurance 97 SERVICE AREA MODEL I. OVERVIEW 98 II. SECTOR DETAIL 99 A. Employment 99

1. Manufacturing and Mining 99

2. Non-Manufacturing 99

3. Wages and Prices 100 C. Demographics 100

0. Housing 100 E. Income 100 APPENDICES APPENDIX 1: Estimation methodology for manufacturing 102 and mining employment APPENDIX 2: Derivation of the distributed lag estimator 104 APPENDIX 2A: The distributed lag estiamtor when both short and long run elasticities are one 109 APPENDIX 3: Estimation methodology for non-manufacturing employment 112 APPENDIX 4: Estimation methodology for wages and prices 113 76 ,

INTRODUCTION The energy and demand forecasting models developed by Middle South and Data Resources have as an important characteristic tne consideration of the local economic environment within which eacn of the five companies operate. The forecasts of energy and demand growth relate the forecasts of the national economy, as developed by both Middle South and Data Resources, to what the impact of the national economy is on the Middle South operating companies. The link between the national economy and energy sales is developed through the modeling of the economies of each operating company's service area. The specification below documents how this essential link is modeled.

The economic models were developed at a relatively high level of detail.

Growth in the national economy may have a wide variety of possible impacts on the service areas' economies. Activity in the national economy will be modified by local characterisitics. These characterisitics include:

regional industrial mix, population trends, demographic mix, the price of energy, uages, growth in local markets, and the business climate generated by state regulations. This approach uses the fact that, while the service areas are not independent of the national economy, their own peculiar characteristics cause the impact of national events to result in changes unique to their economies.

For the Middle South forecasting project, five separate models were developed:

1) Arkansas state model

2) Arkansas-Missouri Power Company service area model

3) Louisiana Power and Light Company service area model

4) Mississippi Power and Light Company service area model

5) New Orleans Public Service Inc., service area model A state model was developed for Arkansas for use in Arkansas Power and Light Company's forecasting. A state model was used after considering the trade-offs between a state model and a service area specific model.

The benefit of a state model is that more accurate, detailed, and more easily accessible data is available at the state level. The benefit of a service area specific model (and, therefore, a drawback of a state -

model) is that the data for a state may not accurately reflect economic activity within the company's service area. Developing service area models requires a great deal more effort in assembling data. It may be the case that state agencies which serve as the source of data may be uncooperative in supplying the data. Service area data does not experience the same high degree of quality control that state data does as it passes from state to federal agencies and from federal agencies to the Data Resources' regional databank librarian.

After considering all of these elements, it was detemined that the best choice to maximize accuracy and minimize cost for data collection was to use a state model for Arkansas Power and Light's forecasts; each of the other four companies' forecasts are based on service area specific models.

77

The specification of the two model types, state-wide and service area specific, are documented below. The state model specification is pre-sented at a relatively high level of detail. The service area mosel specification is developed in less detail. Because the service area model is similar in most respects to the state model, the reader is referred to the detailed description in the state model documentation.

Only contrasting details, required by data limitations on a service area basis, are oeveloped to a significant level in the service area scecification.

e e 78

STATE YODEL I. Overview The analysis of the state's economy is divided into seven major categories:

Employment Wages and Prices Demographics Housing Income Fiscal State Product The general structure of the model is shewn in Figure 1. As the figure demonstrates, the core of the model is the labor market. The labor market is emphasized because data on employments is the most complete and most detailed available on a state basis. The figure shows that the only strictly exogenous source of causs! factors is the U.S. economy. Given these external forces, the seven sectors are highly interdependent. To cite just one example of the interaction of sectors, suppose that there is substantial growth in industrial production nationally. The national growth will lead to increased growth within the state. The increased demand for employees will lead to higher wages or more job opportunities in the state. The subsequent increased income to workers will increase the demand for services and retail goods. This derived demand in the non-manufacturing sector will lead to higher incomes paid to employees in that sector. Increased income implies even more jobs. The process will continue.

The point of this example is to show the interactions withi* the state.

The model as specified considers these interactions in its analysis of the state's economic activity. In the next few paragraphs, a description of each sector and a brief discussion of its interdependence with other sectors is given.

The emoloyment secto' considers the employees in manufacturing industries by 2-digit SIC classifications. At this level of detail, the impact of the national economy on :he state can be analysized based on the mix of industries within the state. Non-manufacturing is considered in six sub-categories. This level of detail allows the analysis of the growth in differing tynes of non-manufacturing industries to vary with consideration for sub-category peculiarities. The level of employment feeds into all other sectors of the monel. For more detail, see the other sector des-criptions below.

Within the wages and prices sector, the average hourly earnings in manufacturing and the consumer price index are considered. Both rely heavily on national economic conditions. Wages and prices both feed into the employment sector as explanatory variables.

79

O 6 e FIGURE 1 U.S.

ECONOMY I I I I I I I I I I l EMPLOYMENT I

' I I

I l l I A l I

/ \s I l

I A"

DEMOGRAPHICS WhhfE l I

1 I

I  ;

I  % V g ... l I

l I HCUSING .

I I

I i l i I

l A V i I

i I

I INCOME l I

I I

I I

I I I I i 80

The demographics sector considers the growth in population, the age dis-tribution of coculation, and the civilian lacor force. The growth in population feeds into the employment sector in two ways. First, increased population implies an increased market for the state's production. Second, increased population, modified for the age distribution, is the cool of individuals frcm which enployees are hired. The civilian labor force wnich measures the share of the population seeking employment is a deter-minant for certain ty;es of income.

The housing sector depends on the changing demographics of the state. It, in turn, feeds into

• enployment sector through the demand for construction werkers.

Tne income sector includes the major components of personal income: wage and salary disbursenents, other labor income, property income, proprietors' -

income, and net transfer payments. The income sector depends heavily on emoloyments, as wage and salary disbursements are the largest of all the components of income. At the same time. income feeds into the employ-ment sector since the higher the income is in the state, the greater the local market is for both manufacturing and non-manufacturing output.

The fiscal sector is relatively insignificant in the model as it now stands. The growth of government in the state increases both employment opportunities and income. The growth in government activity depends on the economic growth of state through increased tax receipts.

State Product summarizes all economic activity within the state. It is derived from the other six sectors but does not feed into any of them.

Its definition and derivation is best left for further discussion below.

The next section deals with each sector in detail.

II. SECTOR ::ETAIL Given tne general flew of the state model, we new c::nsider the catailed specifications of eacn sector.

A. Employment

1. Manufacturing and Mining Employment in manufacturing and mining is related to production within the sector. As a general rule. increases or decreases in production will lead to the hiring and firing of employees. In the long run, however, production per employee will increase as a result of technological changes which cause a more efficient use of labor. Thus, the demand for labor within a manufacturing group is related to the level of production in the grouc with a correction for technological innovation.

The growth of production in an SIC (Standard Industrial Classifi-cation) category within the state depends essentially on two sets of factors: national market conditions and local conditions which lead to more or less growth relative to the nation.

National market conditions are summarized in the Federal Reserve Board production indices for the various 2-digit SIC groupings.

The factors influencing relative growth of the state versus the nation are the relative cost of inputs (wage and energy prices specifically), the state business environment, (as exemplified by relative corporate tax rates), and the relative growtn of the local market (modeled by relative income, state to nation). One factor remains for consideration: the use of labor as opposed to other input depends on the cost of labor relative to the costs of other inputs. For this reason, the real (in constant dollars) average hourly earnings for manufacturing is used to represent the cost of hiring labor. To capture the effect of minimum wage legislation on the demand for labor in low-wage industries, the ..

real minimum wage is also included.

We surmiarize the demand for employment within the SIC class with the general functional fonn:

Ejj = F(JQIND , jAHEM / jAHEM, PEINDj/PELECIND, CORPTX/RTCGSL, YP j /YP, AHEM /CPIS, j

MINWAGE/CPIS , TIME) 92

where:

i = SIC Ccde j = State JOIND = The Federal Reserve Board Production Index (1976 weights, i suoscript represents SIC group)

AHEM = Average hourly earning, manufacturing (the subscript "j" represents the state value of the variable; without j, the national value).

PEIND = Price of electricity to industrial customers (derived from operating company schedules).

PELECIND = National average cost of electricity to industrial customers CORPTX = State corporate tax rates RTCGSL = Average state corporate tax rates for all U.S. states YP = Personal income (note: j)

CPIS = Consumer price index, southern U.S.

MINWAGE = Legislated minimum wage for U.S.

TIME = Time trend (1st quarter 1947:1.0)

A distributed lag was used in estimating the employment relationships.

Changes in production do not lead to immediate changes in employment.

When production falls as a result of diminished demand for a firm's output, the firm will not immediately lay off personnel. The reasons -

for the apparent inertia are varied. First, the company has under-gone some cost in training the employee. If the employee is laid off, he may find another job causing the company which originally hired htn to lose some of its returns from the training. If the company feels production will increase, they will try to keep him as an employee even though his output does not justify it. Second, there is an inertia which is the converse of this behavior. If production rises, the firm may hesitate to hire new emoloyees. The increase in production may be temporary. If it is, the firm will be forced to lay off the new employ-ees without getting returns on the training they have received.

The inertia in hiring and firing leads us to a distributed lag method of estimation. Past values of the independent variables are considered since companies in the service area will hire or fv e employees only if the underlying causal factors persist. Thus, not just the current production index or wage are important, but the past history of these and the other independent variables as well.

83

The derivation of the distributed lag astimator and the specific form of the equations to be estimated are ciscussed in detail in Appendices 1 and 2.

2. Non-Manufacturing Six major categories of non-manufacturing emoloyment were considered.

These are:

- Personal Services

- Trade - wholesale and retail

- Finance, insurance, and real estate

- Transportation, communications and public utilities

- Contract Construction

- Government

a. Services Within these si; categories, a more general group called services, was treated siailarly. Included in this group are personal services, trade, finance, insurance and real estate, transportatior.,

communi'.ations, and public utilities.

The growth in the service industries' employees in the state is constrained by the growth in population in the state. Service industries, unlike manufacturing and mining, face a local market.

Since they service only local markets, growth in the sectors can come from two sources: growth in the population served, and growth in the number of employees per capita. The growth of the state's -

population is considered in the demographics section below. In modeling state service industry employment, we look at the growth in employees per capita.

The demand for the output of the service industries is caused by a variety of factors, changes in tastes, income, and others. Most of the relevant variables are not quantifiable at the state level.

Consequently, we use the national ratio of service industry employees to population to proxy the growth in the demand for service industry output. Since we can collect income data at the state level, we use the ratio of per capita income in the state to per capita income nationally to modify the basic relationship to account for the relative growth cf the state's population's ability to purchase the industry's output to the growth of the nation's population's ability to purchase.

'4

The final causal step is to relate the state's demand for output of the sector to the sector's demand for labor. For this ourcose, we include real average hourly earnings in manufacturing and the real minimum wage. Manufacturing earnings are used as a proxy for non-manufacturing earnings because variations in non-manufacturing wages generally follow those in manufacturing since a widening or narrowing gap between the two will lead employees to move from one sector to tne other. Although the levels of earnings between the two sectors may differ, manufacturing earnings will serve as an appropriate proxy for non-canufacturing earnings if the two generally vary together.

We can summarize the service industries class of non-manufacturing in the general functional form:

Ejj/Nj = F(E j/N, (YP /N j )/(YP/N),

j AHEM /CPIS, j

MINWAGE/CPIS) where:

i = Service category j = State E = Employees, service industry category N = Population YP = Personal income AHEM = Average hourly earnings, manufacturing CPIS = Consumer price index, southern U.S.

MINWAGE = Federally legislated minimum wage ..

The form of the equations estimated for each category in this group was multiplicative. Since the lag adjustment process was also considered to be important here, the distributed lag estimator discussed in Appendix 2 was used. Some details of estimation are discussed in Appendix 3.

b. Construction There are two major types of construction: residential and non-residential. In modeling the demand for construction emoloyees, the causal factors relating to both types are considered.

35

The most reliable set of data available at the state level to capture residential construction activity is the number of hcusing permi ts issued. No comparable series is available for non-residen-tial construction. To capture the construction in plants and facilities, we use the growth rate in non-agricultural employment to proxy this demand. The rationale for this approach is that the

?rowth in employment will lead to a corresponding increase in places of employment.

To relate the demand for construction to the demand for labor, tne real wage is also included as an independent variable. The estimations were performed on a per capita bases since, as with all non-manufacturing employments, the growth in demand is constrained by the growth in population.

Thus we write the general functional form:

ECj/Nj = F(HUATj/Nj, EEA3/EEAj (-1), AHEMj/CPIS) where:

j = State EC = Employment, construction N = Population HUAT = Housing permits issued EEA = Employment, non-agricultural industries AHEM = Average hourly earnings, manufacturing CPIS = Consumer price index, southern U.S.

- a

c. Government The demand for government employees per capita is also modeled. ,

The demand for employees by state and local authorities was specified as a function of state income. Income represents the state's residents ability to afford services offered by local governments. Since we are modeling per capita emoloyment, per capita inccme is used as the independent variable.

For the demand for federal government employees witnin the state, the federal government employees per capita is used. To capture wage-induced impacts, real wages are also included.

The general functional form reads:

j EGj/N3 = F(YPj/Nj/CPIS, EGF/N, AHEM /CPIS, MINWAGE/CPIS) where:

j = State EG = Employment, government N = Population YP = Personal income CPIS = Consumer price index, southern U.S.

EGF = Federal government employees AHEM = Average hourly earnings, manufacturing MINWAGE = Federally legislated minimum wage .-

The lag method of estimation is discussed in Appendix 2.

B. Wages and Prices The average hourly earnings in manufacturing and the consumer price index for the southern region of the U.S. are modeled within this sector. The consumer price index (CPIS) is assumed to be tied to the prices of consumer goods at the national level. It is assumed the inflation in prices nationally causes an identical inflation in the southern region.

37

. 4 Since the people of the southern region generally have lower per capita incomes than otner national counterparts, foca will tend to be a more sianificant portion of their cuogets and, consecuentiv, their or1ce index. :o account for tnis differential market basket, inflation in tne South is related to the inflation of the total national consumer price index and the crice index for food. Inflation in the region is constrained to be a weighted sum of the inflation in food and all goods.

Since the assumption is made that the long-term market for labor is national in scope, average hourly earnings within the state are constrained to be unit elastic with respect to national average hourly earnings in manufacturing.

The differences in the cost of living between the state and nation are considered by looking at real earn'ngs (deflated by the relevant price indices). Differential impacts of the cycle are also considered by includ-ing the share of the state's population engaged in non-agricultural employment to the identical national ratio as an independent variable. A final variable included is a qualitative variable used to account for the impact of wage and price guideposts used during the 1960's.

The formulation of average hourly earnings in the state is summarized in the general equation:

AHEM /CPIS = F(AHEM / CPI, (EEAj /Nj )/(EEA/N), DGP0ST) j The actual estimated form, embodying constraints, is presented in Appendix 4.

To complete this sector, average hourly earnings in manufacturing for the U.S. must be forecast. A closely related concept, an index of non-farm hourly earnings is forecast by DRI; however, the index reoresents straight time earnings while average hourly earnings is the average of straight and overtime earnings. Since average earnings is the only concept available for the state, national average hourly earnings in manufacturing are used in our models as the independent variable. The sector is closed by specifying national average hourly earnings in manufacturing for the U.S.

as a function of the ncn-fann earnings index and an index of capital utilization to reflect the presence of overtime. -

Thus we write:

AHEM = F(JAHEADJEA, UCAPFRBM) where:

AHEM = Average hourly earnings JAHEADJEA = Index of hourly earnings UCAPFRBM = Index of capital utilization 35

C. Demographics Witnin the demographics sector, there are three major subcategories:

- Population

- Age distribution of population

- Civilian labor force

1. Population By definition, the population in any period is the sum of last period's population, net migration, and births less deaths. When considering the evolution of population, we look at the three components - births , deaths , and migration--separately.

Figures for migration are not published, but using the definition of the previous paragraph, the level of net migration may be solved algebraically.

That is, MIG 3 = (N3-Nj (-1)) - (BIRj - DEA3 )

where:

j = State MIG = Net migration N = Population BIR = Live births DEA = Deaths Using this solved for number, a model for net migration may be estimated.

Birth and death rates for the state are related to their national equivalents with modifications made for available regional characteristics. For births, the clasticity of the state's rate is estimated freely with relative per capita income used as a modifying characteristic.

39

. o The gereral form of the equation is:

BIRj /Nj = F(SIR /M, (iPj/Nj )/(YP/N))

where:

j = State BIR = Number of live births N = population YP = personal income The death rate is compared to the national rate with the relative number of people over 65 years of age, used as a modifying charac-teristic. The functional form reads:

DEA j /N3 = F(DEA /N, N65&j/N65&)

where:

j = State DEA = Number of deaths N65& = Population age 65 & older Migration is an extremely difficult activity to model. Certain causal factors can be considered and do, in fact, show significant explanatory power. Extremely difficult to model is the timing of migration.

Consequently, we should expect that the percent variation in migration ..

we can explain to be small.

The general functional form for migration is:

MIGj = F(EMj/EM, AHEMj/ AHEM, NR65&/NR65& (-1))

where:

j = State MIG = Net migration of people into the state EM = Employment manufacturing AHEM = Average hourly earnings, manufacturing

~

NR65& = Population 65 years and older 93 -

. e

2. Age Distribution of Pooulation Two age breakdowns of population are considered - persons 21 to 64 years and oersons 65 years and older. In any period, the number within each classification include:

- Those surviving members remaining within the age classification

- Those moving into the classification from a younger cohort

- Those having migrated to the state since the pre-vious period Estimates of the number in each group are derived from the relationship:

ENjj = Njj (-1)* SRj + Nj.),j

• SR ,)$ + ag

• MIGj where:

i = Age group j = State EN = Estimated population N = Population SR = Survival rate ai = Historical percent of migrants within age group i MIG = Net migration -

The estimated population breakdowns are compared to the actual in order to correct for statistical error.

3. Civilian Labor Force The factors determining the labor force are the pool of people available for work and the wcges that can be earned. Thus the functional form used for the estimation of this sector is:

LC 3 = F(N21@643 , AHEMj /CPIS) 9'

where:

j = State LC =

Civilian labor force N21@64 = Population 21 to 64 years of age AHEM = Average hourly earnings, manufacturing CPIS = Consumer price index, southern U.S.

D. Housing The concept considered in this sector is housing permits issued.

It is forecast for use in forecasting construction employment. Per capita housing permits are estimated by considering the cyclical and long-term changes embodied in a related national concept: hous.ng starts. Differences in trend are measured by considering the growth of per capita income in the state relative to growth in per capita income for the country as a whole.

Summarizing: -

HUATj /Nj = F(HUSTS/N, (YP j /N j )/(YP/N))

where:

j = State HUAT = Housing permits issued HUSTS= Housing starts, national N = Population YP = Personal income E. Fiscal The only concept currently developed in the fiscal sector is wage and salary disbursements to government employees. For a discussion of the estimation of wage and salary disbursements, see Income below, t

92

F. Income The income sector, which feeds into most other sectors of the model, is examined by considering each of its comconents. We can begin by inspecting the income identity (ignoring state identifying sub-scripts):

YP = WSD + V + YOL + YPPROP + YENT + RES - TWPEP where:

YP = Personal income WSD = Wage and salary disbursements V = Governmental transfer payme'ts YOL =

Other labor income YPPROP = Property income YENT = Proprietors' incnme RES = Resident adjustment TWPER =

Personal contributions to social insurance

1. Wage and salary disbursements Wage and salary disbursements are modeled for nine major categories:

- Manufacturing

- Construction

- Government (see Fiscal)

- Mining

- Transportation, communications, and real estate

- Personel services

- Trade - wholesale and retail

- Other 93

The acproach is similar for each. Average hourly earn %gs in manufacturing is taken as a proxy for compensation per employee in each category. The product of average hourly earnings in manufacturing and the number of employees within the catecory is used as the independent variable. 't.'hile seemingly qui te simplistic, this approach explains nearly all variation in wage and salary disbursement for each group. Each category follows the general form:

WSDjj = F(AHEMj

• Ejj) where:

i = Employment category j = State AHEM = Average hourly earnings, manufacturing E = Total employment

2. Transfers Transfers per capita for the state are elated to corresponding national concept. Modifying the fundamental relationship are variables to reflect the impact of cyclical variables on trans-fers and the increasing propensity for the state to pass legis-lation creating transfers as its economic condition improves.

Transfers per capita are specified with the functional form:

Vj /N j = F(VG/N, (EEAj/LCj )/ (EEA/LC), (YPj/Nj)/(YP/N))

where:

j = State V = State transfer payments N = Population VG = Government transfer payments, nationally EEA = Non-agricultural employment LC = Civilian labor force YP = Personal income p.

3. Other Labor Income Cther labor income is an aggregate including incentive compensation, commissions, and a variety of other items. Since these types of income follow other income types, other ' abor income is related to the total of wage and salary disbursenents.

YOLj = F(WSDj) where:

j = State YOL = Other labor incomes 4 Property Income Per capita property income for the state is related to national concepts with modifications for state peculiarities.

The functional form may be written:

YPPROP j /Nj = F((YRENT + INTBUS + DIV)/N, (EMj/Nj)/(EM/N))

where:

YPPROP = Property income N = Population YRENT = Rental inccme INTBUS = Interest income DIV = Dividends EM = Manufacturing employment

5. Proarietors' Income Proprietors' income is divided into two sub-categories - farm proprietors' income and business and professional proprietors' income. Farm proprietors' income per capita is related to the national farm proprietors' income, with the ratio of employ-ment in food and kindred products within the state to employment in ?ood and kindred products, nationally, to reflect the growth in merkets for produce in the state relative to the country as a who1e.

95

The functional form reads:

YENTAF j /N = F(YENTAFADJ/N, (E20j/Mj)/(E20/M))

where:

YENTAF = Farm proprietors' inccme N = Population YENTAFADJ = Farm proprietors' income, U.S. with adjustments E20 = Employment, food, and kindred products Non-farm proprietors' income is modeled similarly to farm proprietors' income. Per capita values for the state and nation are compared with the ratic of state to national non-agricultural employment included to p oxy relative growth in markets for proprietory businesses. The functional form of the relationship is written:

YENTEAFj/Nj = F(YENTNFADJ/N, (EEA j /Nj)/(EEA/N))

where:

j = State YENT = Relevant income concepts N = Population EEA = Non-agricultural employment

6. Resident Adjustment Since 1969 components of income have been collected on the basis of place of work. As a result, the sum of the individual com-ponents of income differs from that earned by tne state's resi-dents as out-of-state residents earn money within the state and in-state residents generate earnings outside of the state. In forecasting personal income for the state, we must also consider this adjustment.

The adjustment is related to those factors which cause individuals to seek employment outside of their own state of residence -

out-of-state employment and income possibilities.

96

Therefore, the general functional form:

RESj = F(WSDj + YOLj + YENTj, AHEM /j AHEM, EMj /EM) considers:

RES = Residential adjustment WSD, YOL, YENT = Previously defined components of income AHEM = Average hourly earnings, manufacturing EM = Employment, manufacturing

7. Personal Contributions to Social Insurance Personal contributions to social insurance are simply social security payments which are deleted from wages and salaries. Consequently, the historical share is estimated:

TWPERj = F(WSDj) where:

j = State TWPER = Personal contributions to social insurance WSD = Total wage and salary disbursements l

97

SERVICE AREA MODEL

. Overview The model for service areas which do not fit a state definition has the same general structure as the state model specified above. As in the state model, the labor market is the key sector. However, it is often the case that the level of detail for employments is less than at the state level. This requires the demand for employees to be estimated at a more highly aggregated level. Employees of two or more closely re-lated manufacturing groups must often be combined into a new, more general grouping. In non-manufacturing, the level of aggregation may even go to the extreme of estimating all non-manufacturing employees as one class. The other sectors are aggregated as well. Some sectors are excluded entirely in the modeling of the service area. Specifically, the service area model includes the following sectors:

Employment Wages and Prices Demographics Housing income Explicitly excluded are:

Fiscal State Product In describing the service area models, comments are directed at the similarities and contrasts with the state model. Where similarities exist, the reader is referred to the state model specification for details. Only contrasting details will be fully developed.

• e 90

II. Sector Detail A. Employment

1. . Manufacturing and Mining The only essential difference between the service area and state models is the level of detail considered. Employees of two or more similar groups will be combined if (1) data are only available at a more aggregate level from state agencies, or (2) employees within a given group or groups are so insignificant as to cause problems in estimation. See the state model specification for further details.

2. Non-manufacturing For non-manufacturing, aggregation may require that a different specification be used. Given below is the speci-fication for the case when all non-manufacturing employees must be estimated as a single group.

The general functional form reads:

ENMj /N3 = F(ENM/N, (YP /N )/(YP/N),

33 AHEMj /CPIS, MINWAGE/CPIS) where:

j = Service Area ENM = Employees, non-manufacturing N = Population YP = Personal Income AHEM = Average hourly earnings, manufacturing CPIS = Consumer price index, southern region MINWAGE = Federally legislated minimum wage When more detail is available, the specifications shown for the state model will be used.

99

3. Wages and Prices The service area specification for wages and prices is equivalent -

to tnat shown for the state model.

C. Demographics The variables considered under the heading of demographics in the state model are generally not available on a service area basi s . Thus while we use the specifications shown there, cer-tain assumptions are necessary to proceed.

1) the birth rate is the same in the service area as in the state of which it is part.

2) the death rate is the same as in the state

3) the survival rates are the same as in the state Under these assumptions, a forecast of population and the age distribution of population may be made for the service area.

The concept of civilian labor force is not available and, therefore, not estimated or forecast.

D. Housing The variable forecast, permits issued, is not available for the service area. Since the concept is useful for forecasting construction employment, for those service area models where construction employment is forecast separately from total non-manufacturing employment, the number of permits issued by the state of which the service area is part will be estimated on .

service area based independent variables. The implicit assumotion made is that activity outside the service area is similar to that within the service area. If the results of estimation challenge this assumption, the housing sector will be dropped from the service area model.

E. Income The detail of income by type available at the state level is not available for the service area. Thus the total concept of personal income will be estimated with the relevant causal factors identified for the separate components of income in the state model included as independent variables.

130

Considering the definition of personal income in Section II.F of the state model and the subsecuent soecification for the com-ponents of personal income, we have the general functional form:

YPj /N3 = F(AHEM j

• EEAj/Nj, VG/N, (EEAj /Nj )/(EEA/N),

(YRENT + INTSUS + DIV)/M, YENTAFADJ/1, YENTNFADJ/N) where:

j = Service Area YP = Personal Income N = Population AHEM = Average hourly earnings, manufacturing EEA = Total, non-agricultural employment VG = Government Transfers YRENT = Rental Income INTBUS = Interest Income DIV = Dividends YENTAFADJ = Farm proprietors' income YENTNFADJ = Non-farm proprietors' income 101 '

Appendix 1 Estimation methodology for manufacturing and mining employment.

The general functional form for the demand for manufacturing and mining employment is:

E jj = F(JQIND t, AHEM j/ AHEM, PEIND3 /PELECIND, CORPTX3 /RTCGSL, YP)/YP, AHEM /WPIj , MINWAGE/WPI j , TIME) 3 where:

i = Subscript denoting SIC code classification j = Subscript denoting state name (non-subscripted variables are national variables)

E = Number of employees JQIND = Federal Reserve Board Production Index AHE_M = Average hourly earnings, manufacturing PEIND = Price of electricity to industrial customers (from company rate schedules)

PELECIND = National price of electricity to industrial customers CORPTX = State corporate tax rate RTCGSL = Average state corporate tax, all U.S.

YP = Personal income WPI = Wholesale price index for industry output ,

MINWAGE = Federally legislated minimum wage TIME = Time trend For estimation, the fonn of the relationship is specified to be multi-plicative. The multiplicative form together with the distributed lag estimator described in Appendix 2, yields: .

t a, E

jj = A

• JQINDj ba

• JQINDj (-1)b * (AHEM3/ AHEM)c (AHEM (-1)/ AHEM (-1))c' * (PEIND /PELECIND)da ,

j 3 Continued...

102

t (PEIND (-1)/PELECIND(-1))d * (CCRPTX/RTCGSL)**

• 4 (CCRPTX(-1)/RTCGSL(-1))*1 * (YP j /YP) * *

(YP,(-1)/YP(-1))# 1 *

(AHEM 4 /WPI )9' 4

( AHEM j (-1)/WPI

(-1))9' * (MINWAGE/WPI $

)ho (MINWAGE(-1)/WP!(-1))ht

• exp k* TIME *Ejj(-1)

The regressions are performed linearly using the naLural logarithms of the dependent and independent variables. That is, regression equations are of the form:

log (E $)) = log (A) + bo

• log (JQIND$ ) + b t

• log (JQIND$

(-1)) +

ca

• log (AHrMj/ AHEM) + ct

• log (AHEMj (-1)/ AHEM (-1)) +

do

• leg (PEINDj/PELECIND) + di

• log (PEIND g (-1)/PELECIND(-1)) +

eo

• log (CORPTX/RTCGSL) + et

• log (CORPTX(-1)/RTCGSL(-1)) +

fa

• log (YPj /YP) = ft

• log (YP (-1)/YP(-1))

j

+ go

• log ( AHEMj/WPI$ )+

• log (AHEM /(-1)/WPI (-1)) + ho

• log (MINWAGE/WPI ) + hi*

gt j 4 $

log (MINWAGE(-1)/WPI $ (-1)) + k

• TIME + m

• log (Ejj(-1))

The test for long-term elasticity described in Appendix 2 implies that 1-m should not be significantly different from bo + bt in the equation above.

103

Accendix 2 Cerivation of the Distributed Lag Estimator The example to be presented considers the simple case of a dependent variable (Y) as a function of the current and lagged values of only one inoependent variable (X). We can write the equation:

1) Y = a + ba

• X + bi

• X( -1 ) + b2

• X(-2)+ b 3

• X(-3) + . . .

Notice: 1) X(-i) denotes the variable X lagged i periods

2) the subscripts on the coefficients b are organized such that the coefficient on X lagged i periods is bi While we believe that the variable Y responds to a number of lagged X 's, the coefficients, b- cannot be freely estimated because (1) the inclusion of all X's will cause serious multicollinearity and (2) the number of degrees of freedom necessary for statistical testing will be seriously reduced. To avoid this problem, the bt are parameterized.

That is, they will not be freely estimated, but will be forced to be related in a systematic way.

The coefficient on the current X , b , will be freely estimated; but 3

all others - b t , b 2 , b 3 , . . .- will be constrained to be proportional to a geometric distribution with an unknown decay rate. This para-meterization requires some clarification.

A geometric distribution can be written:

i

2) c4 = A That is, a given element of the distribution is a constant fraction, A ,

of the element ininediately preceding it. The fraction, A , is the decay rate.

The b , for i greater than zero, are said to be proportional to a geomekric series. This yields:

I

3) bj = d

• c4=d*A for i>o where: d is the proportionality factor, all other variables have been previously defined. ,

Let me cite an example: suppose d= .5 and A = .9, 104

a ,

then: 31 =d A = .45 b2 =c*A = .405

.1 r, , =c=i = .174 As we will see, this parameterization causes us to estimate only be , d, and A rather than the large number of b4 's required without tne parameterization.

Using equation (3), we can rewrite equation (1) as:

4) Y = a + ba

• X + d

• A

• X(-1) + d

• A*

• X (-2) + d

• A'

• X(-3) + . . .

Using (4) we can write the equation for Y(-1).

d') Y(-1) = a + bo

• X (-1) + d

• A

• X (-2) + d

• A

• X(-3) + . . .

Multiplying both sides of (4') by A yields:

4") A*Y (-1)= A

• a + A

• b,

• X (-1) + d

• A

• X (-2) + d

• A'

• X (-3) + . . .

Sub'.cacting (4") from (4)

5) Y - A

• Y (-1) = a(1-A) + b o

• X + A * (d-bs )

• X (-1 )

Notice that in subtracting, all X(-1) for i greater than one drop out. -

Solving for Y we have:

6) Y= a(1-A) + ba

• X + A * (d-bo )

• X(-1) + A

• Y (-1) which our algebra has shown to be equivalent to equation (4).

Next we consider how the estimates of the individual bi will be derived.

The equation estimated can be rewritten:

7 ) Y = a + 3,

• X + St

• X (-1) + 6

• Y (-1) so that least-squares regression will yield estimates for a, Sn, 31 and 6.

~

105

s .

Comparing equations (6) and (7) we see:

so =b3 3: = A * (d- bo) 5 =A Using these three equations, we can solve for the underlying coefficients:

b,d,A.

3 In fact, bo = So A =5 d = Si/ 6 + 3o Thus estimates of each of the bj can be formed bo = So bj= (St/6 + So)

• Si , for i>o I should make a point here which will help to avoid problems later. Since A and, therefore, 6 is certainly positive, the sign of b6 and d should be the same. Both, however, may be positive or negative depending on the theoretical relationship between X and Y. Notice, however, that while be and d must be of the same algebraic sign, so and Si need not be. Since So is the estimate of bo, it must be the correct sign; but, since the sign of Si is determined by the difference between d and bo, it can be either positive or negative.

If bo is greater than d in absolute value, which we can expect to happen ouite often, 3 will be opposite in sign to Bo. While this may seem puzzling, 2

the algebra shown proves it to be correct. We must make certain, however, that the estimate of d, derived above, is the same sign as bo.

Let us move on to another consideration in the estimation of the distributed lag. We define the long-term effect of X on Y to be the sum of all the b '

(In the case of logarithmic specification, this would be called the long j s.

term elasticity). The long-term effect can be found by summing the bj's.

Long-tem effect = bo + b; + b2 +b+...

3

= bo + d

• f + d

• A + d

• A' + . . .

2 2 3

= bo + d * (A + A +A.....)

106

Mcw:

3 ,

A+A'+r + A + ... . = ^/ 1-A wnich can be verified by long division. So, the long-term effect equals ba + d = A/(1-A)

We may have a prior belief as to the magnitude of this long-term effect.

For example, in our manufacturing employment equations, we might believe the long-term elasticity of the production indices (JQIND) to be 1. What the following discussion shows is how t.his prior belief can be inputted into the estimation of the manufacturing employment equations.

If the long-term effect, or the sum of the b 'sj is one, we have:

1 = bo + d

• A/(1-A) or, 1-A = ba * (I-A) + d

• A or, A = l-(ba + A * (d-bo))

Notice, that using our previous definitions:

So = bo S = A * (d-ba) t 6 =A the unitary constraint implies:

S = l-(So + St)

So that our regression equation (7) may be rewritten:

(8) Y = a + So

• X + St

• X(-1) + (1-So-St)

• Y(-1) 107

We see that with our constraint we now estimate only three coefficients -

1, 3o, e:, - to derive the four basic coefficients - a, be, d, A.

In fact, A = (1-3 -3 )

3 3 bo = S 3 d =3 3 + 3 /(1-So-Si) 3 a = a/(So + St)

To embody the constraint we estimate the equation (collecting terms in 3 and 3 3 1 in equation (8)):

9) Y-Y (-1) = a + 3e * (X-Y (-1)) + Si * (X(-1) -Y(-1))

An t-statistic can be formed comparing the explanatory power of (9) versus the unconstrained estimate shown in equation (7) .

~

109

Accendix 2a The distributed lag estimator when both short and long run elas-ticities are one.

Appendix 2 develops the distributed lag estimator used in the economic estimations. Equation 9 presents the constrained version when the long-term elasticity of X is believed to be identically one.

On some occasions the freely estimated So will take on values equal to or greater then one. In this case the implicit estimate of "d" is almost always negative which violates our theory. In this appendix, a method for constraining "d" to be zero will be shown. Also demostrated will be the equivalence of d=0 and the long and short run elasticities both equalling one.

, It will become apparent that this form of the estimator is not of much interest if there is not at least one other independent variable other than the one having the constraint imposed on its coefficients.

Therefore, we can write following equation 1 in Appendix 2:

la) Y=a+ba

• X + bi

• X(-1) + . . . + ca* Z + ci

• Z(-1) + . . . .

Again, following Appendix 2, in general, we say that the b9 and e j both followed a geometric distribution for i greater than zero.

Denoting the proportionality -parameters d and d for g and c$

respectively, we see the equation 6 of appdndix 2 h,ecomes:b 6a) Y=a*(1-A) + ab

• X (-1) + A*(dx -bo)

• X(-1) +

c

• Z + A

• D_~z-c )

• Z(-1) + A

• Y(-1)

As before if the long run elasticity of X is 1, A must equal 1-(bo+ A*(d -ba)) so that if (6a) is rewritten 7a) Y=A+S,

• X + St

• X(-1) + 4a

• Z + $1 Z(-1) + -

6

• Y(-1) the constraint implies 6 = 1 - (Sa+St) as before 109

v .

So far, nothing new has been introduced. Rather this discussion serves to introduce the reader to the use of the estimator with more than one independent variable. Notice that no constraint has been imposed on the c4 . In fact, the long run elasticity of Z (if the b's are unconstrained) is c, + d *A/(1-A) 7 or, equivalently, 4, + (41/6 + 4 )

• 6/(1-6) or, (4, + 9t)/(1-6) ,

In the constrained ca$e (where the sum of the b's equals one),

6 = l-(8, + 8t)

,- so that the long run elasticity of Z is (4,+41)/(8,+st)

So much for introduction, we now consider the case where the long run and short run elasticity of X is one. By defintion this implies two things, a) b, = 1 b) b, + b +b 2 i

+ . . ..=1 These, of course, imply c) bt +b 2 +b 3 + . . ..=0 Since the b's must be the correct theoretical sign or zero, (c) implies:

bg = 0 for all i>0 d)

Referring back to equation 3 in Appendix 2

3) bg=d*A I so, for (d) above to hold either

, d x =0 or, A =0 I

or, both 110

This is where the need for the introduction of a second independent variable becomes apparent. Since a second variable entering the equation with a distributed lag exists, A/ 0. Therefore, the first condition d =x 0 must hold for the short run and log run elasticities to be one.

Recalling the definitions of Appendix 2 .

So = bo Si = A * (d x-bo) 6 =A The two conditions for both elasticities equalling one (b = 1, d = 0) imply x

8. = 1 Si = -A* bo = - 6

. 6 = A which using (7a) implies 8a)Y= a+ X + (-6)

• X(-1) + 4

• Z + 4:

• Z(-1)

+ 6

• Y(-1) or collecting terms in coefficients 9a)Y-X = a + 6 * (Y(-1) - X(-1)) + 4.

• Z + 4

• Z(-1) which the estimable form of the equation. The long run elasticity of Z is:

($ + 4i)/(1-6) e t

111

• w .

Accendix 3 Estimation methecolcgy for ncn-manufacturing employment.

A. Services The distributed lag estimator described in Appendix 2 is used in the estimation of services employment. The functional fom is assumed to be multiplicative so that estimaticn is performed linearly en the natural icgarithms of the series, log (E93/Nj) = log (A) + be

• log (E4 /N) + b t

• log (E$ (-1)/N(-1))

+co

• log (YP j /Nj /(YP/N)) + ct* log (YP j (-1)/Nj (-1)/

(YP(-1)/N(-1))) + da

• log (AHEMj/CPIS) + d i

• log (AHEM j

(-1)/CPIS(-1)) + ea

• log (MINWAGE/CPIS)

+ et

• log (MINWAGE(-1)/CPIS(-1)) + f

• log (E$3(-1)/Nj (-1))

Since we suspect the long-tem elasticity for E /N 3 may be one, the regression was also run embodying the constraint. The con-straint implies f = l-b -b which was implemented and tested for statistical significance as described in Appendix 2.

B. Construction The form of estimation was log-linear as described in A. However, two technical points must be made. First, there were no prior beliefs on any long-term elasticities which could be ased. Second, the variable, housing pemits issued, was not available on the same definition through the entire historical period used in es-timation. The approach usad to include the two sets of variables available --one available :60-1967; the other, 1968-1977--was to allow the fomer set to 've explanatory power only from 1960-1967; the latter, from 1968-1977. Inputting the variables in this f ashion allows us to use the entire set of historical data for the dependent and dther independent variables. .

C. Goverment The fom of estimation is the same as described in A. No con-strained estimation was implemented.

112

e ~

!.coencix 4 Estimation methodology for wages and prices. -

A. Prices Inflation in the consumer price index of the southern U.S. is specified to be a weighted combination of inflation in the consumer price index in the entire U.S. and the price index for food. Total inflation in the region is constrained not to be greater than the comoination of

, the inflation of the two components. That is, the sum of the elastici-ties of the two indices as one.

We write: ,

1) log (CPIS) = a + b

• log (CPI) + c

• log (CPIFOOD) wnere:

CPIS = Consumer price index, southern U.S.

CPI = Consumer price index, U.S.

CPIF000 = Consumer price index, food The constraint on the sum of the elasticites implies b+c = 1 So that implementation of the constraint implies a regression of the forn:

2) log (CPIS) - log (CPIF000) = a + b * (log (CPI) - log (CPIF000))

B. Wages

1) State manufacturing wages The wage equation is specified to be multiplicative. Thus, the estimation is on the natural logarithms of the dependent and independent variables.

The lag estimator described in Appendix 2 is used with the long-term elasticity of national real wages constrained to be 1. Thus the estimable form is:

1) log (AHEMj /CPIS) - log (AHEM j (-1)/CPIS(-1)) =

log (A) + b, * (log (AHEM / CPI) - log (AHEMj(-1)/CPIS(-1)))

+ b, * (log (AHEM (-1)/ CPI (-1)) - log (AHEMj (-1)/ PIS(-1)))

113

= -

2) National manufacturing wages lhe national variable, AHEM, is estimated:

Icg(AHEM / CPI) = a + b

• iog(JAHEADJEA/ CPI) + c

• log (UCAPFRBM)

Where:

AHEM 2 Average hourly earnings, manufacturing CPI = Consumer price index JAHEA0JEA = Index of hourly earnings of production workers UCAPFRBM = Federal Reserve Board index of capital utilization 114