On the Economic Value of Wetlands in the St. John’s Bayou-New … · 2015-08-03 · and led to the the building of the Birds Point–New Madrid Floodway located in...

On the Economic Value of Wetlands in the St. John’sBayou-New Madrid Floodway

William L. WeberDepartment of Economics and Finance

Southeast Missouri State UniversityCape Girardeau, MO 63701

[email protected]

July 28, 2015

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Abstract

The paper examines the system of levees for flood control on the Lower Missis-sippi River that were a consequence of the Jadwin Plan stemming from the 1928Flood Control Act. Part of the Jadwin plan allows the Army Corps of Engineersto dynamite a fuse-plug levee at Birds Point Missouri allowing floodwaters to flowinto the New Madrid Floodway and lower water levels at Cairo, Illinois. A gap be-tween two levees near New Madrid allows floodwaters to back into the lower partof the Floodway, harming agricultural interests but creating important wetlands. Ashadow pricing model is used to estimate the environmental benefits of the wetlandsformed 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 woulddestroy wetlands that generate $60 to $105 million in value.

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1 Introduction

In the early spring of 2011 the New Madrid Floodway gained national attention asthe Army Corps of Engineers blew a hole in the levee at Birds Point Missouri nearthe 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 threeand ten miles wide. Beginning at Birds Point a frontline levee next to the MississippiRiver and a setback levee extend to New Madrid. A 1500 foot gap between the twolevees provides a link with the land and the river at New Madrid. Even beforethe Corps blew the levee the Floodway had attracted debate between competinginterests in either maintaining or closing the 1500 foot gap in the levee systemincluding the Army Corps of Engineers, the US Fish and Wildlife Service, the statesof 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 Floodwayduring 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 farmlandin the rich alluvial soils. This paper examines the levee system and the controversysurrounding the 1500 foot gap between the two levees. In addition, a shadow pricingmodel is developed and estimated for public lands in 51 counties in five statessurrounding the New Madrid Floodway and St. John’s Bayou. The model is usedto estimate shadow price of wetlands and simulate the change in value if the gap inthe levees were to be closed.

2 The Levee System

Ten thousand River Commissions, with the mines of the world at theirback, 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 floodinghas led those living along the river to seek higher ground or to build levees asprotection against rising waters. The people of New Orleans built the first leveessurrounding the city during 1718-1727 (Rogers 2011). State governments and localcitizens were the primary levee builders but in 1849-50, the federal government

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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 sellthe 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 Federalgovernment agreeing to pay up to a maximum of two thirds of the cost of leveeconstruction and maintenance if local drainage districts and citizens agreed to paya minimum of one third the cost. Local interests took advantage of the subsidyand by 1927 the US Army Corps of Engineers had built 1,582 miles of levees onboth sides of the river from Cairo, Illinois to New Orleans, Louisiana. Today thereare 3,727 miles of levees and flood walls and 2,216 miles of mainline levees alongthe Mississippi River including 596 miles along the Arkansas and Red rivers in theAtchafalaya Basin (Rogers 2011).

According to the Mississippi River Commission and the US Army Corps of En-gineers the most important levee in the lower Mississippi basin is the Commerce toBirds 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 agricul-tural bottom land in Missouri and Arkansas and approximately 2.5 million acres intotal (Camillo 2012, Olson and Morton 2013B). Without this levee the MississippiRiver would cut a swath into the 40 mile wide and 200 mile long St. Francis Riverbasin and not return to the main branch of the Mississippi River until the mouthof 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 theFlood Control Act of 1928. This Act appropriated $325 million for flood controland led to the the building of the Birds Point–New Madrid Floodway located inSoutheast Missouri at a cost of $21 million. The Floodway (Figure 1) is encompassedby a front-line levee adjacent to the Mississippi River with a northern terminuslocated at Birds Point and a southern terminus at New Madrid. A set-back leveewith a northern terminus at Birds Points runs southwest to New Madrid protectingthe nearby towns of Wyatt, Anniston, and East Prairie from flooding. The two leveesextend to New Madrid, Missouri but two gaps in the levees allowed water to flowinto 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 ofFloodway residents as the Corps prepared to blow the levee. Charleston, Missouri

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resident Thad Snow described the procession and uncertainty of the residents:

I have been flooded, have seen floods and flights ahead of floods thatcame 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 andmud. But never before have I, or the oldest gray-beard inhabitant, seenit 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 34degrees and the coldest possible rain is falling steadily.

. . .

Then the behavior of this flood when it finally tops the levee is unpre-dictable, because the “floodway” is new and untried. It is now to receiveits first baptism. Eminent engineers disagree as to how it will perform, sohow are we poor, ignorant farmers to guess what will happen? Naturally,the terror of the unknown is felt even by the hardiest veteran of manyfloods.

Thad Snow, St. Louis Post-Dispatch January 27, 1937

On January 25, 1937 the Floodway was operated for the first time as the ArmyCorps of Engineers dynamited the levee at Birds Point to help lower water levelsat Cairo, Illinois, a town with 14,000 residents. Many of the people living in theFloodway moved to higher ground and repaired only barns and sheds necessary forfarming. By spring of 1937 the Corps had placed an emergency ring levee around thedynamited part of the levee which saved crops from another round of rising watersalong the Mississippi.

The Flood Control Act of 1946 authorized the closing of the 4200 foot gap inthe St. John’s Bayou and the gap was closed by 1953 with a gravity floodgate in-stalled. The Bayou area includes approximately 324,000 acres and extends northwestof the setback levee and includes the towns of East Prairie, Charleston, Sikeston,and Commerce (Ledwin and Roberts 2000). Today, the area is prime agriculturalfarmland 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 watercan overflow those ditches and cause flooding in low lying areas when high water onthe Mississippi River causes the floodgate to be closed.

A second 1500 foot gap between the setback levee and the frontline levee allowswater from the Mississippi River to back into the Floodway and also serves as an

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outlet in the event of the fuse-plug levee being blown. The Floodway encompassesapproximately 133,000 acres and is designed to take 550,000 cubic feet of water persecond and lower the gage at Cairo by seven feet in the event of activation. TheFlood Control Act of 1954 authorized the closing of the 1500 foot gap which wouldhave 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 theFloodway for which flowage easement rights had not been obtained. A lack of localsupport for the project delayed the start of construction. Today, the 1500 foot gapremains.

A key characteristic of the Floodway is the fuse-plug levee at Birds Point thatextends for approximately eleven miles and is part of the front-line levee. This typeof 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 minimizedamage to the remainder of the front-line and set-back levees (Rogers). Today, thefuse-plug levee is embedded with plastic pipe which can be injected with liquid TNTto artificially blow the levee. The fuse-plug levee is to be activated artificially bydynamite when the water level reaches 58 feet and is forecast to reach 60 feet orhigher on the gage at Cairo.

Section 4 of the Flood Control Act states that the the federal government canuse cost/benefit analysis to determine the amount of compensation to be paid tolandowners in the event that the Floodway is used:

The United States shall provide flowage rights for additional destructivefloodwaters that will pass by reason of diversions from the main channelof the Mississippi River: Provided, That in all cases where the executionof the flood-control plan herein adopted results in benefits to propertysuch benefits shall be taken into consideration by way of reducing theamount 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-NewMadrid Floodway is part has been modified numerous times since its inception withthe Flood Control Act of 1928. Prior to 1928, the Mississippi River Commissionbuilt 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

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Figure 1: The New Madrid Floodway

flood control system that would withstand the maximum probable flood–the projectdesign flood. The project design flood uses data on past major storms occurring ina hypothetical sequential order consistent with frontal movements and atmospheric

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conditions. The current project design flood was developed in 1954 and consists ofthree storms hitting the Mississippi basin: the 1937 storm that struck the Ohio andlower Mississippi River basins followed three days later by the 1950 storm over thesame area followed by the 1938 storm that struck 90 miles north with rain rotatedby 20 degrees. These three storms maximize the amount of precipitation coverageover the project design flood area (Mississippi River Commission 2008). The projectdesign flood also accounts for water storage at Kentucky Lake, Barkley Lake, andthe New Madrid Floodway. The building of the dam across the Tennessee Riverforming Kentucky Lake in 1944 and across the Cumberland River forming BarkleyLake in 1966 allowed greater water storage in the event of flooding along the LowerMississippi River. In 1965, the front line levee in the New Madrid Floodway wasraised to a height of 62.5 feet on the Cairo gage, the set-back levee was raised to65.5 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 feetwith an average annual high of 46.7 feet. Flood stage at Cairo occurs at 40 feetand the river has been in flood stage at least once in 76 out of the 85 years from1930 to 2014. In addition, the river at Cairo has exceeded 50 feet on the gage in 35years since 1930. The maximum high water mark occurred on May 2, 2011 whenwater measured 61.72 feet on the gage. The project design flood forecasts peak flowsat Cairo, Illinois of 2.3 million cubic feet per second from the Ohio River into theLower Mississippi River. Such a flow would be consistent with a river gage of 66 feetat Cairo. However, use of the New Madrid Floodway with its 550,000 cubic feet persecond 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, constantlyseeking 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 resultingin the most favorable soil.

To move water more quickly through the levee system the Corps of Engineers alsoshortened the river as part of the Project Design Flood. Thirteen cutoffs betweenArkansas City, Arkansas and Natchez, Mississippi shortened the river by about 115miles and with the levees has helped the river carry six to seven times its natural

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flow (Harrison 1950). As early as 1950 part of the unintended consequences of thelevee system gained notice as the shorter river began to undercut its embankmentin an attempt to regain its natural meander. Writing in Land Economics USDAeconomist Robert W. Harrison pointed out the “New” Mississippi Problem as theneed to provide revetment and bank stabilization along 200 to 250 miles of thelower Mississippi River with costs projected to be $250 to $300 million, an amountapproximately equal to $2.5 billion in 2015.

Other problems have arisen as levees raised in one area caused higher water inother areas. In the 1980s the Len Small Levee in southern Illinois was strengthenedputting additional pressure on the Commerce to Birds Point Levee during the floodof 1993. Recently, additional pressure during high water events has been placed onthe Birds Point Levee as levees in southern Illinois and at Hickman, Kentucky havebeen raised and strengthened (Olson and Morton 2013b).

3 The 2011 Flood

A series of papers by Kenneth Olson and Lois Wright Morton (Olson and Morton2012, 2013a, 2013b, 2014a, 2014b, Morton and Olson 2012, 2013) provide detailedgeologic history, maps, soil characteristics, and examine the damage the 2011 Ohioand Mississippi River flooding caused in southern Illinois to the Cache River, Horse-shoe Lake, and adjacent agricultural lands and in southeast Missouri to land in theNew Madrid Floodway.

Record rains during April 2011 in the Ohio River basin states of Illinois, Indi-ana, Ohio, Pennsylvania, Kentucky, and West Virginia and caused flooding alongunprotected areas. Rainfall amounts much above average occurred in the Missis-sippi River basin in Arkansas, Missouri, Iowa, Wisconsin, and Minnesota (NOAANational Overview April 2011). Flooding that began in Minnesota during early Aprilmoved down through the Mississippi River basin. By later April 2011 floodwaterswere putting significant pressure on the Ohio and Mississippi River levees protectingCairo, Illinois. On May 2, 2011 the Major General Michael Walsh of the US ArmyCorps of Engineers ordered the fuse plug levee at Birds Point blown to allow flood-waters to move into the New Madrid Floodway and lessen pressure on the levees atCairo.1 A day later the frontline levees at Big Oak Tree State Park and the lower

1Passive activation of the Floodway had begun earlier on May 2 as water over-topped lowersections of the frontline levee.

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fuse plug levee at New Madrid were blown to allow an outlet for the water. Waterdiversion into the Floodway lowered the Mississippi River at Cairo by 2.7 feet within2 days (Olson and Morton 2012) even though it took three days for the Floodwayto reach capacity (Camillo 2012).

Water flowing into the New Madrid Floodway flooded 133,000 acres of Missourifarmland with damage to 200 buildings including 75 homes (Olson and Morton2013A). Although 20,000 to 30,000 acres of winter wheat were lost, farmers wereable to plant approximately 90,000 acres of soybeans by mid-July, although thelate planting resulted in lower yields. Landowners in New Madrid and Mississippicounties received approximately $16.2 million in payments from the USDA RiskManagement Agency (Olson and Morton 2013a). According to Olson and Morton(2013a) flooding costs are expected to exceed $100 million. The 2011 flood leftsmall 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 aremixed into the topsoil in 2011 or 2012, little significant loss in future crop yield willoccur as long as the Floodway is not flooded again.”

In addition to the damage at the New Madrid Floodway the Len Small leveewas breached just a few hours before the Birds Point Levee was blown on May 2causing flooding to southern Illinois farmland. In an unsuccessful attempt to preventactivation of the New Madrid Floodway the attorney general of Missouri had suedthe Army Corps of Engineers to prevent the blowing of the Birds Point levee. If thelevee had been blown sooner, it might have alleviated pressure on the Len Smalllevee and prevented its breaching. In Kentucky, a relative lack of levees allowedfloodwaters from both the Ohio and Mississippi rivers to move into the naturalfloodplain 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 forthey do not want to see southeast Missouri made the dumping groundto protect Cairo, Illinois, much as we love Cairo. That is all the Jadwinplan does. Indeed, it is doubtful it accomplishes that objective.

Dewey Short, U.S. Representative fromMissouri 1930. op. cit. C. Camillo2012. Divine Providence.

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Representatives fromMissouri criticized Major General Edgar Jadwin’s proposedNew Madrid Floodway as making Missourians bear all of the costs of flood protec-tion. Across the river, citizens in Illinois, Kentucky, and Tennessee decried Missouri’slevee system as raising the waters in their own states. In December of 1928 PresidentCoolidge authorized that landowners in the Floodway receive a one-time indemnityfor flowage rights, although some landowners argued that they were not receivingadequate compensation.

In late April and early May of 2011, before the Birds Point levee was blown, thestate of Missouri filed suit to prevent the Corps from artificially breaching the levee.Missouri politicians including Eighth Congressional District Representative Jo AnnEmerson, state representatives from southeast Missouri, Governor Jay Nixon, andAttorney General Chris Koster all opposed blowing the levee. Across the river inIllinois, the city leaders of Cairo and Governor Pat Quinn were in favor of blowingthe levee. Of course, no vote was taken as the final decision resided with MajorGeneral 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 con-structed until 50% of the landowners agreed to accept compensation for sellingthe government a perpetual flowage easement. By 1936, 77% of the landowners hadagreed. Payments from the government for the easement averaged $16.47 on 106,759acres 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 these20,088 acres were not acquired since backwater flooding would have inundated theselands before artificial breaching. Although some landowners argued that the fuse-plug levee constituted a taking under the Fifth Amendment the Flood Control Actof 1928 stated that “No liability of any kind shall attach to or rest upon the UnitedStates 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 theCairo 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 ofthe river critical of the Corps’ operational plan. On February 4, 1937 the owner andeditor of the Enterprise Courier in Charleston, Missouri penned a sarcastic editorial

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titled “Apparently Cairo Has Been Saved.”

Forget, if you can, for a moment the misery and the suffering, the lossof livestock and household goods, the sacrifice of human life—forgetthe 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 hasbeen saved.

And remember that the Army Engineers have been vindicated.

. . .

Art Walhausen, Sr.

Later that same year, Lucius T. Berthe—former Panama Canal engineer andconsulting engineer for the Little River Drainage District in Southeast Missouri—published a pamphlet criticizing the Jadwin plan for its hubris and lack of impartialexternal 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 beforeconstruction, none can deny, insofar as the Cairo area is concerned, thatit has received perfectly competent review since. The 1937 flood hasgiven 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 floodwaterscould only be considered a taking if the flooding of property was permanent orwould 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 SupremeCourt 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 theplaintiff–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 againstthe plaintiff. Specific mention was made to the fact that flood control programs

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provide benefits as well as costs and that the Flood Control Act of 1928 “expresslyprovided that in purchasing flowage easements, the benefits of the flood controlplan” should be considered in determining the amount of compensation to be paidto 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 upondeliberately turning floodwaters upon the homes and property of peopleeven though the right to do so may have been paid for in advance.

Major General Edward Markham Chief of Engineers, testifying beforethe House Committee on Flood Control

The Jadwin plan for flood control on the Lower Mississippi received harsh crit-icism from the beginning. Some people argued that President Calvin Coolidge hadauthorized only $300 million of flood control constraining what could be accom-plished. In addition, the plan was criticized for making the Floodway too small andfor allowing too little freeboard—only one foot—for the levees at Cairo, and thefrontline and setback levees of the New Madrid Floodway when three feet of free-board was necessary to accommodate high winds which could erode the levees viawave action (Berthe 1937).

The Army Corps of Engineers has been a proponent of closing the 1500 footgap in the New Madrid Floodway ever since the 1954 Flood Control Act authorizedits closing. In 1965, the flowage easements in the Floodway were modified to allowartificial breaching of the fuse plug levee using liquid dynamite. The Corps paid atotal 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 300feet mean sea level (MSL). With the gap open, such lands had been subject tobackwater flooding. In the event of artificial breaching of the levee, those landsbelow 300 feet MSL would be inundated. However, local revenue sources as requiredby the 1917 Flood Control Act were unavailable and the gap remained opened.Finally, the Water Resources Development Act of 1996 allowed federal revenue fromrural enterprise zone programs given to East Prairie, Missouri to be used as paymentfor the non-federal source of the cost of the New Madrid Floodway and St. John’sBasin project.

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In 2000, the Corps issued a Supplemental Environmental Impact Statement onthe Floodway which was revised in 2002 and again in 2006. The EnvironmentalImpact Statement and its revisions came under fire from various government envi-ronmental agencies about the environmental impacts of the Floodway project. Rep-resentatives from the Environmental Protection Agency, the US Fish and WildlifeService, the Missouri Department of Natural Resources, the Missouri Departmentof Conservation, and the Council on Environmental Quality met with the Corps todiscuss the impacts of the project on wetlands. In May 2006 construction resumedon the Floodway project. However, on September 13, 2007 the US District Court forthe 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 footgap, install two pumping stations, modify 23 miles of ditches in the St. John’s BayouBasin, and provide watershed management. The Corps’ projected an annual benefitto 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 USFish and Wildlife case against the Corps’ project to close the 1500 foot gap betweenthe frontline and setback levees: “The proposed project design changes and actionsdo nothing to avoid fish and wildlife resource losses and the minimization measuresare nominal considering the significant scope and magnitude of these losses (Scott2002, p. 2).” Although the Floodway project would create a sump area comprising20,000 acres in the lower Floodway, Scott argued that in seven of the ten years from1993 to 2002, river levels were sufficient to provide 30,000 acres of fish spawninghabitat. In addition, Scott argued that the project would have “profound impactson wetland hydrology” and serve to reduce the value of wetlands remaining in theSt. John’s Bayou and New Madrid Floodway and eliminate or degrade more than18,000 acres of wetland habitat.

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4.4 Environmental Groups and other Stakeholders

The Army Corps of Engineers lists fourteen environmental organizations opposedto the Corps’ plan for the New Madrid Floodway and St. Johns Bayou.2 Theseorganizations argue that the project violates Section 404 of the Clean Water Act,does harm to wildlife by destroying habitat, and reduces the proper functions ofwetlands. In addition, various environmental groups argued that the Corps did notcount the benefits of wetlands which would be destroyed as part of the costs of theproject.

Although environmental groups were unanimous in opposition to the Floodwayproject, Missouri’s US Senator Roy Blunt and US Representative Jason Smith sup-ported the project and argued that residents in the Floodway and surrounding areasshould take precedence over the environmental impacts of the project. The St. John’sBayou Basin Board of Directors also supported the project. However, officials withthe Consolidated Drainage District #1 expressed concern that farmland plantingwould be delayed until late in the planting season due to operation of the sump andthat 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 withwater is the dominant factor determining the nature of soil development and thetypes of plant and animal communities living in the soil and on its surface. Techni-cally, wetlands are lands transitional between terrestrial and aquatic systems wherethe water table is usually at or near the surface or the land is covered by shallowwater (Status and Trends 1983, p. 9).” Marine wetlands include lagoons, bays, coralreefs and the beach out to the continental shelf. Estuarine wetlands are partiallyexposed to the ocean but might also be partially surrounded by land. Estuarinewetlands 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 flood-plain surrounding those rivers. Lacustrine wetlands are depressions or dammed river

2These 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 Conser-vancy, The National Wildlife Federation, Great Rivers Environmental Law Center, Missouri Coali-tion for the Environment, and the Sierra Club.

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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 riverineor lacustrine; for example, swamps, bogs, and prairie potholes.

Wetlands provide numerous functions: ecologic, biologic, hydrologic, and eco-nomic (Heimlich et al. 1983). The ecological functions of wetlands include absorbingsediment from decaying plant matter, serving as a sponge for chemical precipitantsand runoff, and reducing silt in rivers and lakes. Wetlands provide biologic functionsby serving as estuaries for fish and amphibians and providing nesting areas for birdsand habitat for mammals. The hydrologic functions of wetlands include storing wa-ter and reducing peak flows which helps helps reduce downstream flooding. Finally,the economic value of wetlands consist of direct market benefits from activities suchas timber harvesting and indirect benefits to commercial and recreational fishersby serving as fish nurseries, and to hunters who harvest waterfowl, deer, and otherspecies. By reducing silt in rivers and lakes, wetlands can also lower the costs ofobtaining potable water.

Maintaining and preventing the conversion of wetlands to alternative uses suchas residential or agriculture imposes an opportunity cost—economic value in suchuses are foregone. Furthermore, wetlands in the southern U.S. served as a breedingground for mosquitoes and malaria (McGuire and Coelho 2011) which the levee andditch system helped reduce.

According to Heimlich et al. (1983), there were approximately 221–224 millionacres of wetlands when the colonists first set foot in America. Most wetland conver-sion to agricultural and urban use occurred after 1885. Table 1 reports the amountsof wetlands from the 1950s to the 2000s in the United States. Today there are ap-proximately 153 million acres of wetlands, an amount that has remained relativelystable or slightly increased in recent years. The data for riverine wetlands duringthe 1950s to 1970s are missing and the data for lacustrine wetlands do not includethe approximately 56 million acres of coastal wetlands around the Great Lakes from1986 to 2009, so the 1986 to 2009 wetlands’ estimates are more comparable withthemselves than with the data for the 1950s to 1970s.

Today the number of wetland acres has stabilized. Factors contributing to thedecline in wetland conversion include relatively low agricultural prices and reducedagricultural subsidies, private efforts such as those by the Nature Conservancy andDucks Unlimited, and regulations such as the Clean Water Act’s Section 404, state

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Table 1: Freshwater Wetlands in the US, 1950 to 2009, 1000s of acres

Marine and TotalEstuarine Riverine Lacustrine1 Palustrine Wetlands

1950s-1970s 20,459 . 56,563 102,523 179,545Mid-1970s 24,385 5,123 57,640 100,319 187,570

1986 22,974 6,291 14,608 100,799 144,6721998 23,009 6,766 16,611 102,334 148,7202004 24,565 7,518 16,786 104,253 153,1222009 24,562 7,511 16,860 104,275 153,208

Source: U.S. Fish and Wildlife Service, Status and Trends of Wetlands andDeepwater 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. In1992, the largest stock of wetlands was located in the Midwest and Southeast, fol-lowed by the Delta and Gulf regions, Northeast, with the Mountain, Pacific, andCentral Plains regions having the fewest wetlands.

5.1 Wetland Policies

Although the preservation and enhancement of wetlands guides wetland policy to-day, The Swampland Acts of 1849, 1850, and 1860 gave more 64.9 million acresto the states to reclaim wetlands via the construction of levees and ditches. TheArmy Corps of Engineers began work on the Mississippi River flood control systemin the 1870s. Approximately 800,000 acres of wetlands were lost annually before1954. Concern among policy makers and environmentalists over the loss of wetlandsgradually 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 enhancewetlands to increase waterfowl habitat. In 1961, the Wetlands Loan Act allocatedfunds for the government to purchase wildlife refuges and waterfowl protection ar-eas. The National Environmental Policy Act of 1970 gave Congress the power toregulate public construction, including the Corps’ construction of levees and otherflood control projects. The year 1970 also saw a Water Bank established to make an-nual payments to landowners who agreed to maintain wetlands. Section 404 of The

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1974 Clean Water Act regulated the discharge of dredged and fill material into waterresources. In 1977, Executive Order 11990 required federal agencies to minimize thedestruction and degradation of wetlands by avoiding construction or managementpractices that harmed wetlands (Heimlich et al. 1993). From the mid-1950s to themid-1970s the rate of wetlands conversion fell to 458,000 acres annually

The 1985 Food Security Act provided Swampbuster provisions that denied agri-cultural benefits to farmers who drained wetlands. The Wetlands Reserve Program(WRP) was established with the 1990 Farm Bill and began in 1992 with a pilotstudy in nine states which was extended nationwide in 1995. The WRP is a vol-untary program in which the USDA works with landowners to increase or enhanceexisting wetlands to augment wetland habitat for fish and wildlife. The program of-fers landowners the option of receiving payments for a permanent easement, a thirtyyear easement, or a cost-sharing approach with the USDA paying 75% to 100% ofthe cost of wetland restoration. Wetlands’ conversion was reduced to only 59,000acres 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 asTable 1 shows a slight increase in total wetlands from 2004 to 2009. The AgriculturalAct 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 inthe Wetlands Reserve Program. This study examines counties in Arkansas, Illinois,Missouri, Kentucky, and Tennessee. By 2012, counties in these five states averagedmore agreements and more acres enrolled in the WRP than the average for countiesin the rest of the US. Whereas the total number of acres enrolled per county in thefive states averaged 3,459 in 2013, the average per county acreage for the rest of theUS was only 2,388. The 2008 Farm Bill allowed slightly more than 3 million acresto 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 benefitsof wetlands can also spillover to third parties. As such, market prices tend to un-dervalue the true social benefits of wetlands and indirect imputation methods mustbe used to obtain social values. These indirect methods can include surveys to mea-sure willingness to pay, methods that measure the damage averted by wetlands fromflood control or storm surges (Barbier et al. 2013), or shadow pricing methods whichmeasure the opportunity cost of wetlands from an underlying production technol-

18

Table 2: Average Number of Agreements and Acres in the Wetlands Reserve Program

Agreements in Acres inAR, 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 4,3322010 39 28 5,347 5,5722011 27 21 3,489 3,9662012 32 18 4,639 3,2892013 24 14 3,459 2,388Prior Years 325 182 79,123 32,499Total 470 274 99,413 49,085

Source: Natural Resources Conservation Service

ogy (Bostian and Herlihy 2014). Revealed preference methods such as the travelcost approach and weak complementarity approach are sometimes used when thewetlands provide underlying recreation benefits to hunters, fishers, or bird watchersand value is inferred from the increased use of nearby sites or by the increased useof complementary items, such as guns, fishing rods, and binoculars that would notbe consumed were it not for the person’s use of the wetland.

When new sites are proposed, but not yet available, the benefit transfer methodis 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 lacustrinewetlands have $200 of value per acre at an existing site, and if the new site has 500riverine 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 particularindirect valuation method and by the site being studied, the values from numerousstudies are sometimes combined to obtain the marginal values for various wetlandcharacteristic in a process known as meta-analysis.

Woodward and Wui (2001) performed a meta-analysis of 39 wetland valuationstudies 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 studyon wetland quality. Weak econometric studies tended to impute higher values onwetlands than strong econometric studies. They also found that wetlands that of-ferred bird watching or commercial fishing services were more valuable than other

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wetlands’ functions such as bird hunting, flood control, or environmental amenities.Ghermandi et al. (2010) used 418 value estimates derived from 170 different studiesin a meta-analysis of wetlands’ value. They found that human-made and marinewetlands had higher values than other types of wetlands and that water qualityimprovements, population, and increases in per capita income contributed to higherwetlands’ values. Patton et al. (2013) employed a meta-analysis of willingness to payfor the flood control and water quality functions of wetlands in four National WildlifeRefuges. They estimated that a 1% increase in the number of acres of wetlands or a1% increase in population reduced willingness to pay for an additional wetland acreby about 0.5%. In 2010 dollars, the mean annual willingness to pay for an extra 1000acres per 1000 population ranged between $90 to $980 for the water quality functionof wetlands and between $130 and $550 for the flood control function of wetlands.Similarly, Chaikumbung, Doucouliagos, and Scarborough (2015) employed a metaanalysis of 379 studies that valued wetlands in developing countries. They foundthat value decreased as the size of the wetland increased, urban wetland sites weremore valuable than rural sites, marine wetlands were more valuable than other typesof 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 mustbe first be derived. Barbier et al. (2013) examined how wetlands mitigate stormsurge in southeastern Louisiana. Controlling for the ratio of wetlands to water andfor the amount of vegetative matter in wetlands they found that a 0.1 increasein the wetland to water ratio helped reduce flood damages by $592,000-$792,100and a 0.001 increase in bottom friction due to vegetative matter helped reduce flooddamages by $114,000-$258,000. Withey and van Kooten (2014) examined agriculturein Canada using mathematical programming to allocate land between alternativeagricultural uses—wheat, oats, barley, canola—and wetlands to maximize profits.Controlling for climate change effects the authors found that the profit maximizingarea devoted to wetlands declined by 38% if the external benefits of wetlands areaccounted for and by 74% if the external benefits of wetlands are ignored. In effect,climate change can accelerate wetlands’ losses when government policy encouragesbiofuels’ production which gives farmers greater incentive to drain wetlands.

Bostian and Herlihy (2014) used a deterministic method to estimate a direc-tional output distance function and obtain shadow prices for a constructed index ofwetland condition for sites in the Nanticoke River watershed. A one unit increase

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in the index of wetland condition had an average shadow price of $19.83. Usingthis shadow price estimate the authors found that reductions in inefficiency couldenhance wetlands’ condition by approximately $390/acre. Kozak et al. (2010) inves-tigated how fast willingness to pay falls as geographical distance from the wetlandincreases for wetlands along the Des Plaines River and Cache River in Illinois. Whenwillingness to pay becomes zero for people living more than 1 km from wetland, thevalue of the Cache River system is only $28,258. In contrast, if willingness to payremains positive until a person lives more than 1000 km from wetland, the value ofthe Cache River system is $440 million given a log-linear decay function and $2.5billion 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 coun-ties are in the Army Corps of Engineers Water Resource Planning (WRPA) Areas2 and 3. A shaded map of the counties is provided in Figure 2.

Table 3 summarizes data obtained from the National Levee Database. Arkansashas the most leveed acres and miles of levees with 576.3 miles of levees protecting 2.4million acres. Missouri has 182 miles of levees protecting 279,819 acres. The threecounties in Illinois include levees along both the Ohio and Mississippi River withthose levees protecting 82,126 acres. The counties in Tennessee and Kentucky havethe fewest leveed acres.

Table 3: Miles of Levees and Leveed Acreage in the Study Region

Number of Miles of LeveedLevee Segments Levees Acreage

Illinois 14 90.6 82,126Missouri 9 182.3 279,819Arkansas 37 576.3 2,412,327Tennessee 7 29.7 12,074Kentucky 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 theSt. Francis River and Castor River. This area also includes Wappapello Lake whichis an Army Corps of Engineers flood control reservoir formed by a dam across theSt. Francis River. Moving to the east and south are the levees that protect landin Arkansas from floodwaters along the Mississippi River, St. Francis River, WhiteRiver, and Cache River. In Illinois, the Len Small levee and other levees protectfarmland in Alexander county in southern Illinois from flooding along the MississippiRiver and the Ohio River. In addition, Cairo, Illinois is completely surrounded bylevees protecting the city from flooding to the east from the Ohio River and floodingfrom the west from the Mississippi River. Levees in Kentucky protect from floodingalong 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 theLower Mississippi Delta Region (LMDR) under the 1988 Lower Mississippi DeltaDevelopment Act. Former Arkansas Governor and then President Bill Clinton wasthe former state’s chairman of the LMDR Commission which had a mission of foster-ing policies to enhance economic development. Weber and Devaney (1995) comparedrural counties in the LMDR with rural counties in the rest of the US and found thatpeople in LMDR counties had lower per capita income, a higher percent of femaleheaded households, higher rates of poverty, less education, fewer hospital beds, lowerpopulation growth rates, and higher rates of unemployment than people in otherUS rural counties.

Table 4 reports various statistics for counties in the region compared to othercounties residing in Arkansas, Illinois, Kentucky, Missouri, and Tennessee from 2001to 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 ineach 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. Regionalcounties in Arkansas, Illinois, and Kentucky all experienced declines in population.Regional counties in Arkansas, Kentucky, and Tennessee had greater average percapita incomes in 2013 than their non-regional counterparts. Except for the sixcounties in Kentucky, the counties in the region have higher average rates of povertyand a smaller percent of their population aged 25 years and older with a collegedegree.

6.2 Public Lands in the Region

Table 5 reports the total number of acres and the number of different kinds ofpublic land sites in the five states. Thirteen National Wildlife Refuges3 cover 348thousand acres and include the Cache River NWR in Arkansas where the oncethought extinct Ivory-billed woodpecker was seen in 2004, although recent sitingshave not been confirmed. The Cache River NWR had been created in 1986 aftera federal judge in 1972 halted Corps’ levee construction for not complying withthe National Environmental Policy Act of 1970. Three national forests-Shawnee inIllinois, Mark Twain in Missouri, and St. Francis in Arkansas cover 290 thousandacres. The 51 counties also include 28 state parks covering 73 thousand acres, 173conservation and wildlife management areas covering 501 thousand acres and ninesites classified as “other” covering 3,701 acres. In all, 1.2 million acres of land providewildlife habitat and recreational opportunities.

3The 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.

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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 0.030AR-Region 19 0.234 0.222 -0.039IL-Other 99 0.182 0.204 0.011IL-Region 3 0.259 0.252 -0.125KY-Other 114 0.099 0.133 0.047KY-Region 6 0.199 0.210 -0.048MO-Other 102 0.132 0.156 0.045MO-Region 13 0.179 0.142 0.017TN-Other 85 0.101 0.149 0.091TN-Region 10 0.156 0.172 0.042

Per capitaIncome 2013 Poverty College

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%

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Table 5: Acres of Public Lands in 49 Counties

National ConservationNational Wildlife and Wildlife StateForests Refuges Areas Parks Other Total

AR 22,687 260,223 245,762 14,736 1,506 544,915IL 30,533 10,000 17,318 1,591 554 59,996KY 0 3,885 34,266 182 1,601 39,934MO 237,137 21,676 106,036 27,631 40 392,520TN 0 52,617 98,371 29,080 0 180,068Total acres 290,357 348,401 501,753 73,220 3,701 1,217,433# of sites 3 13 173 28 9 226

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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 indi-rectly. To obtain prices for public lands—which we then use to price wetlands in theNew Madrid Floodway—we specify a production technology and then use the di-rectional output distance function as a functional representation of that technology.Using the duality between the revenue function and the directional output distancefunction we obtain shadow prices of the non-market outputs (Färe, Grosskopf, andWeber 2001). The shadow price of the non-market output represents its opportunitycost 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 toproduce y = (y1, . . . , yM ) outputs. The output possibility set gives the set of outputsthat 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 movefrom a set to a functional representation of the technology we use the directionaloutput distance function. This function was developed by Chambers, Chung, andFäre (1996, 1998) who adapted Luenberger’s (1992) consumer benefit function foruse in production theory. Let g = (g1, . . . , gM ) represent a directional vector thatscales 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 vectorgives the maximum addition to each output that can be feasibly produced giveninputs 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. Frontieroutputs represented by point B correspond to (y1 + βg1, y2 + βg2).

27

y =Public Lands

y =Real Incomeg

g

g

A

B

1

1

220

P(x)

y

y

y +βg

y +βg2 2

1

1

1

2

Figure 4: Directional Output Distance Function

The value of the directional vector chosen determines how outputs are scaled tothe 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 directionalvector 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 directionalvector 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 thereciprocal of the Shephard output distance function minus one equals the directionaloutput distance function:

→Do(x, y; g) = 1

Do(x,y) − 1, where Do(x, y) is the Shephardoutput distance function.4

The directional output distance function completely characterizes the productiontechnology in that

y ∈ P (x)⇐⇒→Do(x, y; g) ≥ 0. (3)

The properties of the directional output distance function are inherited from the4The Shephard output distance function is defined as Do(x, y) = min{θ : y

θ∈ P (x)}.

28

production technology. For y ∈ P (x) these properties are

(i.)→Do(x, y; g) ≥ 0,

(ii.) y′ ≤ y,→Do(x, y′; g) ≥

→Do(x, y; g),

(iii.) x′ ≥ x,→Do(x′, 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 mono-tonicity condition on outputs and inputs. If a firm produces more outputs given in-puts its inefficiency will not increase and if a firm uses more inputs to produce givenoutputs its inefficiency will not decrease. Property 4(iv.) is the translation propertywhich is an additive representation of the technology similar to the homogeneityproperty of Shephard output distance functions.

To derive shadow prices for the non-market outputs we exploit the dualitybetween the directional output distance function and the revenue function. Letp = (p1, . . . , pM ) represent a vector of output prices. The revenue function is definedas

R(x, p) = maxy{py : y ∈ P (x)}

R(x, p) = maxy{py :

→Do(x, y; g) ≥ 0}. (5)

The revenue function gives the maximum revenue for feasible output vectors andsince y +

→Do(x, y; g)g is a feasible output vector we can write

R(x, p) ≥ py + p→Do(x, y; g)g. (6)

The inequality in (6) derives from the fact that once outputs are scaled to thefrontier and all technical inefficiency is eliminated, revenues associated with thefrontier outputs (py + p

→Do(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)− pypg

. (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 berecovered as

pm = pj∂→Do(x, y; g)/∂ym

∂→Do(x, y; g)/∂yj

. (10)

Figure 5 illustrates the shadow pricing method. The directional output distancefunction projects producer A’s outputs to point B on the frontier. The slope ofthe frontier at point B, dy1/dy2 is the marginal rate of transformation between thetwo 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 ∂→Do(x,y;g)/∂ym

∂→Do(x,y;g)/∂yj

represents the marginal rate of transformation Thus, if the jth price is known andthe marginal rate of transformation can be estimated, the shadow price of outputm can be obtained.

It is important to note that the choice of directional vector will affect themarginal rate of transformation for inefficient producers. In Figure 5, if g1 > 0and g2 = 0 producer A’s outputs would be projected to point C resulting in a lowershadow price for the public good. Alternatively, if g1 = 0 and g2 > 0 producer A’soutputs would be projected to point D resulting in a higher shadow price for thepublic good.

7.2 Functional Form

To operationalize the shadow pricing formula given by (10) we need to choose afunctional form for the directional output distance function. The translog form hasbeen used extensively to estimate Shephard input and output distance functions.However, while the parameters of the translog function can be imposed to satisfy ahomogeneity property, the directional output distance function needs to satisfy thetranslation property. Chambers (1998) suggests a quadratic form for the directionaloutput distance function. The quadratic serves as a second-order approximation to

30

y =Public Lands

y =Real Incomeg

g

g

A

B

1

1

220

P(x) dy /dy = -p /p

C

D

1 12 2

Figure 5: Shadow Pricing

the true, but unknown function and the parameters can be restricted to satisfy thetranslation property and monotonicity properties given by (4).

The quadratic directional output distance function is given as

→Do(x, y; g) =α0 +

M∑m=1

αmym +N∑

n=1βnxn + 1

2

M∑m=1

M∑m′=1

αmm′ymym′

+12

N∑n=1

N∑n′=1

βnn′xnxn′ +M∑

m=1

N∑n=1

δmnymxn +T∑

t=2γtDTt. (11)

Symmetry restrictions for the cross-output and cross-input effects are imposedso that αmm′ = αm′m and βnn′ = βn′n. The translation property requires that∑M

m=1 αmgm = −1,∑M

m′=1 αmm′gm = 0,m = 1, . . . ,M , and∑M

m=1 δmngm = 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 deterministicdirectional output distance function using linear programming. This method mini-mizes the sum of the distances of the observed inputs and outputs of each producerto 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, αmm′ , βn, βnn′ , δmn and

31

γt to

T∑t=1

K∑k=1

→Do(xt

k, ytk; g)− 0 subject to

(i.)→Do(xt

k, ytk; g) ≥ 0, k = 1, . . . ,K, t = 1, . . . , T,

(ii.) ∂→Do(xt

k, ytk; g)/∂yt

km ≤ 0,m = 1, . . . ,M, k = 1, . . . ,K, t = 1, . . . , T,

(iii.) ∂→Do(xt

k, ytk; g)/∂xt

kn ≥ 0, n = 1, . . . , N, k = 1, . . . ,K, t = 1, . . . , T,

(iv.) αmm′ = αm′m, βnn′ = βn′n,

(v.)M∑

m=1αmgm = −1,

M∑m′=1

αmm′gm = 0,m = 1, . . . ,M, and

M∑m=1

δmngm = 0, n = 1, . . . , N. (12)

The restrictions given by (12i) require that the observed output and inputs befeasible for every observation in each year. The restrictions in (12ii and iii) imposethe monotonicity conditions for outputs and inputs. Symmetry conditions for thecross-output and cross-input effects are imposed by (12iv). Finally, the restrictionsassociated with the translation property are imposed by (12v).

Although different directional vectors can be chosen the directional vectors needto be common for all observations to avoid having to parameterize the directionalvectors in the quadratic form.

7.3 Data and Estimates

To implement the shadow pricing model we employ pooled data on 51 countieslocated in five states during the period 2009-2012. We assume that public landswould be employed in agriculture in their next best alternative so each county’sagricultural output is used as the private good. Agricultural output (y1) equals theinflation adjusted (base year=1984) value of crop revenues derived from corn, soy-beans, wheat, cotton, and rice. We sum acres of National Forest land and NationalWildlife Refuges in each county to get federal land acres (y2) and the acres that arestate 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, fer-tilizer, 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 byyear. The number of square in the county, and the number of acres of federal landand state land are constant for the four years.

Table 6: Descriptive Statistics for County Outputs and Inputs1

Mean Std. Dev Minimum Maximum

x1=farm labor 648 383 102 2304x2=fertilizer, $1000s 11,391 8,499 244 35,335x3=petroleum and 22,857 13,848 2,583 60,961

other expenses, $1000sx4=square miles 561 213 163 1034y1=crop revenues, $1000s 903,584 2,520,011 67,865 17,564,812y2=federal lands (acres) 12,525 24,448 0 96,454y3=state lands (acres) 11,347 10,560 0 53,274

1. Fertilizer, petroleum and other expenses, and crop revenues are in constant 1984dollars.

Table 6 provides descriptive statistics. The average number of square miles acresin a county is 561 (358,940 acres) with less than 1% of that area (23,872 acres) de-voted to public lands comprising 12,525 federal acres in the form of National WildlifeRefuges or National Forests and 11,347 acres of state lands in the form of wildlifemanagement areas, state parks, or other state lands. The average county employs648 farm workers, uses $11.3 million in fertilizer, and $22.8 million in petroleum andother farm expenditures to generate crop revenues of $903.5 million.

To estimate (12) a directional vector must be chosen. As shown previously thechoice of directional vector will determine the projection of observed outputs to theproduction frontier and the slope of the frontier at the projected point. We chooseseven 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 thedirectional vectors influences the estimates through the restrictions implied by thetranslation property in (12v). We report the parameter estimates for the quadraticdirectional distance function given g = (1, 1, 1) in Table 7.5

We divided all outputs and inputs by 1000 before estimating. We note that the5Parameter estimates for the other directional vectors are available upon request.

33

Table 7: Parameter Estimates for the Quadratic Directional Output Distance Func-tion for g = (1, 1, 1)

Parameter Variable Estimate Parameter Variable Estiate

α0 constant 3.395 δ11 y1x1 -0.074α1 y1 -0.690 δ12 y1x2 -0.040α2 y2 -0.159 δ13 y1x3 0.002α3 y3 -0.151 δ14 y1x4 0.340β1 x1 6.089 δ21 y2x1 0.180β2 x2 1.182 δ22 y2x2 0.022β3 x3 0.394 δ23 y2x3 -0.001β4 x4 -2.180 δ24 y2x4 -0.346α11 y2

1 0.011 δ31 y3x1 -0.106α12 y1y2 -0.005 δ32 y3x2 0.018α13 y1y3 -0.006 δ33 y3x3 -0.001α22 y2

2 0.002 δ34 y3x4 0.006α23 y2y3 0.003 γ2010 Year=2010 0.725α33 y2

3 0.003 γ2011 Year=2011 -0.341β11 x2

1 -1.631 γ2012 Year=2012 0.438β12 x1x2 0.436β13 x1x3 -0.059β14 x1x4 -1.528β22 x2

2 0.101β23 x2x3 -0.006β24 x2x4 0.257β33 x2

3 -0.004β34 x3x4 -0.114β44 x2

4 6.652

estimates of the time effects, γ2010 and γ2012, are positive indicating that the frontiershifted to the Northeast in 2010 and 2012 relative to 2009. Such a shift might be dueto technological progress or better growing conditions in 2010 and 2012 relative to2009. However, γ2011 is negative indicating an inward shift in the production frontierin 2011. Such an inward shift is consistent with the high water during the spring of2011 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 causedsome farmers to plant soybeans rather than corn resulting in lost revenues.

Table 8 reports the estimates of the directional output distance function and thenumber of frontier counties. for various directional vectors. For the directional vectorg = (1, 1, 1), inefficiency averages 6.08 for the pooled sample implying that if theaverage county were to produce on the best-practice production frontier state landscould increase by 6080 acres, federal lands could increase by 6080 acres, and countyfarm income could increase by 6.08 million. The number of frontier counties rangedfrom two in 2010 to five in 2011, with a total of 14 counties defining the productionfrontier. Production among the 51 counties exhibited the least inefficiency in 2011and the most inefficiency in 2012.

The estimates of inefficiency change for other choices of directional vector. Ineffi-ciency is the least for the four directional vectors that expand real farm revenues andeither increase or hold constant federal land acres and state land acres. In addition tog = (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 thedirectional vectors that hold crop revenues constant and either expand or hold con-stant 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, statelands could be expanded by 24.85 thousand acres under such a scenario.

The shadow price estimates for federal (∧p2) and state lands (∧p3) are reportedin Table 9 for various directional vectors. These shadow price estimates are derivedfrom (10) using the parameter estimates for the quadratic directional output distancefunction. Assuming that the real price of crop revenues (y1) is the known marketprice with p1 = 1, the shadow prices for federal lands (∧p2) and state lands (∧p3) areestimated as

pm = p1 ×α1 +

∑Mm′=1 α1m′ym′ +

∑Nn=1 δ1nxn

αm +∑M

m′=1 αmm′ym′ +∑N

n=1 δmnxn

,m = 2, 3. (13)

All shadow price estimates are in 1984 dollars, but can be converted to 2015dollars by multiplying by the 2015 mid-year CPI of 2.37088. The directional vectorg = (1, 1, 1) generated a shadow price of federal lands equal to $445.8 and a shadowprice for state lands equal to $604.2. Now, consider the three directional vectorswhere federal lands are expanded, but either crop revenues, state lands, or both are

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Table 8: Estimates of Inefficiency

2009 2010 2011 2012 All years

g = (1, 1, 1)→Do(x, y; g) 5.93 6.03 5.11 7.25 6.08# on frontier 3 2 5 4 14







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 priceof federal lands increases to $3,573. When state lands are expanded, but either croprevenues, federal lands, or both are held constant the directional vectors correspondto g = (1, 0, 1), g = (0, 1, 1), and g = (0, 0, 1). In these cases the shadow price

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Table 9: Mean Shadow Price Estimates for Public Lands1

2009 2010 2011 2012 All years

g = (1, 1, 1)Federal Lands=∧p2 411.0 484.7 490.4 397.2 445.8State Lands=∧p3 553.7 650.6 664.2 548.4 604.2





g = (0, 1, 0)Federal Lands=∧p2 1944.8 3680.6 4585.4 4047.3 3572.5State Lands=∧p3 0 0 0 0 0


1. Shadow prices are in 1984 dollars.

of state lands increases relative to the g = (1, 1, 1) directional vector. State landsachieve their highest shadow price, $1,128, for the directional vector g = (0, 1, 1).

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7.4 Using the Model to Value Wetlands in the New Madrid Flood-way and St. John’s Bayou

Table 10 reports details on the outputs and inputs for Mississippi and New Madridcounties, home to the St. John’s Bayou and New Madrid Floodway. Mississippicounty has 6,446 acres of state lands and zero federal lands. New Madrid county has6,322 acres of state lands and zero federal lands. New Madrid county has greaterreal crop revenues partly attributable to a larger land area—678 square miles inNew Madrid county versus 413 square miles in Missississippi county. Crop revenuesincreased from 2009 to 2012, but the gap between the two counties was greatest in2011 when New Madrid county produced 82% more real crop crop revenues thanMississippi county. However, despite the larger farm output, New Madrid county wasless efficient than Mississippi county in each of the four years. In fact, Mississippicounty was one of the frontier counties in 2012 and exhibited lower inefficiency onaverage than the other counties in the study (see Table 8). In contrast, New Madridcounty exhibited greater inefficiency in each of the four years than other counties inthe study.

Now, consider the data for 2009 for the two counties. If Mississippi county hadrealized greater inefficiency an extra $2.92 million in crop revenues, an extra 2920acres of federal lands, and an extra 2920 acres of state lands would have beenproduced resulting in frontier quantities of y∗ = (58513, 2920, 9366).6 For thosequantities, the shadow price of federal lands is $508 and the shadow price of statelands in $634. In New Madrid county, greater efficiency could have allowed real croprevenues to increase by $12.42 million, federal lands to increase by 12,420 acres, andstate lands to increase by 12,420 acres giving y∗ = (95034, 12420, 18742). At thosequantities, the shadow price of an acre of federal land is $463 and the shadow priceof an extra acre of state lands is $626. The shadow prices vary by year because eachcounty employs different amounts of farm labor, fertilizer, and petroleum and otherexpenses to produce farm outputs measured by real crop revenues. The shadowprices 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 (1000acres), Seven Island Conservation Area (1381 acres), and Ten Mile Pond Conser-

6Frontier output is y∗ = (y + β∗g), where β∗ equals the estimate of the directional outputdistance function,

→Do(x, y; g).

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Table 10: Outputs, Inefficiency and Shadow Prices of Public Lands in Mississippiand New Madrid Counties: g = (1, 1, 1)

Real Farm Shadow price1 of

Income Federal StateYear (1000s)

→Do(x, y; g) Lands=∧p2 Lands=∧p3

Mississippi County2009 55,593 2.92 508 6342010 57,988 1.31 667 8142011 59,531 3.45 403 5462012 73,434 0 576 806

New Madrid County2009 82,614 12.42 463 6262010 96,982 6.90 1117 14402011 108,531 5.19 731 10632012 105,776 14.42 178 417

1. Shadow prices are in 1984 dollars.

vation Area (3755 acres) all important wetland areas. Two of these areas (Big OakTree SP and Ten Mile Pond CA) lie within the Floodway and Seven Island Con-servation Area lies between the frontline levee and the Mississippi River. In NewMadrid county Donaldson Point Conservation Area (5785 acres) also lies betweenthe 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 30,622acres of wetlands in the St. John’s Bayou basin and 36,883 acres of wetlands in theNew Madrid Floodway (Ledwin and Roberts 2000). Mississippi and New Madridcounties (of which the Bayou and Floodway are part) also have more diverse habitatsand wildlife and fish species than other counties in the Missouri bootheel. Under theauthorized Corps’ plan wetlands would decline by almost 24,000 acres to only 6,710acres in the St. John’s Bayou. Under the Corps’ plan wetlands in the New MadridFloodway would decline by approximately 7,000 acres to 29,770 acres. Given only6,136 acres of public lands in Mississippi county and only 6,322 acres of publiclands 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 forstate lands in 2010, the 32,138 acres of wetlands currently located on private propertyare generating approximately $26 million in value in 1984 dollars which convertedto 2015 dollars equals $61.6 million.7 A lower bound estimate using the 2011 shadowprice of $403 for federal lands in Mississippi county yields approximately $13 millionin value in 1984 dollars or $31 million in 2015 dollars.

Under the authorized Corps’ plan the 31,000 acre decline in wetlands shouldbe considered an environmental cost which should be added to the proposed $165million price tag for closing the 1500 foot gap in the levees encompassing the Flood-way. These costs can be reasonably approximated using the range of shadow pricesreported in Table 10. Using the high shadow price of $814 in Mississippi county thelost value of wetlands is 814×31000 = $25.23 million in 1984 dollars. Using the highshadow price of $1440 for New Madrid county the lost value of wetlands would be1440 × 31000 = $44.64 million. Lower bound estimates can be similarly obtained.Converted to 2015 dollars the lost value of wetlands ranges between $60 to $106million if the Corps’ plan is implemented.

8 Conclusions

The 1928 Flood Control Act increased the oversight of the Army Corps of Engineerswith a charge of reducing the damage from flooding through the Lower MississippiRiver. Under the vision and oversight of Major General Edgar Jadwin the Corps builtlevees and floodways and shortened and straightened the river to move water morequickly through the basin. The New Madrid Floodway was an important part of theplan. Covering 133,000 acres the Floodway consists of a frontline and set-back leveethat begin at Birds Point. Both levees then run in a south/southwesterly directionbefore drawing close again at New Madrid. A 1500 foot gap in the two levees nearNew Madrid allows water from Mississippi River flooding to back into the lowerpart of the Floodway helping to maintain important wetlands but simultaneouslyreducing potential farm outputs in the lower lying areas.

Although the Floodway gap was once authorized to be closed, a lack of localrevenues and then a lawsuit brought by environmental groups has kept it open.

7Private 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 in1984.

40

The lower 10-15% of the Floodway lies in New Madrid county. A directional outputdistance function was estimated for 51 counties in the five state region surroundingthe Floodway and used to estimate shadow prices of federal land acres in the formof National Wildlife Refuges and National Forests, and state land acres in the formof wildlife management/conservation areas, state parks and other state land acres.Many of these public lands consist of wetlands and in Mississippi and New Madridcounties almost all of the public lands are wetlands.

The shadow price of public lands was used as an estimate of the value of wet-lands 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 inMississippi county. The Corps’ plan to close the 1500 foot gap between the frontlineand setback levees has been forecast to cost $165 million. Farmers in the low lyingareas of the Floodway and St. John’s Bayou including residents of East Prairie, Mis-souri 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 sideof the ledger. These external costs correspond to the 31,000 acres of wetlands thatwould be lost in the New Madrid Floodway and St. John’s Bayou valued at theirshadow prices.

Whether or not the 1500 foot gap in the levee should be closed has attracteddebate from numerous parties: The Army Corps of Engineers, the US Fish andWildlife Service, property owners within the Floodway and in St. John’s Bayou,politicians from both sides of the Mississippi River, independent drainage districtsand engineers, and environmentalists. Perhaps an alternative policy where the Fed-eral government would pay private landowners for their low lying acres and establisha new National Wildlife Refuge or several new wildlife management/conservationareas instead of spending even more money on closing the Floodway gap would bea step in the right direction to satisfy the disparate interests.

41

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