sales due to being on call for AS. Similarly, the second

term compensates generators for the labor costs of op-

erating capacity on call as AS not yet called upon to

generate. Hence, even though the generator may not

be required to produce electricity when on call for AS,

it is, nevertheless, compensated because it missed out

on the opportunity to use its productive capacity for

other lucrative endeavors.

At this point, the generators' equilibrium sales of

electricity and AS can be explicitly evaluated by sub-

stituting Equations 11 and 12 into Equations 4 and

5, then solving simultaneously. While this approach

would certainly yield the desired results, some effort

can be avoided by using some intuition about the na-

ture of perfectly competitive markets. Since it was as-

sumed that all generators are identical and both elec-

tricity and AS requirements are fixed at XT and XT,

respectively, in equilibrium each generator will sell its

pro-rated share of the overall requirements into each

market. This then leads to the following:

Conjecture I X*

aPXT i-

a pi'

Conjecture 2 Y* = D yXT ypi.

Verification of these is left for the Appendix.

4. Empirical Analysis

Using California market data, we can empirically test

the hypothesis developed in Section 3, viz., P{ - PY =

Sl(+f7)XT + ed1+)JXT. Equivalently, we can ex-

press this as:

Pj = P + OXT (13)

Intuitively, this says that the spot price of electricity is

equal to the spot price of AS plus:

1. the pro-rated incremental fuel cost of producing

both electricity and AS that are called, and

2. the pro-rated incremental labor cost of producing

AS that are called.

It is this hypothesis, i.e., Equation 13, that we will test

using data available from the California markets.

Before proceeding with the analysis, however, some

speculation is required as to which California markets

are closest to the ideal markets in our perfectly com-

petitive model. For the AS, the spinning reserve hour-

ahead market is used, and for the electricity spot mar-

ket, the ex-post supplemental energy prices and quanti-

ties are used. Hourly data for one year (1 June 1999 to

31 May 2000) obtained from the CAISO are analyzed.

During some hours, trading in the ex-post supplemen-

tal energy market did not occur, so only those hours

with available data for both markets are used in the

analysis. In order to be consistent, only the four re-

gions that are common to both markets in question

are analyzed. Finally, we take into account the fact

that the CAISO had imposed various levels of price

caps on all of its markets during the time period be-

ing studied. In 1999, price caps were set at $250/MW

until they were raised to $750/MW in October. In or-

der to simplify the analysis, we discard all data points

for which the ex-post supplemental energy price was

strictly greater than $250/MW. In terms of both num-

ber of data points and volume of energy traded, only

a fraction of the data is discarded (almost 99% of the

data points are retained or 98% of the energy volume

is retained).

In order to test Equation 13, we cannot simply con-

struct the following linear regression model and per-

form an ordinary least squares (OLS) regression:

Pi = a + bXi + pi

(14)

Here, Pi refers to the month i average energy price,

Xi is the month i cumulative energy volume, and pi

is a disturbance term that should be independent of

Xi. However, because both the energy price and quan-

tity are endogenous to the model, OLS estimators for a

and b will likely be biased. In order to avoid this bias,

we use the two-stage least squares (TSLS) regression

procedure instead of OLS. For this, we need to specify

some exogenous variables that are related to the en-

dogenous ones, but not to the disturbances. We elect

to use average monthly temperature (Ti for month i)

and cumulative monthly precipitation (Ri) as the ex-

ogenous variables.3 The structural model is then:

Xi= + = hPi + pi

(15)

(16)

Xi = To + i1Pi + T2Ti + T3Ri + vi

Equation 15 can be thought of as the "supply" expres-

sion, and Equation 16 can be considered the "demand"

expression. The reduced form of this system is readily

obtained by solving the structural model equations si-

multaneously:

Pi = 710 + 11Ti + w12Ri + Eli (17)

3We obtain these data from the Western Regional Climate

Center (http://www.wrcc.dri.edu). For each CAISO zone, we

selected a weather station in the most populous area. For

Humboldt, it's Eureka (station 042910); for NP15, it's Sacra-

mento (station 047633); for San Francisco (SF), it's SFO (station

047769); and for SP15, it's Los Angeles (station 045115).