On the Economic Value of Wetlands in the St. John`s Bayou

On the Economic Value of Wetlands in the St. John’s
Bayou-New Madrid Floodway
William L. Weber
Department of Economics and Finance
Southeast Missouri State University
Cape Girardeau, MO 63701
[email protected]
July 28, 2015
1
Abstract
The paper examines the system of levees for flood control on the Lower Mississippi River that were a consequence of the Jadwin Plan stemming from the 1928
Flood Control Act. Part of the Jadwin plan allows the Army Corps of Engineers
to dynamite a fuse-plug levee at Birds Point Missouri allowing floodwaters to flow
into the New Madrid Floodway and lower water levels at Cairo, Illinois. A gap between two levees near New Madrid allows floodwaters to back into the lower part
of the Floodway, harming agricultural interests but creating important wetlands. A
shadow pricing model is used to estimate the environmental benefits of the wetlands
formed by the St. John’s Bayou and New Madrid Floodway in Southeast Missouri.
The shadow price estimates suggest that closing the gap in the two levees would
destroy wetlands that generate $60 to $105 million in value.
2
1
Introduction
In the early spring of 2011 the New Madrid Floodway gained national attention as
the Army Corps of Engineers blew a hole in the levee at Birds Point Missouri near
the confluence of the Mississippi and Ohio Rivers to alleviate flood risk at Cairo,
Illinois. The Floodway encompasses 130,000 acres in an area that is between three
and ten miles wide. Beginning at Birds Point a frontline levee next to the Mississippi
River and a setback levee extend to New Madrid. A 1500 foot gap between the two
levees provides a link with the land and the river at New Madrid. Even before
the Corps blew the levee the Floodway had attracted debate between competing
interests in either maintaining or closing the 1500 foot gap in the levee system
including the Army Corps of Engineers, the US Fish and Wildlife Service, the states
of Missouri and Illinois, landowners in the Floodway, drainage district engineers,
and environmental groups.
The 1500 foot gap in the two levees allows backwater to enter the Floodway
during high water events. Such backwater creates wetland habitat for fish, birds,
and wildlife in the lower part of the Floodway but also reduces the value of farmland
in the rich alluvial soils. This paper examines the levee system and the controversy
surrounding the 1500 foot gap between the two levees. In addition, a shadow pricing
model is developed and estimated for public lands in 51 counties in five states
surrounding the New Madrid Floodway and St. John’s Bayou. The model is used
to estimate shadow price of wetlands and simulate the change in value if the gap in
the levees were to be closed.
2
The Levee System
Ten thousand River Commissions, with the mines of the world at their
back, cannot tame that lawless stream, cannot curb it or confine it,
cannot say to it, Go here or Go there, and make it obey. – Mark Twain,
Life on the Mississippi
The Mississippi River Basin drains 41% of the United States. Periodic flooding
has led those living along the river to seek higher ground or to build levees as
protection against rising waters. The people of New Orleans built the first levees
surrounding the city during 1718-1727 (Rogers 2011). State governments and local
citizens were the primary levee builders but in 1849-50, the federal government
3
became involved with passage of The Swamp Acts after a series of floods on the river.
Missouri gained 5,230 square miles in the Second Swamp Act and was allowed to sell
the land to the public and use the proceeds to construct levees and drainage ditches
(Rogers 2011). By 1880, 991 miles of levee had been built below Cape Girardeau,
Missouri. In 1917 the First Federal Flood Control Act was passed with the Federal
government agreeing to pay up to a maximum of two thirds of the cost of levee
construction and maintenance if local drainage districts and citizens agreed to pay
a minimum of one third the cost. Local interests took advantage of the subsidy
and by 1927 the US Army Corps of Engineers had built 1,582 miles of levees on
both sides of the river from Cairo, Illinois to New Orleans, Louisiana. Today there
are 3,727 miles of levees and flood walls and 2,216 miles of mainline levees along
the Mississippi River including 596 miles along the Arkansas and Red rivers in the
Atchafalaya Basin (Rogers 2011).
According to the Mississippi River Commission and the US Army Corps of Engineers the most important levee in the lower Mississippi basin is the Commerce to
Birds Point mainline levee which connects with the set-back levee at Birds Point.
Starting at Commerce, Missouri this levee protects 1 million acres of prime agricultural bottom land in Missouri and Arkansas and approximately 2.5 million acres in
total (Camillo 2012, Olson and Morton 2013B). Without this levee the Mississippi
River would cut a swath into the 40 mile wide and 200 mile long St. Francis River
basin and not return to the main branch of the Mississippi River until the mouth
of the St. Francis, below Memphis but about seven miles above Helena, Arkansas.
The Great Flood of 1927 left 313 people dead, inundated 18 million acres of land,
caused $300 million in damage (Hoyt and Langbein 1955) and led to passage of the
Flood Control Act of 1928. This Act appropriated $325 million for flood control
and led to the the building of the Birds Point–New Madrid Floodway located in
Southeast Missouri at a cost of $21 million. The Floodway (Figure 1) is encompassed
by a front-line levee adjacent to the Mississippi River with a northern terminus
located at Birds Point and a southern terminus at New Madrid. A set-back levee
with a northern terminus at Birds Points runs southwest to New Madrid protecting
the nearby towns of Wyatt, Anniston, and East Prairie from flooding. The two levees
extend to New Madrid, Missouri but two gaps in the levees allowed water to flow
into the St. John’s Bayou and the New Madrid Floodway during high water events.
In mid-January of 1937 rising waters on the Ohio River led to the evacuation of
Floodway residents as the Corps prepared to blow the levee. Charleston, Missouri
4
resident Thad Snow described the procession and uncertainty of the residents:
I have been flooded, have seen floods and flights ahead of floods that
came and flights from floods that failed to top the levee and didn’t come.
Almost always, the pitiful labor of evacuation must be done in rain and
mud. But never before have I, or the oldest gray-beard inhabitant, seen
it done over six inches of frozen sleet that affords cruel footing for man,
beast, and truck. As I write, the sleet is thawing, the temperature 34
degrees and the coldest possible rain is falling steadily.
...
Then the behavior of this flood when it finally tops the levee is unpredictable, because the “floodway” is new and untried. It is now to receive
its first baptism. Eminent engineers disagree as to how it will perform, so
how are we poor, ignorant farmers to guess what will happen? Naturally,
the terror of the unknown is felt even by the hardiest veteran of many
floods.
Thad Snow, St. Louis Post-Dispatch January 27, 1937
On January 25, 1937 the Floodway was operated for the first time as the Army
Corps of Engineers dynamited the levee at Birds Point to help lower water levels
at Cairo, Illinois, a town with 14,000 residents. Many of the people living in the
Floodway moved to higher ground and repaired only barns and sheds necessary for
farming. By spring of 1937 the Corps had placed an emergency ring levee around the
dynamited part of the levee which saved crops from another round of rising waters
along the Mississippi.
The Flood Control Act of 1946 authorized the closing of the 4200 foot gap in
the St. John’s Bayou and the gap was closed by 1953 with a gravity floodgate installed. The Bayou area includes approximately 324,000 acres and extends northwest
of the setback levee and includes the towns of East Prairie, Charleston, Sikeston,
and Commerce (Ledwin and Roberts 2000). Today, the area is prime agricultural
farmland but at one time it was an extensive hardwood bottomland and swamp.
When it rains in the Bayou area ditches drain water toward New Madrid, but water
can overflow those ditches and cause flooding in low lying areas when high water on
the Mississippi River causes the floodgate to be closed.
A second 1500 foot gap between the setback levee and the frontline levee allows
water from the Mississippi River to back into the Floodway and also serves as an
5
outlet in the event of the fuse-plug levee being blown. The Floodway encompasses
approximately 133,000 acres and is designed to take 550,000 cubic feet of water per
second and lower the gage at Cairo by seven feet in the event of activation. The
Flood Control Act of 1954 authorized the closing of the 1500 foot gap which would
have allowed greater agricultural use of low lying areas in the Floodway. However,
closing the gap would cause a sump area of 26,000 acres in the lower part of the
Floodway for which flowage easement rights had not been obtained. A lack of local
support for the project delayed the start of construction. Today, the 1500 foot gap
remains.
A key characteristic of the Floodway is the fuse-plug levee at Birds Point that
extends for approximately eleven miles and is part of the front-line levee. This type
of levee is shorter in height than the remainder of the frontline and setback levees.
When water breaches the levee, the current helps tear it down and helps to minimize
damage to the remainder of the front-line and set-back levees (Rogers). Today, the
fuse-plug levee is embedded with plastic pipe which can be injected with liquid TNT
to artificially blow the levee. The fuse-plug levee is to be activated artificially by
dynamite when the water level reaches 58 feet and is forecast to reach 60 feet or
higher on the gage at Cairo.
Section 4 of the Flood Control Act states that the the federal government can
use cost/benefit analysis to determine the amount of compensation to be paid to
landowners in the event that the Floodway is used:
The United States shall provide flowage rights for additional destructive
floodwaters that will pass by reason of diversions from the main channel
of the Mississippi River: Provided, That in all cases where the execution
of the flood-control plan herein adopted results in benefits to property
such benefits shall be taken into consideration by way of reducing the
amount of compensation to be paid.
Appendix E. 1928 Flood Control Act. Seventieth Congress, Sess. 1. Ch.
596. 1928
The Mississippi River and Tributaries Project of which the Birds Point-New
Madrid Floodway is part has been modified numerous times since its inception with
the Flood Control Act of 1928. Prior to 1928, the Mississippi River Commission
built levees to a height to allow them to withstand the last great flood. In 1928,
under the leadership of Major General Edgar Jadwin, the policy changed to design a
6
Figure 1: The New Madrid Floodway
flood control system that would withstand the maximum probable flood–the project
design flood. The project design flood uses data on past major storms occurring in
a hypothetical sequential order consistent with frontal movements and atmospheric
7
conditions. The current project design flood was developed in 1954 and consists of
three storms hitting the Mississippi basin: the 1937 storm that struck the Ohio and
lower Mississippi River basins followed three days later by the 1950 storm over the
same area followed by the 1938 storm that struck 90 miles north with rain rotated
by 20 degrees. These three storms maximize the amount of precipitation coverage
over the project design flood area (Mississippi River Commission 2008). The project
design flood also accounts for water storage at Kentucky Lake, Barkley Lake, and
the New Madrid Floodway. The building of the dam across the Tennessee River
forming Kentucky Lake in 1944 and across the Cumberland River forming Barkley
Lake in 1966 allowed greater water storage in the event of flooding along the Lower
Mississippi River. In 1965, the front line levee in the New Madrid Floodway was
raised to a height of 62.5 feet on the Cairo gage, the set-back levee was raised to
65.5 feet and the fuseplug section of the levee was raised to 60.5 feet.
Since 1930, the annual low water mark at the Cairo gage has averaged 9.58 feet
with an average annual high of 46.7 feet. Flood stage at Cairo occurs at 40 feet
and the river has been in flood stage at least once in 76 out of the 85 years from
1930 to 2014. In addition, the river at Cairo has exceeded 50 feet on the gage in 35
years since 1930. The maximum high water mark occurred on May 2, 2011 when
water measured 61.72 feet on the gage. The project design flood forecasts peak flows
at Cairo, Illinois of 2.3 million cubic feet per second from the Ohio River into the
Lower Mississippi River. Such a flow would be consistent with a river gage of 66 feet
at Cairo. However, use of the New Madrid Floodway with its 550,000 cubic feet per
second capacity is projected to reduce the gage at Cairo to 59 feet.
2.1
New Problems Arise
The natural lower Mississippi River “writhes like an imprisoned snake, constantly
seeking to establish and maintain a state of equilibrium between its length; its slope;
and the volume and velocity of its discharge (Elliot 1932, op. cit. Harrison 1950,
p.302).” The natural meander of the river slows the water leaving oxbows, sloughs,
and wetlands as it deposits fine grained sediment along the natural banks resulting
in the most favorable soil.
To move water more quickly through the levee system the Corps of Engineers also
shortened the river as part of the Project Design Flood. Thirteen cutoffs between
Arkansas City, Arkansas and Natchez, Mississippi shortened the river by about 115
miles and with the levees has helped the river carry six to seven times its natural
8
flow (Harrison 1950). As early as 1950 part of the unintended consequences of the
levee system gained notice as the shorter river began to undercut its embankment
in an attempt to regain its natural meander. Writing in Land Economics USDA
economist Robert W. Harrison pointed out the “New” Mississippi Problem as the
need to provide revetment and bank stabilization along 200 to 250 miles of the
lower Mississippi River with costs projected to be $250 to $300 million, an amount
approximately equal to $2.5 billion in 2015.
Other problems have arisen as levees raised in one area caused higher water in
other areas. In the 1980s the Len Small Levee in southern Illinois was strengthened
putting additional pressure on the Commerce to Birds Point Levee during the flood
of 1993. Recently, additional pressure during high water events has been placed on
the Birds Point Levee as levees in southern Illinois and at Hickman, Kentucky have
been raised and strengthened (Olson and Morton 2013b).
3
The 2011 Flood
A series of papers by Kenneth Olson and Lois Wright Morton (Olson and Morton
2012, 2013a, 2013b, 2014a, 2014b, Morton and Olson 2012, 2013) provide detailed
geologic history, maps, soil characteristics, and examine the damage the 2011 Ohio
and Mississippi River flooding caused in southern Illinois to the Cache River, Horseshoe Lake, and adjacent agricultural lands and in southeast Missouri to land in the
New Madrid Floodway.
Record rains during April 2011 in the Ohio River basin states of Illinois, Indiana, Ohio, Pennsylvania, Kentucky, and West Virginia and caused flooding along
unprotected areas. Rainfall amounts much above average occurred in the Mississippi River basin in Arkansas, Missouri, Iowa, Wisconsin, and Minnesota (NOAA
National Overview April 2011). Flooding that began in Minnesota during early April
moved down through the Mississippi River basin. By later April 2011 floodwaters
were putting significant pressure on the Ohio and Mississippi River levees protecting
Cairo, Illinois. On May 2, 2011 the Major General Michael Walsh of the US Army
Corps of Engineers ordered the fuse plug levee at Birds Point blown to allow floodwaters to move into the New Madrid Floodway and lessen pressure on the levees at
Cairo.1 A day later the frontline levees at Big Oak Tree State Park and the lower
1
Passive activation of the Floodway had begun earlier on May 2 as water over-topped lower
sections of the frontline levee.
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fuse plug levee at New Madrid were blown to allow an outlet for the water. Water
diversion into the Floodway lowered the Mississippi River at Cairo by 2.7 feet within
2 days (Olson and Morton 2012) even though it took three days for the Floodway
to reach capacity (Camillo 2012).
Water flowing into the New Madrid Floodway flooded 133,000 acres of Missouri
farmland with damage to 200 buildings including 75 homes (Olson and Morton
2013A). Although 20,000 to 30,000 acres of winter wheat were lost, farmers were
able to plant approximately 90,000 acres of soybeans by mid-July, although the
late planting resulted in lower yields. Landowners in New Madrid and Mississippi
counties received approximately $16.2 million in payments from the USDA Risk
Management Agency (Olson and Morton 2013a). According to Olson and Morton
(2013a) flooding costs are expected to exceed $100 million. The 2011 flood left
small crater lakes, sand deposits, gullies, and crevasses in the Floodway. However,
according to Olson and Rogers (2012) “If the thin, organic silt and clay coatings are
mixed into the topsoil in 2011 or 2012, little significant loss in future crop yield will
occur as long as the Floodway is not flooded again.”
In addition to the damage at the New Madrid Floodway the Len Small levee
was breached just a few hours before the Birds Point Levee was blown on May 2
causing flooding to southern Illinois farmland. In an unsuccessful attempt to prevent
activation of the New Madrid Floodway the attorney general of Missouri had sued
the Army Corps of Engineers to prevent the blowing of the Birds Point levee. If the
levee had been blown sooner, it might have alleviated pressure on the Len Small
levee and prevented its breaching. In Kentucky, a relative lack of levees allowed
floodwaters from both the Ohio and Mississippi rivers to move into the natural
floodplain and little damage occurred from the flood.
4
Stakeholders in the New Madrid Floodway
I do not think that my people have ever been in favor of that plan for
they do not want to see southeast Missouri made the dumping ground
to protect Cairo, Illinois, much as we love Cairo. That is all the Jadwin
plan does. Indeed, it is doubtful it accomplishes that objective.
Dewey Short, U.S. Representative from Missouri 1930. op. cit. C. Camillo
2012. Divine Providence.
10
Representatives from Missouri criticized Major General Edgar Jadwin’s proposed
New Madrid Floodway as making Missourians bear all of the costs of flood protection. Across the river, citizens in Illinois, Kentucky, and Tennessee decried Missouri’s
levee system as raising the waters in their own states. In December of 1928 President
Coolidge authorized that landowners in the Floodway receive a one-time indemnity
for flowage rights, although some landowners argued that they were not receiving
adequate compensation.
In late April and early May of 2011, before the Birds Point levee was blown, the
state of Missouri filed suit to prevent the Corps from artificially breaching the levee.
Missouri politicians including Eighth Congressional District Representative Jo Ann
Emerson, state representatives from southeast Missouri, Governor Jay Nixon, and
Attorney General Chris Koster all opposed blowing the levee. Across the river in
Illinois, the city leaders of Cairo and Governor Pat Quinn were in favor of blowing
the levee. Of course, no vote was taken as the final decision resided with Major
General Michael Walsh.
4.1
Landowners and Local Interests
During construction of the Floodway land values were between $50-$150 per acre.
According to the Flood Control Act of 1928 the fuse-plug levee could not be constructed until 50% of the landowners agreed to accept compensation for selling
the government a perpetual flowage easement. By 1936, 77% of the landowners had
agreed. Payments from the government for the easement averaged $16.47 on 106,759
acres within the Floodway (Final Tract Register 1950). One large tract of land—
the Matthews Tract—lay below 300 feet in elevation and flowage easements on these
20,088 acres were not acquired since backwater flooding would have inundated these
lands before artificial breaching. Although some landowners argued that the fuseplug levee constituted a taking under the Fifth Amendment the Flood Control Act
of 1928 stated that “No liability of any kind shall attach to or rest upon the United
States for any damage from or by the floods or flood waters at any place . . . (op. cit.
Lee 2012, p. 185).”
Due to rising waters on the Ohio River and a forecast of over 60 feet on the
Cairo gage, the Floodway was put into operation for the first time on January 25,
1937. Not surprisingly, the aftermath of the flood left people on the Missouri side of
the river critical of the Corps’ operational plan. On February 4, 1937 the owner and
editor of the Enterprise Courier in Charleston, Missouri penned a sarcastic editorial
11
titled “Apparently Cairo Has Been Saved.”
Forget, if you can, for a moment the misery and the suffering, the loss
of livestock and household goods, the sacrifice of human life—forget
the work of 5,000 men for the past ten days, and the original cost of
$21,000,000 sunk in the golden spillway dream of the Army Engineers—
forget all that. The salient, the only, fact to remember is that Cairo has
been saved.
And remember that the Army Engineers have been vindicated.
...
Art Walhausen, Sr.
Later that same year, Lucius T. Berthe—former Panama Canal engineer and
consulting engineer for the Little River Drainage District in Southeast Missouri—
published a pamphlet criticizing the Jadwin plan for its hubris and lack of impartial
external review:
“Military or civil, there is no such thing as the Supermind. No authority,
military or civil, can view the plan of its own creation with impartial eye.
...
If the Jadwin Plan was denied the benefit of such [external] review before
construction, none can deny, insofar as the Cairo area is concerned, that
it has received perfectly competent review since. The 1937 flood has
given an unbiased verdict. Let Old Man River Speak!
L.T. Berthe Old Man River Speaks, p. 3
In 1917 the Supreme court ruled in United States v. Cress that floodwaters
could only be considered a taking if the flooding of property was permanent or
would inevitably occur (Lee 2012). In the 1939 case Danforth v. United States,
where property in the Birds Point-New Madrid Floodway was at issue, the Supreme
Court ruled that the government’s actions could not be designated a taking since
“water on water is not a taking.”
After the 2011 flood, a class action lawsuit claiming a taking was filed by the
plaintiff–Big Oak Farms, Inc., et al.–against the United States (Big Oak Farms, Inc.
2012). In this case, Judge Nancy Firestone relied on previous rulings to rule against
the plaintiff. Specific mention was made to the fact that flood control programs
12
provide benefits as well as costs and that the Flood Control Act of 1928 “expressly
provided that in purchasing flowage easements, the benefits of the flood control
plan” should be considered in determining the amount of compensation to be paid
to the landowner and that such benefits would likely reduce compensation.
4.2
The Army Corps of Engineers
I am now of the opinion that no plan is satisfactory which is based upon
deliberately turning floodwaters upon the homes and property of people
even though the right to do so may have been paid for in advance.
Major General Edward Markham Chief of Engineers, testifying before
the House Committee on Flood Control
The Jadwin plan for flood control on the Lower Mississippi received harsh criticism from the beginning. Some people argued that President Calvin Coolidge had
authorized only $300 million of flood control constraining what could be accomplished. In addition, the plan was criticized for making the Floodway too small and
for allowing too little freeboard—only one foot—for the levees at Cairo, and the
frontline and setback levees of the New Madrid Floodway when three feet of freeboard was necessary to accommodate high winds which could erode the levees via
wave action (Berthe 1937).
The Army Corps of Engineers has been a proponent of closing the 1500 foot
gap in the New Madrid Floodway ever since the 1954 Flood Control Act authorized
its closing. In 1965, the flowage easements in the Floodway were modified to allow
artificial breaching of the fuse plug levee using liquid dynamite. The Corps paid a
total of $25,901 for modified easements on 78,769 acres in the Floodway. In addition,
closing the gap would allow agricultural development to occur on lands below 300
feet mean sea level (MSL). With the gap open, such lands had been subject to
backwater flooding. In the event of artificial breaching of the levee, those lands
below 300 feet MSL would be inundated. However, local revenue sources as required
by the 1917 Flood Control Act were unavailable and the gap remained opened.
Finally, the Water Resources Development Act of 1996 allowed federal revenue from
rural enterprise zone programs given to East Prairie, Missouri to be used as payment
for the non-federal source of the cost of the New Madrid Floodway and St. John’s
Basin project.
13
In 2000, the Corps issued a Supplemental Environmental Impact Statement on
the Floodway which was revised in 2002 and again in 2006. The Environmental
Impact Statement and its revisions came under fire from various government environmental agencies about the environmental impacts of the Floodway project. Representatives from the Environmental Protection Agency, the US Fish and Wildlife
Service, the Missouri Department of Natural Resources, the Missouri Department
of Conservation, and the Council on Environmental Quality met with the Corps to
discuss the impacts of the project on wetlands. In May 2006 construction resumed
on the Floodway project. However, on September 13, 2007 the US District Court for
the District of Columbia ruled against the Corps and not only halted construction,
but required the Corps to undue any construction already underway.
As of 2015 the Corps’ plan involved spending $165 million to close the 1500 foot
gap, install two pumping stations, modify 23 miles of ditches in the St. John’s Bayou
Basin, and provide watershed management. The Corps’ projected an annual benefit
to cost ratio of two to one for the project.
4.3
The US Fish and Wildlife Service
In a letter dated June 6, 2002, Field Supervisor Charles M. Scott laid out the US
Fish and Wildlife case against the Corps’ project to close the 1500 foot gap between
the frontline and setback levees: “The proposed project design changes and actions
do nothing to avoid fish and wildlife resource losses and the minimization measures
are nominal considering the significant scope and magnitude of these losses (Scott
2002, p. 2).” Although the Floodway project would create a sump area comprising
20,000 acres in the lower Floodway, Scott argued that in seven of the ten years from
1993 to 2002, river levels were sufficient to provide 30,000 acres of fish spawning
habitat. In addition, Scott argued that the project would have “profound impacts
on wetland hydrology” and serve to reduce the value of wetlands remaining in the
St. John’s Bayou and New Madrid Floodway and eliminate or degrade more than
18,000 acres of wetland habitat.
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4.4
Environmental Groups and other Stakeholders
The Army Corps of Engineers lists fourteen environmental organizations opposed
to the Corps’ plan for the New Madrid Floodway and St. Johns Bayou.2 These
organizations argue that the project violates Section 404 of the Clean Water Act,
does harm to wildlife by destroying habitat, and reduces the proper functions of
wetlands. In addition, various environmental groups argued that the Corps did not
count the benefits of wetlands which would be destroyed as part of the costs of the
project.
Although environmental groups were unanimous in opposition to the Floodway
project, Missouri’s US Senator Roy Blunt and US Representative Jason Smith supported the project and argued that residents in the Floodway and surrounding areas
should take precedence over the environmental impacts of the project. The St. John’s
Bayou Basin Board of Directors also supported the project. However, officials with
the Consolidated Drainage District #1 expressed concern that farmland planting
would be delayed until late in the planting season due to operation of the sump and
that the tax base of local areas might be adversely effected.
5
Wetlands
The US Fish and Wildlife Service defines a wetland as “land where saturation with
water is the dominant factor determining the nature of soil development and the
types of plant and animal communities living in the soil and on its surface. Technically, wetlands are lands transitional between terrestrial and aquatic systems where
the water table is usually at or near the surface or the land is covered by shallow
water (Status and Trends 1983, p. 9).” Marine wetlands include lagoons, bays, coral
reefs and the beach out to the continental shelf. Estuarine wetlands are partially
exposed to the ocean but might also be partially surrounded by land. Estuarine
wetlands include mangrove swamps, tidal mudflats, and salt or brackish marshes.
Freshwater wetlands are generally classified into three types: riverine, lacustrine,
and palustrine. Riverine wetlands include rivers and streams, but exclude the floodplain surrounding those rivers. Lacustrine wetlands are depressions or dammed river
2
These organizations include American Rivers, Atchafalaya Basin Committee of the Sierra Club,
Audubon Missouri, Bird Conservation Network, Illinois Sierra Club, Kentucky Waterways Alliance,
Missouri Parks Association, Missouri Sierra Club, The Nature Conservancy, Wolf River Conservancy, The National Wildlife Federation, Great Rivers Environmental Law Center, Missouri Coalition for the Environment, and the Sierra Club.
15
channels and must be at least twenty acres or have depths greater than two meters
(Status and Trends 1983). Lacustrine wetlands includes lakes, small ponds, bayous,
and sloughs. Palustrine wetlands include all other wetlands not classified as riverine
or lacustrine; for example, swamps, bogs, and prairie potholes.
Wetlands provide numerous functions: ecologic, biologic, hydrologic, and economic (Heimlich et al. 1983). The ecological functions of wetlands include absorbing
sediment from decaying plant matter, serving as a sponge for chemical precipitants
and runoff, and reducing silt in rivers and lakes. Wetlands provide biologic functions
by serving as estuaries for fish and amphibians and providing nesting areas for birds
and habitat for mammals. The hydrologic functions of wetlands include storing water and reducing peak flows which helps helps reduce downstream flooding. Finally,
the economic value of wetlands consist of direct market benefits from activities such
as timber harvesting and indirect benefits to commercial and recreational fishers
by serving as fish nurseries, and to hunters who harvest waterfowl, deer, and other
species. By reducing silt in rivers and lakes, wetlands can also lower the costs of
obtaining potable water.
Maintaining and preventing the conversion of wetlands to alternative uses such
as residential or agriculture imposes an opportunity cost—economic value in such
uses are foregone. Furthermore, wetlands in the southern U.S. served as a breeding
ground for mosquitoes and malaria (McGuire and Coelho 2011) which the levee and
ditch system helped reduce.
According to Heimlich et al. (1983), there were approximately 221–224 million
acres of wetlands when the colonists first set foot in America. Most wetland conversion to agricultural and urban use occurred after 1885. Table 1 reports the amounts
of wetlands from the 1950s to the 2000s in the United States. Today there are approximately 153 million acres of wetlands, an amount that has remained relatively
stable or slightly increased in recent years. The data for riverine wetlands during
the 1950s to 1970s are missing and the data for lacustrine wetlands do not include
the approximately 56 million acres of coastal wetlands around the Great Lakes from
1986 to 2009, so the 1986 to 2009 wetlands’ estimates are more comparable with
themselves than with the data for the 1950s to 1970s.
Today the number of wetland acres has stabilized. Factors contributing to the
decline in wetland conversion include relatively low agricultural prices and reduced
agricultural subsidies, private efforts such as those by the Nature Conservancy and
Ducks Unlimited, and regulations such as the Clean Water Act’s Section 404, state
16
Table 1: Freshwater Wetlands in the US, 1950 to 2009, 1000s of acres
Marine and
Total
Lacustrine1
Palustrine
Wetlands
.
56,563
102,523
179,545
24,385
5,123
57,640
100,319
187,570
1986
22,974
6,291
14,608
100,799
144,672
1998
23,009
6,766
16,611
102,334
148,720
2004
24,565
7,518
16,786
104,253
153,122
2009
24,562
7,511
16,860
104,275
153,208
Estuarine
Riverine
1950s-1970s
20,459
Mid-1970s
Source: U.S. Fish and Wildlife Service, Status and Trends of Wetlands and
Deepwater Habitats in the Conterminous United States.
1. Does not include waters of the Great Lakes from 1986 to 2009.
wetland laws, and the Swampbuster provisions of the 1985 Food Security Act. In
1992, the largest stock of wetlands was located in the Midwest and Southeast, followed by the Delta and Gulf regions, Northeast, with the Mountain, Pacific, and
Central Plains regions having the fewest wetlands.
5.1
Wetland Policies
Although the preservation and enhancement of wetlands guides wetland policy today, The Swampland Acts of 1849, 1850, and 1860 gave more 64.9 million acres
to the states to reclaim wetlands via the construction of levees and ditches. The
Army Corps of Engineers began work on the Mississippi River flood control system
in the 1870s. Approximately 800,000 acres of wetlands were lost annually before
1954. Concern among policy makers and environmentalists over the loss of wetlands
gradually began to slow and then reverse the conversion of wetlands to other uses.
In 1903, the first national wildlife refuge was established at Pelican Island,
Florida. The Migratory Bird Hunting Stamp Act of 1934 provided a fund to enhance
wetlands to increase waterfowl habitat. In 1961, the Wetlands Loan Act allocated
funds for the government to purchase wildlife refuges and waterfowl protection areas. The National Environmental Policy Act of 1970 gave Congress the power to
regulate public construction, including the Corps’ construction of levees and other
flood control projects. The year 1970 also saw a Water Bank established to make annual payments to landowners who agreed to maintain wetlands. Section 404 of The
17
1974 Clean Water Act regulated the discharge of dredged and fill material into water
resources. In 1977, Executive Order 11990 required federal agencies to minimize the
destruction and degradation of wetlands by avoiding construction or management
practices that harmed wetlands (Heimlich et al. 1993). From the mid-1950s to the
mid-1970s the rate of wetlands conversion fell to 458,000 acres annually
The 1985 Food Security Act provided Swampbuster provisions that denied agricultural benefits to farmers who drained wetlands. The Wetlands Reserve Program
(WRP) was established with the 1990 Farm Bill and began in 1992 with a pilot
study in nine states which was extended nationwide in 1995. The WRP is a voluntary program in which the USDA works with landowners to increase or enhance
existing wetlands to augment wetland habitat for fish and wildlife. The program offers landowners the option of receiving payments for a permanent easement, a thirty
year easement, or a cost-sharing approach with the USDA paying 75% to 100% of
the cost of wetland restoration. Wetlands’ conversion was reduced to only 59,000
acres annually by 1997 (Status and Trends 2005-2009). By 1998 the US had made
“No net loss” of wetlands a policy goal, a goal that appears to have been reached as
Table 1 shows a slight increase in total wetlands from 2004 to 2009. The Agricultural
Act of 2014 rolled the WRP into the Agricultural Conservation Easement Program.
Table 2 reports the number of agreements and the numbers of acres per county in
the Wetlands Reserve Program. This study examines counties in Arkansas, Illinois,
Missouri, Kentucky, and Tennessee. By 2012, counties in these five states averaged
more agreements and more acres enrolled in the WRP than the average for counties
in the rest of the US. Whereas the total number of acres enrolled per county in the
five states averaged 3,459 in 2013, the average per county acreage for the rest of the
US was only 2,388. The 2008 Farm Bill allowed slightly more than 3 million acres
to be enrolled in the Wetlands Reserve Program.
5.2
Recent Research on the Economic Value of Wetlands
Although private owners bear costs and receive benefits from wetlands, the benefits
of wetlands can also spillover to third parties. As such, market prices tend to undervalue the true social benefits of wetlands and indirect imputation methods must
be used to obtain social values. These indirect methods can include surveys to measure willingness to pay, methods that measure the damage averted by wetlands from
flood control or storm surges (Barbier et al. 2013), or shadow pricing methods which
measure the opportunity cost of wetlands from an underlying production technol18
Table 2: Average Number of Agreements and Acres in the Wetlands Reserve Program
Agreements in
Acres in
AR, IL, MO
Rest of
AR, IL, MO
Rest of
Year
KY, and TN
U.S.
KY, and TN
of U.S.
2009
23
27
3,357
4,332
2010
39
28
5,347
5,572
2011
27
21
3,489
3,966
2012
32
18
4,639
3,289
2013
24
14
3,459
2,388
Prior Years
325
182
79,123
32,499
Total
470
274
99,413
49,085
Source: Natural Resources Conservation Service
ogy (Bostian and Herlihy 2014). Revealed preference methods such as the travel
cost approach and weak complementarity approach are sometimes used when the
wetlands provide underlying recreation benefits to hunters, fishers, or bird watchers
and value is inferred from the increased use of nearby sites or by the increased use
of complementary items, such as guns, fishing rods, and binoculars that would not
be consumed were it not for the person’s use of the wetland.
When new sites are proposed, but not yet available, the benefit transfer method
is sometimes used to infer the value of a new site from existing sites. For instance,
if existing riverine wetlands have $150 of value per acre and existing lacustrine
wetlands have $200 of value per acre at an existing site, and if the new site has 500
riverine acres and 250 lacustrine acres the new site generates 150×200+500×250 =
$155, 000 of value. Since the estimates of wetland values varies by the particular
indirect valuation method and by the site being studied, the values from numerous
studies are sometimes combined to obtain the marginal values for various wetland
characteristic in a process known as meta-analysis.
Woodward and Wui (2001) performed a meta-analysis of 39 wetland valuation
studies to examine not only the effects of wetland characteristics on wetland values,
but also the effects of the quality of the research underlying the valuation study
on wetland quality. Weak econometric studies tended to impute higher values on
wetlands than strong econometric studies. They also found that wetlands that offerred bird watching or commercial fishing services were more valuable than other
19
wetlands’ functions such as bird hunting, flood control, or environmental amenities.
Ghermandi et al. (2010) used 418 value estimates derived from 170 different studies
in a meta-analysis of wetlands’ value. They found that human-made and marine
wetlands had higher values than other types of wetlands and that water quality
improvements, population, and increases in per capita income contributed to higher
wetlands’ values. Patton et al. (2013) employed a meta-analysis of willingness to pay
for the flood control and water quality functions of wetlands in four National Wildlife
Refuges. They estimated that a 1% increase in the number of acres of wetlands or a
1% increase in population reduced willingness to pay for an additional wetland acre
by about 0.5%. In 2010 dollars, the mean annual willingness to pay for an extra 1000
acres per 1000 population ranged between $90 to $980 for the water quality function
of wetlands and between $130 and $550 for the flood control function of wetlands.
Similarly, Chaikumbung, Doucouliagos, and Scarborough (2015) employed a meta
analysis of 379 studies that valued wetlands in developing countries. They found
that value decreased as the size of the wetland increased, urban wetland sites were
more valuable than rural sites, marine wetlands were more valuable than other types
of wetlands, sites in countries with higher per capita incomes were more valuable,
and that increased biodiversity increased the valuable of wetlands.
Of course, to perform a meta-analysis studies individual site estimates must
be first be derived. Barbier et al. (2013) examined how wetlands mitigate storm
surge in southeastern Louisiana. Controlling for the ratio of wetlands to water and
for the amount of vegetative matter in wetlands they found that a 0.1 increase
in the wetland to water ratio helped reduce flood damages by $592,000-$792,100
and a 0.001 increase in bottom friction due to vegetative matter helped reduce flood
damages by $114,000-$258,000. Withey and van Kooten (2014) examined agriculture
in Canada using mathematical programming to allocate land between alternative
agricultural uses—wheat, oats, barley, canola—and wetlands to maximize profits.
Controlling for climate change effects the authors found that the profit maximizing
area devoted to wetlands declined by 38% if the external benefits of wetlands are
accounted for and by 74% if the external benefits of wetlands are ignored. In effect,
climate change can accelerate wetlands’ losses when government policy encourages
biofuels’ production which gives farmers greater incentive to drain wetlands.
Bostian and Herlihy (2014) used a deterministic method to estimate a directional output distance function and obtain shadow prices for a constructed index of
wetland condition for sites in the Nanticoke River watershed. A one unit increase
20
in the index of wetland condition had an average shadow price of $19.83. Using
this shadow price estimate the authors found that reductions in inefficiency could
enhance wetlands’ condition by approximately $390/acre. Kozak et al. (2010) investigated how fast willingness to pay falls as geographical distance from the wetland
increases for wetlands along the Des Plaines River and Cache River in Illinois. When
willingness to pay becomes zero for people living more than 1 km from wetland, the
value of the Cache River system is only $28,258. In contrast, if willingness to pay
remains positive until a person lives more than 1000 km from wetland, the value of
the Cache River system is $440 million given a log-linear decay function and $2.5
billion dollars if an exponential decay function is employed.
6
The Region
This study covers 51 counties in five states: Missouri-13 counties, Illinois-3 counties,
Kentucky-6 counties, Tennessee-10 counties, and Arkansas-19 counties. These counties are in the Army Corps of Engineers Water Resource Planning (WRPA) Areas
2 and 3. A shaded map of the counties is provided in Figure 2.
Table 3 summarizes data obtained from the National Levee Database. Arkansas
has the most leveed acres and miles of levees with 576.3 miles of levees protecting 2.4
million acres. Missouri has 182 miles of levees protecting 279,819 acres. The three
counties in Illinois include levees along both the Ohio and Mississippi River with
those levees protecting 82,126 acres. The counties in Tennessee and Kentucky have
the fewest leveed acres.
Table 3: Miles of Levees and Leveed Acreage in the Study Region
Number of
Miles of
Leveed
Levee Segments
Levees
Acreage
Illinois
14
90.6
82,126
Missouri
9
182.3
279,819
Arkansas
37
576.3
2,412,327
Tennessee
7
29.7
12,074
Kentucky
1
12.2
11,078
Figure 3 depicts a map of the areas in WRPAs 2 and 3 with some overlap into
21
Figure 2: Region of study
other WRPAs. In the northwestern part of the map, levees protect areas along the
St. Francis River and Castor River. This area also includes Wappapello Lake which
is an Army Corps of Engineers flood control reservoir formed by a dam across the
St. Francis River. Moving to the east and south are the levees that protect land
in Arkansas from floodwaters along the Mississippi River, St. Francis River, White
River, and Cache River. In Illinois, the Len Small levee and other levees protect
farmland in Alexander county in southern Illinois from flooding along the Mississippi
River and the Ohio River. In addition, Cairo, Illinois is completely surrounded by
levees protecting the city from flooding to the east from the Ohio River and flooding
from the west from the Mississippi River. Levees in Kentucky protect from flooding
along the Ohio River and Mississippi River near Hickman, Kentucky. In Tennessee,
22
levees protect the town of Dyersburg and surrounding areas.
Figure 3: Leveed Areas in the Region
6.1
Economic Indicators in the Region
The 51 counties in the study region were part of the 219 counties classified as the
Lower Mississippi Delta Region (LMDR) under the 1988 Lower Mississippi Delta
Development Act. Former Arkansas Governor and then President Bill Clinton was
the former state’s chairman of the LMDR Commission which had a mission of fostering policies to enhance economic development. Weber and Devaney (1995) compared
rural counties in the LMDR with rural counties in the rest of the US and found that
people in LMDR counties had lower per capita income, a higher percent of female
headed households, higher rates of poverty, less education, fewer hospital beds, lower
population growth rates, and higher rates of unemployment than people in other
US rural counties.
Table 4 reports various statistics for counties in the region compared to other
counties residing in Arkansas, Illinois, Kentucky, Missouri, and Tennessee from 2001
to 2013. In each state the counties in the region had higher per capita income growth,
and higher labor productivity growth (except for Missouri) than other counties in
each state. In addition, the counties in the region in each state had lower average
23
population growth from 2001 to 2013 than their non-region counterparts. Regional
counties in Arkansas, Illinois, and Kentucky all experienced declines in population.
Regional counties in Arkansas, Kentucky, and Tennessee had greater average per
capita incomes in 2013 than their non-regional counterparts. Except for the six
counties in Kentucky, the counties in the region have higher average rates of poverty
and a smaller percent of their population aged 25 years and older with a college
degree.
6.2
Public Lands in the Region
Table 5 reports the total number of acres and the number of different kinds of
public land sites in the five states. Thirteen National Wildlife Refuges3 cover 348
thousand acres and include the Cache River NWR in Arkansas where the once
thought extinct Ivory-billed woodpecker was seen in 2004, although recent sitings
have not been confirmed. The Cache River NWR had been created in 1986 after
a federal judge in 1972 halted Corps’ levee construction for not complying with
the National Environmental Policy Act of 1970. Three national forests-Shawnee in
Illinois, Mark Twain in Missouri, and St. Francis in Arkansas cover 290 thousand
acres. The 51 counties also include 28 state parks covering 73 thousand acres, 173
conservation and wildlife management areas covering 501 thousand acres and nine
sites classified as “other” covering 3,701 acres. In all, 1.2 million acres of land provide
wildlife habitat and recreational opportunities.
3
The refuges include Dale Bumpers White River, Cache River, Big Lake, Wappanoca, Bald Knob,
Cypress Creek, Mingo, Hatchie, Lower Hatchie, Lake Isom, Chickasaw, Reelfoot, and Clark’s River.
24
Table 4: Economic Indicators in the Region, 2001-2013
Per capita
Labor
# of
Income
Productivity
Population
Counties
Growth
Growth
Growth
AR-Other
56
0.132
0.170
0.030
AR-Region
19
0.234
0.222
-0.039
IL-Other
99
0.182
0.204
0.011
IL-Region
3
0.259
0.252
-0.125
KY-Other
114
0.099
0.133
0.047
KY-Region
6
0.199
0.210
-0.048
MO-Other
102
0.132
0.156
0.045
MO-Region
13
0.179
0.142
0.017
TN-Other
85
0.101
0.149
0.091
TN-Region
10
0.156
0.172
0.042
Income 2013
Poverty
College
Per capita
AR-Other
56
$32,303
20.6%
14.5%
AR-Region
19
$35,299
23.6%
13.9%
IL-Other
99
$41,350
13.4%
19.7%
IL-Region
3
$33,876
23.6%
12.4%
KY-Other
114
$31,494
21.5%
14.7%
KY-Region
6
$39,253
18.8%
15.2%
MO-Other
102
$34,935
17.0%
16.9%
MO-Region
13
$33,909
21.6%
12.9%
TN-Other
85
$33,415
18.9%
15.6%
TN-Region
10
$35,982
21.0%
15.6%
25
Table 5: Acres of Public Lands in 49 Counties
National
Conservation
National
Wildlife
and Wildlife
State
Forests
Refuges
Areas
Parks
Other
Total
AR
22,687
260,223
245,762
14,736
1,506
544,915
IL
30,533
10,000
17,318
1,591
554
59,996
KY
0
3,885
34,266
182
1,601
39,934
MO
237,137
21,676
106,036
27,631
40
392,520
TN
0
52,617
98,371
29,080
0
180,068
290,357
348,401
501,753
73,220
3,701
1,217,433
3
13
173
28
9
226
Total acres
# of sites
26
7
A Shadow Pricing Model for Public Lands
7.1
Theory
Public lands tend to be non-market outputs so their values must be obtained indirectly. To obtain prices for public lands—which we then use to price wetlands in the
New Madrid Floodway—we specify a production technology and then use the directional output distance function as a functional representation of that technology.
Using the duality between the revenue function and the directional output distance
function we obtain shadow prices of the non-market outputs (Färe, Grosskopf, and
Weber 2001). The shadow price of the non-market output represents its opportunity
cost in terms of the value of foregone production of a marketed output.
We assume a set of k = 1, ..., K producers employ x = (x1 , . . . , xN ) inputs to
produce y = (y1 , . . . , yM ) outputs. The output possibility set gives the set of outputs
that can be produced with given inputs and is represented as
P (x) = {y : x can produce y}.
(1)
We assume that P (x) is convex with inputs and outputs strongly disposable. To move
from a set to a functional representation of the technology we use the directional
output distance function. This function was developed by Chambers, Chung, and
Färe (1996, 1998) who adapted Luenberger’s (1992) consumer benefit function for
use in production theory. Let g = (g1 , . . . , gM ) represent a directional vector that
scales outputs. The directional output distance function takes the form
→
Do (x, y; g) = max{β : y + β × g ∈ P (x)}.
(2)
The product of the directional output distance function and the directional vector
gives the maximum addition to each output that can be feasibly produced given
→
inputs and the technology. The function Do (x, y; g) serves as a measure of inefficiency
→
for a given producer. If Do (x, y; g) = 0 a given (x, y) combination is efficient; outputs
→
cannot be feasibly increased given inputs. Inefficient producers have Do (x, y; g) > 0
with larger values indicating greater inefficiency.
Figure 4 illustrates the output possibility set and the directional output distance
function. A county is observed to produce outputs (y1 , y2 ) at point A inside P (x).
County A’s outputs are scaled to the frontier along the directional vector g. Frontier
outputs represented by point B correspond to (y1 + βg1 , y2 + βg2 ).
27
y1=Public Lands
B
y1+βg 1
A
y1
P(x)
g1
0
g
y2
g
2
y2=Real Income
y 2+βg2
Figure 4: Directional Output Distance Function
The value of the directional vector chosen determines how outputs are scaled to
the frontier. For example, when a directional vector of g = (1, 1, . . . , 1) is chosen,
→
Do (x, y; g) gives the maximum unit expansion in all outputs. When a directional
→
vector of g = (1, 0, 0, . . . , 0) is chosen Do (x, y; g) gives the maximum unit expansion
output 1, all other outputs held constant. A special case occurs when a directional
→
vector of g = (y1 , . . . , yM ) is chosen. Here, Do (x, y; g) multiplied by 100% gives
the maximum percentage expansion in all outputs and it can be shown that the
reciprocal of the Shephard output distance function minus one equals the directional
→
output distance function: Do (x, y; g) =
output distance
1
Do (x,y)
− 1, where Do (x, y) is the Shephard
function.4
The directional output distance function completely characterizes the production
technology in that
→
y ∈ P (x) ⇐⇒ Do (x, y; g) ≥ 0.
(3)
The properties of the directional output distance function are inherited from the
4
The Shephard output distance function is defined as Do (x, y) = min{θ :
28
y
θ
∈ P (x)}.
production technology. For y ∈ P (x) these properties are
→
(i.) Do (x, y; g) ≥ 0,
→
→
→
→
(ii.) y 0 ≤ y, Do (x, y 0 ; g) ≥ Do (x, y; g),
(iii.) x0 ≥ x, Do (x0 , y; g) ≥ Do (x, y; g),
→
→
(iv.) Do (x, y + α × g; g) = Do (x, y; g) + α.
(4)
Property 4(i.) is the feasibility property. Properties 4(ii. and iii.) impose a monotonicity condition on outputs and inputs. If a firm produces more outputs given inputs its inefficiency will not increase and if a firm uses more inputs to produce given
outputs its inefficiency will not decrease. Property 4(iv.) is the translation property
which is an additive representation of the technology similar to the homogeneity
property of Shephard output distance functions.
To derive shadow prices for the non-market outputs we exploit the duality
between the directional output distance function and the revenue function. Let
p = (p1 , . . . , pM ) represent a vector of output prices. The revenue function is defined
as
R(x, p) = max{py : y ∈ P (x)}
y
→
R(x, p) = max{py : Do (x, y; g) ≥ 0}.
y
(5)
The revenue function gives the maximum revenue for feasible output vectors and
→
since y + Do (x, y; g)g is a feasible output vector we can write
→
R(x, p) ≥ py + pDo (x, y; g)g.
(6)
The inequality in (6) derives from the fact that once outputs are scaled to the
frontier and all technical inefficiency is eliminated, revenues associated with the
→
frontier outputs (py + pDo (x, y; g)g) might still be less than the maximum because
the frontier outputs are not allocatively efficient. Rearranging (6) yields
→
Do (x, y; g) ≤
R(x, p) − py
.
pg
(7)
The directional output distance function can be recovered from the revenue function
29
as
→
Do (x, y; g) = min
p
R(x, p) − py
.
pg
(8)
Taking the gradient function of (8) with respect to outputs yields
→
∇y Do (x, y; g) =
−p
pg
(9)
and given two outputs, ym and yj , the shadow price of the mth output can be
recovered as
→
pm = pj
∂ Do (x, y; g)/∂ym
→
.
(10)
∂ Do (x, y; g)/∂yj
Figure 5 illustrates the shadow pricing method. The directional output distance
function projects producer A’s outputs to point B on the frontier. The slope of
the frontier at point B, dy1 /dy2 is the marginal rate of transformation between the
two outputs which measures the physical opportunity cost of producing one more
→
unit of output m in terms of foregone output j. In (10) the term
∂ D o (x,y;g)/∂ym
→
∂ D o (x,y;g)/∂yj
represents the marginal rate of transformation Thus, if the j th price is known and
the marginal rate of transformation can be estimated, the shadow price of output
m can be obtained.
It is important to note that the choice of directional vector will affect the
marginal rate of transformation for inefficient producers. In Figure 5, if g1 > 0
and g2 = 0 producer A’s outputs would be projected to point C resulting in a lower
shadow price for the public good. Alternatively, if g1 = 0 and g2 > 0 producer A’s
outputs would be projected to point D resulting in a higher shadow price for the
public good.
7.2
Functional Form
To operationalize the shadow pricing formula given by (10) we need to choose a
functional form for the directional output distance function. The translog form has
been used extensively to estimate Shephard input and output distance functions.
However, while the parameters of the translog function can be imposed to satisfy a
homogeneity property, the directional output distance function needs to satisfy the
translation property. Chambers (1998) suggests a quadratic form for the directional
output distance function. The quadratic serves as a second-order approximation to
30
y1=Public Lands
C
B
A
g1
D
P(x)
g
0
dy1/dy2= -p2 /p
1
y2=Real Income
g
2
Figure 5: Shadow Pricing
the true, but unknown function and the parameters can be restricted to satisfy the
translation property and monotonicity properties given by (4).
The quadratic directional output distance function is given as
→
Do (x, y; g) =α0 +
+
M
X
α m ym +
m=1
N
X
N
X
n=1
βn xn +
M X
M
1 X
αmm0 ym ym0
2 m=1 m0 =1
T
N
M X
X
X
1
γt DTt .
βnn0 xn xn0 +
δmn ym xn +
2 n=1 n0 =1
t=2
m=1 n=1
N
X
(11)
Symmetry restrictions for the cross-output and cross-input effects are imposed
so that αmm0 = αm0 m and βnn0 = βn0 n . The translation property requires that
PM
m=1 αm gm
= −1,
PM
m0 =1 αmm0 gm
= 0, m = 1, . . . , M , and
PM
m=1 δmn gm
= 0, n =
1, . . . , N (Hudgins and Primont 2007). Included in (11) are time indicator variables,
DTt , that allow the distance function to shift from period to period.
To estimate (11) we follow Aigner and Chu (1968) and estimate a deterministic
directional output distance function using linear programming. This method minimizes the sum of the distances of the observed inputs and outputs of each producer
→
to the frontier technology. Recall that Do (x, y; g) = 0 when a producer is on the
frontier. Given k = 1, . . . , K producers we choose α0 , αm , αmm0 , βn , βnn0 , δmn and
31
γt to
T X
K →
X
Do (xtk , ykt ; g) − 0 subject to
(i.)
(ii.)
(iii.)
t=1 k=1
→
Do (xtk , ykt ; g) ≥ 0, k = 1, . . . , K, t = 1, . . . , T,
→
t
∂ Do (xtk , ykt ; g)/∂ykm
≤ 0, m = 1, . . . , M, k = 1, . . . , K, t = 1, . . . , T,
→
∂ Do (xtk , ykt ; g)/∂xtkn ≥ 0, n = 1, . . . , N, k = 1, . . . , K, t = 1, . . . , T,
(iv.) αmm0 = αm0 m , βnn0 = βn0 n ,
(v.)
M
X
m=1
M
X
αm gm = −1,
M
X
αmm0 gm = 0, m = 1, . . . , M, and
m0 =1
δmn gm = 0, n = 1, . . . , N.
(12)
m=1
The restrictions given by (12i) require that the observed output and inputs be
feasible for every observation in each year. The restrictions in (12ii and iii) impose
the monotonicity conditions for outputs and inputs. Symmetry conditions for the
cross-output and cross-input effects are imposed by (12iv). Finally, the restrictions
associated with the translation property are imposed by (12v).
Although different directional vectors can be chosen the directional vectors need
to be common for all observations to avoid having to parameterize the directional
vectors in the quadratic form.
7.3
Data and Estimates
To implement the shadow pricing model we employ pooled data on 51 counties
located in five states during the period 2009-2012. We assume that public lands
would be employed in agriculture in their next best alternative so each county’s
agricultural output is used as the private good. Agricultural output (y1 ) equals the
inflation adjusted (base year=1984) value of crop revenues derived from corn, soybeans, wheat, cotton, and rice. We sum acres of National Forest land and National
Wildlife Refuges in each county to get federal land acres (y2 ) and the acres that are
state parks, wildlife management acres, or other state lands to get state land acres
(y3 ). The inputs include farm employment (x1 ), real farm expenditures on lime, fertilizer, and pesticides (x2 ), real farm expenditures on petroleum and other expenses
(x3 ), and the number of square miles in the county. Crop revenues, farm labor, and
32
farm expenditures for fertilizer, and petroleum and other farm expenditures vary by
year. The number of square in the county, and the number of acres of federal land
and state land are constant for the four years.
Table 6: Descriptive Statistics for County Outputs and Inputs1
Mean
Std. Dev
Minimum
Maximum
648
383
102
2304
x2 =fertilizer, $1000s
11,391
8,499
244
35,335
x3 =petroleum and
22,857
13,848
2,583
60,961
561
213
163
1034
903,584
2,520,011
67,865
17,564,812
y2 =federal lands (acres)
12,525
24,448
0
96,454
y3 =state lands (acres)
11,347
10,560
0
53,274
x1 =farm labor
other expenses, $1000s
x4 =square miles
y1 =crop revenues, $1000s
1. Fertilizer, petroleum and other expenses, and crop revenues are in constant 1984
dollars.
Table 6 provides descriptive statistics. The average number of square miles acres
in a county is 561 (358,940 acres) with less than 1% of that area (23,872 acres) devoted to public lands comprising 12,525 federal acres in the form of National Wildlife
Refuges or National Forests and 11,347 acres of state lands in the form of wildlife
management areas, state parks, or other state lands. The average county employs
648 farm workers, uses $11.3 million in fertilizer, and $22.8 million in petroleum and
other farm expenditures to generate crop revenues of $903.5 million.
To estimate (12) a directional vector must be chosen. As shown previously the
choice of directional vector will determine the projection of observed outputs to the
production frontier and the slope of the frontier at the projected point. We choose
seven alternative directional vectors corresponding to g = (1, 1, 1), g = (1, 1, 0),
g = (1, 0, 1), g = (1, 0, 0), g = (0, 1, 1), g = (0, 1, 0), and g = (0, 0, 1). Each of the
directional vectors influences the estimates through the restrictions implied by the
translation property in (12v). We report the parameter estimates for the quadratic
directional distance function given g = (1, 1, 1) in Table 7.5
We divided all outputs and inputs by 1000 before estimating. We note that the
5
Parameter estimates for the other directional vectors are available upon request.
33
Table 7: Parameter Estimates for the Quadratic Directional Output Distance Function for g = (1, 1, 1)
Parameter
Variable
Estimate
Parameter
Variable
Estiate
α0
constant
3.395
δ11
y1 x1
-0.074
α1
y1
-0.690
δ12
y1 x 2
-0.040
α2
y2
-0.159
δ13
y1 x 3
0.002
α3
y3
-0.151
δ14
y1 x 4
0.340
β1
x1
6.089
δ21
y2 x 1
0.180
β2
x2
1.182
δ22
y2 x 2
0.022
β3
x3
0.394
δ23
y2 x 3
-0.001
β4
x4
-2.180
δ24
y2 x 4
-0.346
α11
y12
0.011
δ31
y3 x 1
-0.106
α12
y1 y2
-0.005
δ32
y3 x 2
0.018
α13
y1 y3
-0.006
δ33
y3 x 3
-0.001
α22
y22
0.002
δ34
y3 x 4
0.006
α23
y2 y3
0.003
γ2010
Year=2010
0.725
α33
0.003
γ2011
Year=2011
-0.341
β11
y32
x21
-1.631
γ2012
Year=2012
0.438
β12
x1 x2
0.436
β13
x1 x3
-0.059
β14
x1 x4
-1.528
β22
x22
0.101
β23
x2 x3
-0.006
β24
x2 x4
0.257
β33
x23
-0.004
β34
x3 x4
-0.114
β44
x24
6.652
estimates of the time effects, γ2010 and γ2012 , are positive indicating that the frontier
shifted to the Northeast in 2010 and 2012 relative to 2009. Such a shift might be due
to technological progress or better growing conditions in 2010 and 2012 relative to
2009. However, γ2011 is negative indicating an inward shift in the production frontier
in 2011. Such an inward shift is consistent with the high water during the spring of
2011 when farmers in the Floodway (and in other areas) lost the winter wheat crop
34
due to flooding. In addition, wet conditions which delayed planting probably caused
some farmers to plant soybeans rather than corn resulting in lost revenues.
Table 8 reports the estimates of the directional output distance function and the
number of frontier counties. for various directional vectors. For the directional vector
g = (1, 1, 1), inefficiency averages 6.08 for the pooled sample implying that if the
average county were to produce on the best-practice production frontier state lands
could increase by 6080 acres, federal lands could increase by 6080 acres, and county
farm income could increase by 6.08 million. The number of frontier counties ranged
from two in 2010 to five in 2011, with a total of 14 counties defining the production
frontier. Production among the 51 counties exhibited the least inefficiency in 2011
and the most inefficiency in 2012.
The estimates of inefficiency change for other choices of directional vector. Inefficiency is the least for the four directional vectors that expand real farm revenues and
either increase or hold constant federal land acres and state land acres. In addition to
g = (1, 1, 1) these directional vectors are g = (1, 1, 0), g = (1, 0, 1), and g = (1, 0, 0).
Relative to when real crop revenues are expanded, inefficiency is greater for the
directional vectors that hold crop revenues constant and either expand or hold constant federal and state land acres. The greatest inefficiency occurs for g = (0, 0, 1).
→
For this directional vector, the estimate of Do (x, y; g) gives the maximum expansion
in state lands holding crop revenues and federal lands constant. On average, state
lands could be expanded by 24.85 thousand acres under such a scenario.
∧
∧
The shadow price estimates for federal (p2 ) and state lands (p3 ) are reported
in Table 9 for various directional vectors. These shadow price estimates are derived
from (10) using the parameter estimates for the quadratic directional output distance
function. Assuming that the real price of crop revenues (y1 ) is the known market
∧
∧
price with p1 = 1, the shadow prices for federal lands (p2 ) and state lands (p3 ) are
estimated as
N
α1 + M
m0 =1 α1m0 ym0 +
n=1 δ1n xn
= p1 ×
, m = 2, 3.
PM
PN
αm + m0 =1 αmm0 ym0 + n=1 δmn xn
P
pm
P
(13)
All shadow price estimates are in 1984 dollars, but can be converted to 2015
dollars by multiplying by the 2015 mid-year CPI of 2.37088. The directional vector
g = (1, 1, 1) generated a shadow price of federal lands equal to $445.8 and a shadow
price for state lands equal to $604.2. Now, consider the three directional vectors
where federal lands are expanded, but either crop revenues, state lands, or both are
35
Table 8: Estimates of Inefficiency
2009
2010
2011
2012
All years
5.93
6.03
5.11
7.25
6.08
3
2
5
4
14
7.06
6.86
8.44
9.91
8.07
5
2
3
3
13
7.76
7.82
8.25
8.76
8.15
3
2
3
5
13
9.54
9.35
21.9
11.34
13.04
6
3
1
3
13
14.71
14.22
13.20
11.94
13.52
2
2
3
7
14
25.39
22.76
21.55
26.67
24.09
1
1
4
3
9
29.78
19.98
22.33
27.29
24.85
1
4
2
4
11
g = (1, 1, 1)
→
Do (x, y; g)
# on frontier
g = (1, 1, 0)
→
Do (x, y; g)
# on frontier
g = (1, 0, 1)
→
Do (x, y; g)
# on frontier
g = (1, 0, 0)
→
Do (x, y; g)
# on frontier
g = (0, 1, 1)
→
Do (x, y; g)
# on frontier
g = (0, 1, 0)
→
Do (x, y; g)
# on frontier
g = (0, 0, 1)
→
Do (x, y; g)
# on frontier
held constant. These directional vectors correspond to g = (1, 1, 0), g = (0, 1, 1),
and g = (0, 1, 0). In each of these cases the shadow price of federal lands increases.
→
For the directional vector g = (0, 1, 0) where Do (x, y; g) gives the expansion in
federal land acres holding crop revenues and state lands constant, the shadow price
of federal lands increases to $3,573. When state lands are expanded, but either crop
revenues, federal lands, or both are held constant the directional vectors correspond
to g = (1, 0, 1), g = (0, 1, 1), and g = (0, 0, 1). In these cases the shadow price
36
Table 9: Mean Shadow Price Estimates for Public Lands1
2009
2010
2011
2012
All years
411.0
484.7
490.4
397.2
445.8
553.7
650.6
664.2
548.4
604.2
494.1
526.1
519.5
475.5
503.8
126.5
141.2
144.5
134.2
136.6
389.6
429.3
413.5
352.5
396.2
809.7
865.6
876.9
818.6
842.7
293.4
301.7
286.7
263.9
286.4
135.9
135.8
134.2
132.2
134.6
504.2
505.6
519.5
524.3
513.4
1067.3
1133.3
1216.1
1095.4
1128.0
1944.8
3680.6
4585.4
4047.3
3572.5
0
0
0
0
0
294.6
346.0
359.1
290.3
322.3
636.6
739.9
960.5
689.1
756.2
g = (1, 1, 1)
∧
Federal Lands=p2
∧
State Lands=p3
g = (1, 1, 0)
∧
Federal Lands=p2
∧
State Lands=p3
g = (1, 0, 1)
∧
Federal Lands=p2
∧
State Lands=p3
g = (1, 0, 0)
∧
Federal Lands=p2
∧
State Lands=p3
g = (0, 1, 1)
∧
Federal Lands=p2
∧
State Lands=p3
g = (0, 1, 0)
∧
Federal Lands=p2
∧
State Lands=p3
g = (0, 0, 1)
∧
Federal Lands=p2
∧
State Lands=p3
1. Shadow prices are in 1984 dollars.
of state lands increases relative to the g = (1, 1, 1) directional vector. State lands
achieve their highest shadow price, $1,128, for the directional vector g = (0, 1, 1).
37
7.4
Using the Model to Value Wetlands in the New Madrid Floodway and St. John’s Bayou
Table 10 reports details on the outputs and inputs for Mississippi and New Madrid
counties, home to the St. John’s Bayou and New Madrid Floodway. Mississippi
county has 6,446 acres of state lands and zero federal lands. New Madrid county has
6,322 acres of state lands and zero federal lands. New Madrid county has greater
real crop revenues partly attributable to a larger land area—678 square miles in
New Madrid county versus 413 square miles in Missississippi county. Crop revenues
increased from 2009 to 2012, but the gap between the two counties was greatest in
2011 when New Madrid county produced 82% more real crop crop revenues than
Mississippi county. However, despite the larger farm output, New Madrid county was
less efficient than Mississippi county in each of the four years. In fact, Mississippi
county was one of the frontier counties in 2012 and exhibited lower inefficiency on
average than the other counties in the study (see Table 8). In contrast, New Madrid
county exhibited greater inefficiency in each of the four years than other counties in
the study.
Now, consider the data for 2009 for the two counties. If Mississippi county had
realized greater inefficiency an extra $2.92 million in crop revenues, an extra 2920
acres of federal lands, and an extra 2920 acres of state lands would have been
produced resulting in frontier quantities of y ∗ = (58513, 2920, 9366).6 For those
quantities, the shadow price of federal lands is $508 and the shadow price of state
lands in $634. In New Madrid county, greater efficiency could have allowed real crop
revenues to increase by $12.42 million, federal lands to increase by 12,420 acres, and
state lands to increase by 12,420 acres giving y ∗ = (95034, 12420, 18742). At those
quantities, the shadow price of an acre of federal land is $463 and the shadow price
of an extra acre of state lands is $626. The shadow prices vary by year because each
county employs different amounts of farm labor, fertilizer, and petroleum and other
expenses to produce farm outputs measured by real crop revenues. The shadow
prices have a smaller range for state lands in Missisissippi county, $546 to $814,
than in New Madrid county where the range is between $178 to $1440.
In Mississippi county the state lands include Big Oak Tree State Park (1000
acres), Seven Island Conservation Area (1381 acres), and Ten Mile Pond Conser6
Frontier output is y ∗ = (y + β ∗ g), where β ∗ equals the estimate of the directional output
→
distance function, Do (x, y; g).
38
Table 10: Outputs, Inefficiency and Shadow Prices of Public Lands in Mississippi
and New Madrid Counties: g = (1, 1, 1)
Shadow price1 of
Real Farm
Income
→
Federal
State
Lands=p3
(1000s)
Do (x, y; g)
∧
Lands=p2
2009
55,593
2.92
508
634
2010
57,988
1.31
667
814
2011
59,531
3.45
403
546
2012
73,434
0
576
806
2009
82,614
12.42
463
626
2010
96,982
6.90
1117
1440
2011
108,531
5.19
731
1063
2012
105,776
14.42
178
417
Year
∧
Mississippi County
New Madrid County
1. Shadow prices are in 1984 dollars.
vation Area (3755 acres) all important wetland areas. Two of these areas (Big Oak
Tree SP and Ten Mile Pond CA) lie within the Floodway and Seven Island Conservation Area lies between the frontline levee and the Mississippi River. In New
Madrid county Donaldson Point Conservation Area (5785 acres) also lies between
the frontline levee and the Mississippi River just east of the town of New Madrid.
This area also consists of wetland and bottomland hardwoods.
According to the US Fish and Wildlife Service there are approximately 30,622
acres of wetlands in the St. John’s Bayou basin and 36,883 acres of wetlands in the
New Madrid Floodway (Ledwin and Roberts 2000). Mississippi and New Madrid
counties (of which the Bayou and Floodway are part) also have more diverse habitats
and wildlife and fish species than other counties in the Missouri bootheel. Under the
authorized Corps’ plan wetlands would decline by almost 24,000 acres to only 6,710
acres in the St. John’s Bayou. Under the Corps’ plan wetlands in the New Madrid
Floodway would decline by approximately 7,000 acres to 29,770 acres. Given only
6,136 acres of public lands in Mississippi county and only 6,322 acres of public
lands in New Madrid county, much of the decline in wetlands would come on private
39
property. Using the highest shadow price for wetlands in Mississippi county, $814 for
state lands in 2010, the 32,138 acres of wetlands currently located on private property
are generating approximately $26 million in value in 1984 dollars which converted
to 2015 dollars equals $61.6 million.7 A lower bound estimate using the 2011 shadow
price of $403 for federal lands in Mississippi county yields approximately $13 million
in value in 1984 dollars or $31 million in 2015 dollars.
Under the authorized Corps’ plan the 31,000 acre decline in wetlands should
be considered an environmental cost which should be added to the proposed $165
million price tag for closing the 1500 foot gap in the levees encompassing the Floodway. These costs can be reasonably approximated using the range of shadow prices
reported in Table 10. Using the high shadow price of $814 in Mississippi county the
lost value of wetlands is 814 × 31000 = $25.23 million in 1984 dollars. Using the high
shadow price of $1440 for New Madrid county the lost value of wetlands would be
1440 × 31000 = $44.64 million. Lower bound estimates can be similarly obtained.
Converted to 2015 dollars the lost value of wetlands ranges between $60 to $106
million if the Corps’ plan is implemented.
8
Conclusions
The 1928 Flood Control Act increased the oversight of the Army Corps of Engineers
with a charge of reducing the damage from flooding through the Lower Mississippi
River. Under the vision and oversight of Major General Edgar Jadwin the Corps built
levees and floodways and shortened and straightened the river to move water more
quickly through the basin. The New Madrid Floodway was an important part of the
plan. Covering 133,000 acres the Floodway consists of a frontline and set-back levee
that begin at Birds Point. Both levees then run in a south/southwesterly direction
before drawing close again at New Madrid. A 1500 foot gap in the two levees near
New Madrid allows water from Mississippi River flooding to back into the lower
part of the Floodway helping to maintain important wetlands but simultaneously
reducing potential farm outputs in the lower lying areas.
Although the Floodway gap was once authorized to be closed, a lack of local
revenues and then a lawsuit brought by environmental groups has kept it open.
7
Private wetland acres in the Floodway are estimated as total wetland acres less state lands:
36, 883 − (1000 + 3755) = 32, 128. The CPI for the first half of 2015 is 237.088 with a base=100 in
1984.
40
The lower 10-15% of the Floodway lies in New Madrid county. A directional output
distance function was estimated for 51 counties in the five state region surrounding
the Floodway and used to estimate shadow prices of federal land acres in the form
of National Wildlife Refuges and National Forests, and state land acres in the form
of wildlife management/conservation areas, state parks and other state land acres.
Many of these public lands consist of wetlands and in Mississippi and New Madrid
counties almost all of the public lands are wetlands.
The shadow price of public lands was used as an estimate of the value of wetlands in the New Madrid Floodway. In 1984 dollars the shadow prices ranged from
$178/acre to $1440/acre in New Madrid county and from $403/acre to $814/acre in
Mississippi county. The Corps’ plan to close the 1500 foot gap between the frontline
and setback levees has been forecast to cost $165 million. Farmers in the low lying
areas of the Floodway and St. John’s Bayou including residents of East Prairie, Missouri would be beneficiaries. However, in addition to the money costs of the Corps’
plan , another $60 to $106 million (2015 dollars) should be added to the cost side
of the ledger. These external costs correspond to the 31,000 acres of wetlands that
would be lost in the New Madrid Floodway and St. John’s Bayou valued at their
shadow prices.
Whether or not the 1500 foot gap in the levee should be closed has attracted
debate from numerous parties: The Army Corps of Engineers, the US Fish and
Wildlife Service, property owners within the Floodway and in St. John’s Bayou,
politicians from both sides of the Mississippi River, independent drainage districts
and engineers, and environmentalists. Perhaps an alternative policy where the Federal government would pay private landowners for their low lying acres and establish
a new National Wildlife Refuge or several new wildlife management/conservation
areas instead of spending even more money on closing the Floodway gap would be
a step in the right direction to satisfy the disparate interests.
41
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[50] St.
Johns
Bayou
Project
History
pendix
D.
U.S.
and
and
New
Applicable
Army
Corps
Madrid
Congressional
of
Floodway,
Missouri:
Authorizations,
Engineers
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Ap-
District.
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47