Environmental Engineering Reference
In-Depth Information
5.6 Econometric Estimation of Shadow Ramsey Prices
Before we proceed with the estimations, the following should be noted:
￿
We must distinguish between Short Run Marginal Costs (SRMC) and Long Run
Marginal Costs (LRMC). In the short run the plant size is
xed, whereas the
LRMC is dTC/dQ, in which plant size is variable. This is the Ramsey Price;
when it is adjusted for market distortions, it becomes the
Shadow Ramsey
Price.
The SRMC is the cost of treating 1 extra cubic meter of water. This is equal to
the energy cost of Reverse Osmosis.
￿
We have Fixed Costs (FC) + Variable Costs (VC) in the long run. The plants
'
￿
borrowing rate for amortization is used to
find a price at which TC = TR. This is
the Breakeven Price.
To repeat, we can think of Ramsey prices as long run marginal cost prices. But
integrating Ramsey prices with the new public economics would require Shadow
Ramsey Prices. That is, for the public sector, it is appropriate to take into account
the price distortions that we
find in the real economy, distortions due to monopo-
listic economic structures. Hence we need to correct for these distortions. As an
illustration, all actual real cost data are reduced by 2 percent to re
ect the estimated
shadow price (for the theory of shadow pricing, see Dreze and Stern ( 1990 ) and
Little and Mirlees ( 1974 ). For those who wish to see
please
multiply the estimated Shadow Ramsey prices by a factor of 1.02 . Details of
shadow pricing techniques are outside the scope of this work. We show the
econometric estimation of Shadow Ramsey Prices for 36 Reverse Osmosis tech-
nology water treatment plants.
We use a log-linear model, adjusted to remove heteroscedasticity, estimated by
Weighted Least Squares (WLS), reported in Eq. 5.27a, b ; and in Table 5.1 below. We
distinguish between desalination of seawater and brackish water using the dummy
variable SEA. For brackish water, SEA = 0. In addition, the interaction term com-
bining the effects of Plant Size
unadjusted prices,
Q
and the dummy variable
SEA,
was estimated and
named
On the basis of the economic theory, the double-log regression model
is determined as the best. In Eq. 5.27a, b , TC is total cost, and Q is plant size.
QSEA.
In TC i ¼ a þ b In Q i þ c SEA i þ d In QSEA i þ li i
ð 5 : 27a Þ
In TC i ¼ 13
:
885652232 þ 0
:
740621837 In Q i þ 0
:
928025419 SEA i
þ 0
:
143438118 In QSEA i
ð 5 : 27b Þ
Standard errors :
ð
0 : 291654726
Þ
ð
0 : 18230551
Þ
ð
0 : 352579975
Þ
ð
0 : 188792389
Þ
T statistics
:
ð
47
:
60990
Þ
ð
4
:
06153
Þ
ð
2
:
63210
Þ
ð
0
:
75977
Þ
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