The Beijer Institute of Ecological Economics

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1 The Beier Intitute o cological conomic DISSSION PPR Beier Dicuion Paer Serie No. 7 Invetment in Land e or Pollution batement nder ncertainty Sandra Lerda The Beier Intitute o cological conomic The Royal Swedih cademy o Science Box S Stockholm Sweden Phone: Fax: mail: beier@beier.kva.e

2 Invetment in Land e or Pollution batement nder ncertainty Sandra Lerda * Beier International Intitute o cological conomic and Deartment o conomic SL May btract Thi aer dicue the iue o how uncertainty aect the deciion o a landowner to convert agriculturally roductive land into wetland. Three iue are dealt with. Firt how doe uncertainty aect the rik avere armer deciion about contructing wetland. Second what i the eect o dierent inormation tructure on the level o land converion carried out. nd inally what i the role layed by irreveribility in the deciion making roce. Land converion might reult rom a rik avere armer trying to diveriy her invetment otion. The oibility o receiving more inormation in the uture lead to either a delay in the armer deciion to retore wetland or to the requirement o a higher ubidy or the deciion to be made even when the deciion i not irreverible. The etablihment o a ublic olicy to encourage wetland contruction hould take thee aect into conideration. The ubidy hould be deigned a an inurance mechanim and the olicy maker hould conider the eect o the inormation availability on the agent behavior. Introduction One o the meaure imlemented by the Swedih Government to reduce the exceive nutrient inut that contribute to the eutrohication o the Baltic Sea i the etablihment and retoration o wetland. in other countrie the Swedih Government ha etablihed ubidie to encourage armer to convert agricultural roductive land into wetland. Park 995 how ometime thee incentive do not achieve exected reult becaue armer eem to require higher ayment in * Thi reearch wa uorted by the MISTR unded MR and SOZOM reearch roect. - mail: andra@beier.kva.e. modiied verion o thi aer will be reented a art o the requirement to obtain the degree o Ph. Lic. rom the Deartment o conomic Swedih niverity o gricultural Science. The uggetion and comment by Mauricio Prado nne-sohie réin Tore Söderqvit and Henrik Scharin to a reviou verion o thi aer are grateully acknowledged. mong other environmental ervice wetland area have roved to contribute to the removal o nutrient and ollutant rom the water both through chemical rocee in the ediment and lant growth. ccording to the Swedih nvironmental Protection gency at leat 000 hectare o wetland and ond will be etablihed or retored on agricultural land by 00 nvironmental Quality Obective: Thriving etland.

3 order to take the invetment deciion to change land ue. ccording to Bytröm 000 in the Swedih cae interet in changing land ue varie acro region thu a ubidy etablihed or wetland contruction doe not have the ame eect in outhern Sweden a in other region o the country. The Swedih incentive mechanim ha been changed recently and armer have hown interet in retoring wetland at leat in the Stockholm area. Bytröm 000 how that the retoration o wetland i worthwhile and the Swedih Government ha exlicit olicie to urther increae the area o retored wetland. But uncertainty i a ervaive henomenon that can aect both the armer deciion-making in relation to contructing wetland and the etablihment o an incentive olicy to retore reviouly drained wetland. Thi aer dicue how uncertainty inluence a armer deciion-making roce and how dierent inormation tructure might aect the deciion to change land ue rom agricultural or other ue into wetland. onidering the interet in an increae in wetland area what would be the neceary ubidy to give incentive or a armer to convert roductive land into wetland in an uncertain world? hat i the role o rik and rik averion on the art o the agent and how doe it aect the deciion to invet in wetland? How doe the armer deciion vary under dierent inormation tructure? Thi aer how that in a tatic world the deciion to invet in wetland can be the reult o the rik avere armer trying to diveriy her invetment in order to reduce uncertainty. In a more dynamic ramework the otential irreveribility o the deciion the oibility o receiving new inormation and uncertainty about rice lay a role in delaying the ocially deirable land ue change and in making it more exenive rom the oint o view o the ocial lanner. ven when the deciion to change land ue i not irreverible a long a the reveribility involve ome cot the armer will rerain rom converting agricultural land into wetland. Thu the deign o a ubidy would have to conider thi reult. Peronal communication with Henrik Scharin rom The Beier Intitute.

4 3 The aer i organized a ollow. The irt ection ha an introductory character and dicue both the imortance o wetland a ecoytem and the Swedih olicie related to wetland contruction and retoration. The econd art introduce the iue o uncertainty and it imortance when dicuing land converion deciion-making. imle tatic model introduce irt the agent rik averion and a imle two-timeeriod tree model reent the iue o how inormation availability aect the deciion-making when the deciion i irreverible. hen no new inormation i orthcoming it i hown that the armer make deciion on the bai o exected ay-o. But when irreveribility and the oibility o getting new inormation are conidered the exected ay-o change and a deciion that would be rational in one cae may be comletely wrong in another. The third art i the core o the aer. It reent a rooition about the imact o dierent inormation availability on the armer deciion to convert agricultural land into wetland. The concluding ection dicue imlication or olicy making. I. hy wetland? etland are imortant a nutrient ink and alo becaue o other ecoytem ervice they rovide. Thi i a motivation or ublic olicie encouraging wetland contruction and retoration. Thi ection reent a brie decrition o wetland a ecoytem and o the Swedih olicie deigned to rotect and increae wetland. I.. etland ecoytem 3 etland are imortant ecoytem correonding to 6% o the land urace on arth. They can be ound in all continent excet ntarctica and even though they can be a divere a the tundra in cool region and the mangrove oret in troical area they conit o three baic eature: a the reence o hallow water or 3 Mot o thi ection i baed on Mitch and Goelink 993. Thank to Åa Janon and Lia Deutch or helul comment.

5 4 aturated oil; b unique oil condition not ound elewhere; c the reence o vegetation adated to wet condition and the abence o looding-intolerant vegetation. In Sweden they conit o 0% o the country total land area totalizing ome 93 thouand quare kilometer. ven though thi i a igniicant area correonding to three time the area o a country like Belgium Swedih wetland have been detroyed by dierent human activitie throughout the lat ew decade. ccording to the Swedih nvironmental Protection gency over 5000 km o wetland have been drained through oretry. 4 The imortance o wetland ecoytem relate to the good and ervice they rovide. large number o animal bird ih and hellih deend on wetland during the whole or art o their lie cycle. Some wetland alo rovide timber and iber. In term o ecoytem ervice wetland rovide water torage and iltration imroving water quality and mitigating the eect o lood. The act that wetland are oten tranition zone between uland and deewater aquatic ytem make them unction a organic exorter or inorganic nutrient ink. etland have imortant role to lay in the global cycle o nitrogen ulur methane and carbon dioxide. It i exactly thi lat eature what make them o intereting or our reearch work. Since they work a ilter between the land and the ea wetland have been identiied a a cot eective way to abate ollution rom agricultural and other human activitie 5. In act according to Mitch and Goelink mineral cycle can have wide variation rom wetland to wetland deending on how oen the ytem i or how at the urace water i relaced. But even in a ytem a oen a a alt marh that i looded daily about 80 ercent o the nitrogen ued by vegetation during a year i recycled rom mineralized organic material Swedih P homeage. 5 See or examle Gren 995 and Gren Turner and ul 000 and Ribaudo et al Mitch and Goelink citing Delaune and Patrick 979.

6 5 In thi ection o the aer we attemt to reent ome baic notion o ecology o wetland and to dicu their beneit and cot and their role a inal nutrient dioal technology. Hydrology o wetland One o the mot imortant actor characterizing a wetland i the water inlow and outlow the o-called water budget. Inlow include reciitation looding river groundwater urace low and tide in cae o coatal wetland. Hydrologic condition in a wetland include alo the urace contour o the landcae and the geological condition and they aect the nutrient availability the ecie comoition the abundance o biota in other word the whole tructure and unctioning o the ytem. Biotic actor in turn like vegetation or animal can alo aect the hydrology o a wetland. very wetland i characterized by a hydroeriod a eaonal attern o the water level like a hydrologic ignature o each wetland tye. 7 wetland can be tidal or non-tidal and be looded ermanently or not throughout the hour o the day tide or the month and year. Thi variable amount o water in a wetland deend on the reciitation the urace and groundwater inlow and outlow the evaotraniration and the tide. Biogeochemical cycle Through water inlow and atmoheric deoition wetland receive nutrient whoe tranormation and availability to the vegetation are alo aected by the hydroeriod o the wetland. Tranormation o nitrogen hohoru ulur and other mineral take lace in wetland ecoytem. Nitrogen rom the atmohere can be ixed by ome lant and microorganim and converted into organic orm. Through denitriication a roce that occur in wetland the exce o nitrogen in the water inlow can be tranormed again into atmoheric nitrogen and that i an imortant contribution rom wetland to the nitrogen cycle. Nitrogen i alo retained 7 Mitch and Goelink

7 6 in wetland by edimentation and through it abortion by the vegetation. In the cae o hohoru it retention in litter and eat or in the ediment i conidered one o the mot imortant attribute o natural and contructed wetland. 8 ven though wetland have been identiied a nitrogen and hohoru ink not all wetland are nutrient ink and the attern o cature torage and releae o nutrient vary acro wetland eaon and year. Some uncertainty remain about the actual amount o nutrient that a wetland i able to retain. 9 In act a wetland can be a ource a ink or a tranormer o chemical deending not only on it tye and hydrologic condition but alo on the length o time and the amount o chemical loading the ytem ha been ubected to. Permanent heavy load o chemical can be unutainable ince a wetland can become aturated. Thi i more likely to haen in the cae o hohoru then in the cae o nitrogen. ointed out reviouly under certain condition nitrogen can be tranormed into atmoheric N through denitriication. But in what concern the hohoru either it i accumulated in a wetland and retained by the ediment and the oil or there may be leakage in cae o heavy chronic load. 0 Biodiverity Mitch and Goelink 993 and Folke and Janon 000 remind u wetland are multiunctional in the ene that they rovide everal environmental good and ervice at the ame time. Beide the already mentioned nutrient abatement unction and the buering o water wetland uort biological diverity. t the ame time the dierent lant and animal grou ound in a wetland ecoytem hae the unction and tructure o the ytem. From mammal to retile dierent kind o bird ih and hellih a wide range o animal deend on wetland ecoytem. The lant diverity i alo imortant with many wetland roviding timber and other vegetation harvet. 8 Mitch and Goelink See or examle rheimer and ittgren Leonardon 994.

8 7 One o the roblem related to wetland i moquitoe. Becaue o the hydrological condition wetland are otential moquito breeding ite articularly in the ummer eaon ince during the cool eaon moquito roduction diminihe. ven though they are alo art o the ood chain and imortant or the biodiverity reervation in troical area moquitoe are aociated with dieae tranmiion to human and other nuiance. Retored or reated etland There are dierent reaon or the retoration or creation o wetland rom the enhancement o wildlie to water treatment or lood control. lo the detruction o wetland throughout the year ha timulated the etablihment o ublic olicie to mitigate the lo o thee ecoytem through the retoration o reviouly detroyed wetland or imly the creation o new one. ccording to Mitch and Goelink the creation and retoration o wetland have been ucceul in many cae but there are alo examle o ailure mainly becaue o hydrologic actor. The uncertainty related to the unctioning o a wetland eem to increae in the cae o created one. ontruction and maintenance cot deend on each cae and are alo diicult to determine. In ome cae wetland mitigation olicie i.e. olicie to oter the creation o wetland a comenation or their detruction elewhere ail becaue it i relatively eay to retore or contruct wetland o low unctional quality. The location actor i an imortant one becaue a wetland retored in an area may not rovide the ame ervice o another wetland in another area. I.. etland in environmental olicy making in Sweden Roeveare exree the Swedih aroach to olicy-making in general could be characterized a a roce o tudy conultation and collective deciion-making See or examle the no net lo olicy in the S Heimlich 994. Bocktael and Irwin 000.

9 8 ollowed by decentralized imlementation. 3 In what concern environmental olicy making the main governmental agencie and intitution involved are the ollowing: the Parliament the Minitry o the nvironment coordination reonibility 3 agencie or the imlementation o olicie including the nvironmental Protection gency the Minitry o Finance the Minitry o griculture the Minitry o Indutry mloyment and ommunication the Swedih nvironmental dviory ouncil and Local uthoritie Local Invetment Programme. The Parliament i the one reonible or etablihing the environmental goal or the Swedih ociety. urrently 5 environmental quality obective guide the governmental action 4 two o which named Zero utrohication and Thriving etland are o our direct concern in thi aer. Incentive to wetland creation in Sweden Since 989 there ha exited in Sweden ome olicy mechanim to give incentive to armer to create wetland 5. From 989 until 99 the main olicy intrument wa the NYL nya inlag i landcaet new eature in the landcae a voluntary mechanim giving a lum um comenation or armer who created an aroved wetland. ter that the Omtällning 90 onverion 90 wa introduced with a bigger budget to give incentive to armer to reduce their arable land area either through wetland creation or converion o agricultural land into oretry or energy cro area. Since 995 when Sweden oined the uroean nion and adoted the ommon gricultural Policy P a new olicy ha been imlemented in accordance with rincile. The new environmental ubidy then created milötöd conited o a contract with 0 year o duration. During that eriod the armer who created a wetland wa entitled to receive SK 4800 er hectare er year during the irt 5 3 Roeveare Swedih nvironmental Protection gency htt:// 5 For an overview o Swedih olicie or wetland creation ee Lindahl 998a and 998b whoe article are ource or thi ection.

10 9 year o the contract and then SK 500 or the ret o the 0year eriod. In addition to that amount the armer could aly or another SK 000 or maintenance. More recently 000 ome new change have been made to the ubidy olicy. The new ubidy varie according to the region where the wetland i to be contructed. From 50 to 90% o the contruction cot i covered; there i a ayment o SK 800 er hectare or maintenance and management cot; and the armer receive a er hectare annual comenation or lo in roduction. 6 But how doe the ubidy aect the armer deciion-making? The next ection review a theoretical ramework or the armer deciion-making about converting agricultural land into wetland and dicue the role o uncertainty and rik averion. II. ncertainty rik averion and inormation mentioned beore thi aer dicue two imortant aect o the uncertainty roblem in deciion-making. The irt i rik averion and the econd i inormation availability or the deciion. For the dicuion o thee aect we ue two dierent model. Section II. reent a dicuion o the rik averion aect. Section II.3 reent a dicuion o the inormation roblem when the deciion i irreverible and ection III dicue urther the inormation availability aect when the deciion to be taken i not irreverible but when it reveribility imoe a cot. II.. ncertainty 7 ven though an imortant art o economic theory ha develoed a i individual made deciion in a world o certainty in a variety o real-world ituation 6 ccording to Henrik Scharin eronal communication in the Mälar region the comenation amount to SK It i quite common to make a ditinction between rik when a robability baed on at exerience can be attached to an event and uncertainty where the robability o a certain event in unknown. Thi ditinction i not made here and both term are ued.

11 0 uncertainty about the outcome o the deciion taken by economic agent i the only ure thing. In the context o the armer deciion about converting agricultural land into wetland dierent aect o the uncertainty roblem can be dicued. Both inut rice and agricultural rice conit in a ource o uncertainty aecting the armer deciion. The ame i valid or the ubidie and how the incentive olicy will evolve in time. ven when the ubidy i certain uture inlation can aect it value i it i not ixed in real term aecting alo the ay-o o dierent trategie the armer mut decide uon. nother oible ource o uncertainty i the cot o contructing and reconverting wetland into agricultural land. The ecological unctioning o ecoytem reent another oible ource o uncertainty. The iue o how wetland work a ollution ink or how much o thi ervice they can rovide i crucial or olicy deign. nalytically thi tye o uncertainty work in the ame way a the irt one mentioned above. The dierence i that in thi cae a long a the armer doe not take into conideration the ecoytem ervice rom a wetland in her deciion they are an externality. The uncertainty in thi cae would motly aect the central lanner deciion-making about olicie to try to internalize thee oitive externalitie. The iue o how inormation i acquired and dieminated i crucial in conomic. ncertainty may arie in the interaction o agent oeing dierent level o inormation i.e. in the reence o aymmetric inormation. In her aer réin 00 exlore the iue o aymmetric inormation in wetland creation. nother aect o the uncertainty iue i related to lack o knowledge or lack o inormation about the deciion to be made. The rik related to a certain deciion may change over time becaue agent may get new inormation. The imortance o dierent inormation availability or the deciion maker i the central iue in ection III o thi aer. The agent behavior toward uncertainty i another aect deerving attention. Rik averion can be deined a the act that when acing choice with comarable return an agent would tend to chooe the alternative reenting le rik. nother way o deining rik averion i by aying that a rik avere agent would reect any

12 invetment ortolio that i a air game i.e. that oer a zero rik remium. it i dicued in the next ection in thi cae uncertainty matter becaue any rik avere armer would require a remium when taking the deciion to invet in wetland contruction. II.. Rik averion e tart with a very imle model where the armer ha acce to a total land area o that he can either ue in agriculture The choice between and or convert into wetland. deend on the marginal net beneit rom the ue o the land in one activity or in the other 8. Thu the beneit rom conventional agricultural roduction uing ollutant ink rom converting veru non-conventional agricultural roduct like into mut be examined. The conventional agricultural roduction i a unction o the land ued in agriculture and ome other actor o roduction that could be labor L : Q L > 0 < 0 From the conventional agricultural roduction the armer earn roit equal to Q Q here tand or the rice o agricultural roduction and Q i ome cot unction deined by the roduction unction given the actor rice. I the armer convert ome o the agricultural land into wetland the roit rom thi new land ue would be equal to a ayment he would get or etting aide land 8 Thi i o i we aume convexity. I not we know that the comarion ha to be made uing total beneit.

13 or environmental uroe 9. Thi ayment Q i a unction o the area converted into wetland Q g. The roit rom the wetland recovery i thi ayment minu the cot o the invetment : Q For imliication we aume here that the ayment i a linear ubidy er unit o area retored into wetland o Q. The total roit are then:. e aume that the roit are uncertain mainly becaue cro rice are uncertain. But the uncertainty could alo come rom the ubidy olicy. 0 The armer maximize exected utility by chooing how much land to convert into wetland. e aume that utility deend on total roit in the ollowing way: [ ] [ ] [ Q Q Q ] The armer maximization roblem i then or each time eriod: Max { [ ]} 9 Here we don t conider the oibility o armer having good will. Söderquit 00 dicue thi iue. 0 The rice uncertainty i introduced here a a roxy or other oible ource o uncertainty that we could exlore later. For examle i a ubidy would be etablihed in relation to the amount o nutrient reduced by a wetland one would have to conider the uncertainty in the ecoytem unctioning and in the amount o nutrient reduced by a certain wetland area. The linear ayment er hectare imlicitly aume that the amount o nutrient aborbed by a wetland i roortional to the area and thi might not be correct.

14 3 To invetigate the role o rik averion a quadratic aroximation around exected roit i ued. It i hown that: Var The dierence between and could be interreted a an indicator o the attitude o the agent toward rik. The endix how that the rik avere rivate agent would be willing to ay to avoid the uncertainty in roit. Thi rik remium would be equal to r.. Var Since the rrow-pratt abolute rik averion coeicient i deined a r The rik remium or the dierence between the exected return and the certainty equivalent roit i r. r. Var Now it i intereting or u to ee what i behind the variance in roit. Going back to our model we aid that roit are uncertain becaue rice and the ubidy are uncertain and. How doe thi uncertainty aect roit? The variance in roit i equal to Var Var Var.. ov I the utility unction i aumed to be concave it i a meaure o the degree o rik averion o the agent or the cot o rik bearing. I the utility unction i convex it i a meaure o rik attraction and i there i no dierence we are in reence o a linear utility unction and a rik neutral behavior.

15 4 Var Var and Q Var Var ov Q Q ov Since the variance are oitive what i imortant here i to know how rice and ubidy relate to each other aecting the variance in roit. I the covariance i negative the diveriication between agricultural land and wetland can be attractive to the rik avere armer. In thi ramework with uncertainty in rice and ubidy the retoration o wetland could be een a a rational deciion rom a rik avere armer. nder which condition would that covariance be negative? hat one would exect i that agricultural rice and wetland ubidie would be oitively correlated. The government agency intereted in more wetland retoration would increae the ubidy when agricultural rice are increaing in order to kee the land ue converion attractive. But it could alo be that the wetland incentive i deigned in a way to rovide inurance to the rik avere armer. For examle in Sweden a in other countrie the armer have the right to receive ome ayment or covering cro loe in cae o natural diater or weather condition that detroy their cro. olicy that could rereent at the ame time income inurance or armer and incentive to wetland retoration could be to attach the ayment o the cro inurance to the ize o the agricultural area that the armer reerved or wetland. In other word the higher the ratio would be the ayment that a armer could get or her cro loe. / the higher I we dro the aumtion o uncertain ubidie the act that the wetland ubidy olicy rovide directly ome kind o roit certainty or ome time eriod would make it attractive or the rivate agent to convert agricultural land into wetland. The rik avere armer choice between an uncertain exected ay-o and a certain one

16 5 even i thi lat one i omewhat maller could then exlain at leat ome wetland retoration. II.3. ncertainty irreveribility and dierent inormation tructure Thi ection ketche a imle model to undertand the role o uncertainty in the deciion to convert agricultural land into wetland. Now the imortant eature are the timing and availability o the inormation together with the irreveribility o the deciion and not the agent rik averion. The model i adated rom rrow and Fiher 974 and Mäler 00. e aume rik neutrality linearity in the beneit unction and only two oible trategie or the armer to chooe between. armer ha an area o land under agricultural exloitation. She i uncertain about the evolution o cro rice and he ha to decide whether to kee her land a agricultural land or to convert it or art o it into wetland. To give incentive to retore the wetland the ocial lanner ha etablihed a ubidy to cover art o the converion cot and the maintenance cot or the wetland area throughout the year a well a a ayment to cover the orgone cro revenue. e aume that agricultural cro rice can take two value a high h and a low one l. The ubidy i known and the net beneit o the agricultural activity B are aumed to be higher lower than the beneit rom the wetland retoration B in cae o high low agricultural rice: B ht> B t> B lt t The armer doe not know cro rice with certainty o the roit rom the agricultural roduction i uncertain. The ubidy ha been etablihed and i known o the armer mut analyze and comare the exected roit rom the agricultural activity and the uture low o ubidy ayment and decide whether to convert land into wetland or not. e aume that B i the ame in both eriod and. See endix.

17 6 I the armer doe not convert her roductive land into wetland he can till take the deciion next year keeing the otion o converting and the oibility o getting more new inormation beore taking the deciion. I the deciion to convert i taken there i an intitutional irreveribility roduced by the act that ater igning the contract with the ocial lanner 3 you cannot undo the wetland at leat or a certain number o year. Beide we aume irreveribility related to the act that there are unk cot i.e. exenditure that cannot be recovered. e will irt analyze the cae a where there i no orthcoming inormation and later take the cae b when new inormation i available by the end o the irt eriod. a No orthcoming inormation In Fig. the roblem when there i no new inormation i reented. The deciion maker mut decide in the beginning o the irt eriod on the bai o the exected ay-o or both eriod exected beneit and oberve the reult in the end o the econd eriod. The reult here are exreed in monetary value not in utility term. The σ are the rior or belie robabilitie o the armer in relation to rice with σ h rereenting the robability o high rice and σ l rereenting the robability that agricultural rice will be low. Nature N determine i cro rice are high or low. The armer ha belie about it but he will not know what the rice are until ater her deciion i made. In the cae where the exected ay-o rom the agricultural activity B i higher than the ay-o or the wetland retoration B the armer would chooe and get the ay-o B σ h. B h σ l.b l. I B B B > B σ h. B h σ l.b l then the armer would be intereted in converting at leat ome area rom agricultural ue into wetland to get the ay-o B B B. In both ituation and becaue o the aumtion we make about no new inormation coming the armer would not chooe in the irt eriod and change the choice to in the econd eriod or vice-vera. On one hand we are auming 3 In the Swedih cae the local government or läntyrelen county adminitration.

18 7 that the choice or i irreverible. On the other the armer would never get the ayo o B h B becaue with the exectation o high agricultural rice valid or both eriod ince no new inormation would arrive there would not be any converion into wetland in any o the eriod. Fig. h B h B h B l B l l B σ h B h B h σ l B l B l h B h B σ h B h B σ l B l B l B l B h B B l B B B σ h B B σ l B B here no new inormation i added the armer mut comare on the bai o her belie or rior about cro rice the exected beneit rom the agricultural activity B with the exected beneit rom the wetland retoration B to make a deciion.

19 8 b ith new inormation more intereting cae i the one deicted in Figure. Here in the end o the irt eriod our armer get to know i the rice will be high or low 4. in the reviou cae the deciion tree i deicted a i it wa a game between the armer and Nature N who determine i cro rice are high or low. In cae o high agricultural rice i the armer had choen in the irt eriod he continue with the agricultural activity or the econd eriod alo getting the ay-o o B h B h. In the cae the armer had choen the agricultural activity in the irt eriod in ace o low agricultural rice he change her mind in the end o the irt eriod and decide to convert ome land into wetland getting the ay-o o B l B. Fig. B h B h h B h B σ h.b h N σ l B l B B l B l l B l B B B N h B σ h B B l σ l B B B B 4 Somehow the aumtion here i that cro rice in the econd time eriod are erect correlated to cro rice in the reviou eriod or at leat a good ignal. hether thi i a reaonable aumtion or not i robably an emirical iue.

20 9 I the armer had choen to convert ome land into wetland beore the inormation arrived in the end o the irt eriod thi deciion cannot be changed or the econd eriod. e aume that the retoration o wetland in an agricultural area i irreverible at leat in the hort run. Thi mean that the armer know rom the beginning that her ay-o in thi cae will be equal to B σ h B σ l B B B. The armer will decide to retore wetland in an agricultural area beore getting inormation i he exect that the beneit o the change in land ue will be higher than the beneit rom the agricultural activity. In thi cae the armer comare her exected beneit rom the wetland retoration B σ h B B σ l B B B B with the exected beneit rom taking the deciion o keeing the area in agricultural roduction i.e. B σ h.b h σ l B l B. in the cae o no new inormation arriving i B > B the irt deciion i in the direction o and i B > B the irt move i toward. The dierence here i that the availability o new inormation change the exected value a we can oberve in the ollowing table ummarizing the exected ay-o in the dierent cae: ae a no new ino b new ino a irt move B σ h B h B h xected σ l B l B l value a irt move B σ h B B σ l B B B σ h B h B h σ l B l B B σ h B B σ l B B

21 0 I the agricultural activity i the bet choice ater the new inormation arrive it mean that it i alo the bet choice when there i no new inormation orthcoming. Thi i o becaue according to our original aumtion B ht> B t> B lt and: σ h B h B h σ l B l B l < σ h B h B h σ l B l B. In the cae o the deciion about retoring wetland the ame i not true. The act that the deciion to retore wetland involve ome degree o irreveribility imlie that i the armer had choen in the irt eriod and at the end o that eriod he get to know that the agricultural rice are high he cannot go back in her deciion to get the ayo o B B h. In cae o low agricultural rice with new inormation i choen a a econd move in the end o the irt eriod and the armer get the ay-o o B l B. I wa the bet choice when no new inormation wa orthcoming it wa becaue the beneit rom the wetland retoration wa exected to be greater that then the exected beneit rom the agricultural activity i.e. σ h B h B h σ l B l B l < B B. But taking into account the new inormation the comarion the armer ha to make in order to invet in wetland retoration i not anymore between B B and the original uninormed exected beneit rom the agricultural activity a in the reviou aragrah. The deciion ha to be taken now by comaring B B B with B σ h B h B h σ l B l B the latter being greater than the exected beneit o agriculture in the no new inormation cae.

22 we can ee the dierence i equal to σ l B - B l. Thi could be een a the value o the inormation received or alternatively the value o not having engaged in an irreverible activity when new inormation i orthcoming. It could alo be een a the remium the armer would require or taking the rik o the irreverible move in the irt lace. III. Forthcoming inormation reveribility cot and land converion Thi ection develo the initial model or the rik avere armer deciion to include two time eriod. It how that even when there i no irreveribility i reverting the deciion to invet imlie ome cot the armer will rerain rom taking the deciion a a irt te or will convert le wetland than he would do in other circumtance. Thi haen even with the aumtion o rik neutrality that we ue here. In our initial model the armer ha acce to a total land area o that he can either ue in agriculture deend on total roit in the ollowing way or convert into wetland. uming that utility [ ] [ ] [ Q Q Q ] the armer maximization roblem or each time eriod i Max { [ ]} and the irt order condition oc or maximization i: d d. 0 or. 0 d d

23 In the one eriod cae the armer will roduce at the level where the ubidy or wetland converion cover the cot o wetland contruction and the oregone roduction rom the agricultural area lot. The imle grahic model o the reviou ection howed the dierence in the armer deciion-making when time i taken into conideration and the deciion involve irreveribility. In thi ection conidering again two time eriod two cae are analyzed earately deending on the amount o inormation the armer ha acce to and on the timing o it availability. The model reented here i a two eriod analyi o behavior under uncertainty with two ituation that dier on the amount o inormation available or the deciion maker. In hi aer tein 980 how that the roect o greater uture inormation dicourage the adotion o an irreverible deciion 5. He alo how ituation where le extreme irreveribility lead to dierent reult according to the kind o model ued or the analyi. Here an alternative verion to tein ramework i ued to how that in what concern a armer deciion to convert agricultural land into wetland there i no need or the deciion to be irreverible to dicourage the invetment. Thi would ugget the need or more incentive or the armer to retore wetland. III.. The cae without new orthcoming inormation In thi cae the armer decide in the beginning o the irt eriod about how much land he will convert into wetland in both eriod i.e. he decide about and. The armer maximization roblem i: Max β { [ ] [ ] } 5 See. 70.

24 3 here: reer to roit the uercrit denoting agriculture or wetland area the ubcrit denoting the time eriod or and are agricultural rice and ubidie the ubcrit denoting the time eriod or i the cot unction aociated to the converion o land into wetland which deend on the amount o land converted the uercrit denoting wetland area the ubcrit denoting the time eriod or β i the dicount rate The dicount actor β doe not aect the reult o the model. Thereore it can be taken away or aumed to be equal to. The irt order condition are then: oc: d { β } 0 d { } 0 Two dierent cot unction are ued: one or the irt eriod deending only on the area that the armer decide to convert into wetland in that eriod ; and another one deending on both the area converted in the irt eriod and the total wetland area in the end o the econd eriod. In thi ormulation the total area converted in the econd eriod i equal to the dierence -. e aume that the cot unction i o the tye γ. Thi mean that the bigger the dierence between the wetland area in both eriod the greater the cot the armer would have to bear. For uch a cot unction the marginal cot would be equal to

25 4 γ and γ nd their derivative would be equal to γ γ Thi mean that deending on the relative ize o and the marginal cot o increaing the wetland area in the irt or in the econd eriod would have the ollowing ign: I > < 0 and > 0 i < > 0 and < 0 The hae o the cot unction i extremely imortant in thi model becaue it contain the idea o both a cot o contructing wetland and a cot o undoing wetland reviouly contructed. It i thi idea that will lead u to the main reult o the model. III.. hen new inormation i orthcoming hen the armer know that new inormation will be available in the end o the irt eriod the roblem become dierent. The armer chooe only in the beginning o the irt eriod leaving the deciion about to be taken on the bai o the new

26 5 inormation in thi cae new inormation could be on agricultural rice or other new inormation relevant or the deciion. For olving the roblem the tarting oint i the armer deciion making about how much wetland to have in the econd eriod taking what wa already converted in the irt eriod a given. The armer then olve the ollowing maximization roblem: [ ] [ ] Max Max The ollowing exreion i the irt order condition or the econd eriod: 0 uming that 0 then 0. The ubidy thu ha to comenate or the lo in roductivity due to the reduction in the agricultural area lu the cot o increaing or retoring the wetland area. From thi condition the exreion or i calculated to ee how the deciion made in the irt eriod aect the amount o wetland contructed in the econd eriod. Taking the condition or olving the maximization roblem in the econd eriod 0 0 and deriving it with reect to

27 6 d d. 0. it i oible to arrive to the ollowing exreion:. 0 < 0 > and 0 < o the exreion i oitive. The dierence between the two roblem i that without new inormation the armer olve the ollowing maximization roblem by oberving the two irt order condition: [ ] [ ] { } Max 0 d d 0 hile with new orthcoming inormation the new roblem and the irt order condition are: [ ] [ ] Max Max

28 7 0 d d 0 it can be oberved in the irt cae the agent maximize over two eriod without receiving any new inormation which mean that i choen on the bai o the exected value o or both eriod. In the cae with new inormation the maximizer i choen on the bai o the exected value o or the irt eriod lu the exected value o the unction ϕ deined a [ ] Max ϕ. The quetion that remain to be anwered i about the ize o in both cae. I larger when there i no orthcoming inormation or when there i inormation orthcoming? In which o the cae would the armer convert more land into wetland in the irt eriod? The anwer to thi quetion deend on the cot curve. Here a beore there are two dierent cae to analyze. The irt when the wetland area by the end o the econd eriod i bigger than what wa converted in the irt eriod. In thi cae 0 > > ; 0 < ; 0 > ; 0 <. In the econd cae the total area converted into wetland by the end o the econd eriod i maller than the area converted in the irt eriod. Thi mean that the armer regretted about her reviou deciion and decide now to undo art o the wetland contructed. In thi cae 0 < < and 0 > ; 0 > ; 0 <. The imortance o thi dierence relate to the

29 8 act that with the oibility o the armer receiving new inormation later in time the uncertainty about how much land to convert into wetland combined with the cot o decontructing the wetland already retored may lead the armer to otone her deciion until more inormation i available. Prooition I there are two oible ituation one more inormative than the other the unctionϕ i concave in and the marginal cot unction i concave with reect to the area o agricultural land converted into wetland will be greater in the cae o le inormation than in the cae where there i orthcoming inormation 6. The armer would convert more land into wetland in cae o no inormation than he would do in cae o more inormation. Thi i o becaue the inormation we are reerring to here i about market rice or agricultural outut. Becaue o the concavity o the cot unction with reect to rice the exected cot o the land converion will alway be maller than the real cot. No inormation would then lead to greater converion. More inormation orthcoming lead to le develoment in the irt eriod even in the cae when there i no irreveribility. I there i a cot in revering the reviou invetment made then it will alway be better or the armer to otone the invetment deciion. From a normative oint o view the ubidy or wetland creation hould be higher to conider thi aect even when the land converion deciion doe not involve irreveribility. IV. xloring oible olicy imlication In the tatic aroach dicued irt the converion rom a roductive agricultural area into a retored wetland area could be the reult o the behavior o a rik avere 6 e aume that more inormation i alway better in the cae o one deciion maker. Thi could be dierent in the cae o a non-cooerative game or in the cae o trategic interaction.

30 9 agent trying to diveriy her invetment in order to reduce uncertainty. e dicued two oibilitie. The irt oibility i that o a certain ubidy. In thi cae a we can oberve in the ollowing diagram even i the beneit rom wetland retoration B are not greater than the exected beneit o the agricultural activity B a long a B i greater than the certainty equivalent beneit rom agriculture B c it i rational or the rik avere agent to take B intead o acing the uncertainty o B. nother oibility i that o uncertainty in both cro rice and ubidy. In thi cae both and are random variable and the covariance between them would have to be negative in order or the wetland retoration to reduce the armer roit variability. I that i the cae negative covariance converion could be a rational choice by the rik avere armer willing to reduce the uncertainty variance in roit. In thi cae intead o the deign o a direct ubidy a an incentive to retore wetland it could be more intereting to have an indirect incentive linking income tabilization and wetland retoration to create through the governmental olicy the negative covariance. In thi context the uncertainty in cro rice hel the deciion to retore wetland even when no rik averion i conidered. I thi i o and i there i an obective o increaing the area dedicated to wetland at the leat cot maybe it would be intereting to exlore more the connection between agricultural rice and ubidie and incentive to wetland retoration. By roviding agricultural ubidie to guarantee a minimum income or the armer the ublic olicy could be creating a ale rice certainty that might revent armer to convert agricultural land into other more environmentally riendly ue. I agricultural ubidie contribute to decreae uncertainty in cro rice at the ame time they make it neceary or the government to give higher ubidie to wetland retoration. I thi were the cae a better coordination o both olicie would make it le exenive to get more area in wetland and imultaneouly give armer the required income ecurity.

31 30 B i B B B B l B c B B h B B In the ramework o the model in ection II.3 intead and auming rik neutrality the agent now would avoid taking the deciion to convert agricultural land into wetland becaue o the aumtion o irreveribility in the invetment in wetland and the oibility o receiving new inormation to eed the deciion-making roce. The irreveribility imlie now that the armer require an extra remium ayment in order to decide or the converion a a irt move. Thi remium correond to the value o the inormation i.e. the dierence between the exected value o the beneit rom the agricultural activity without inormation and thoe beneit when inormation i orthcoming. Thi value i equal to σ l B - B l. In ection III the aroach attemt to integrate the idea reented in ection II in a imle model o behavior under uncertainty with dierent inormation availability or the deciion. It illutrate the otential connection between uncertainty in cro rice and deciion that involve a cot or revering the deciion. It i hown that the armer would otone the deciion to convert agricultural land into wetland a long a there i the erective o receiving more inormation in the uture. nd thi i o even i the deciion to retore wetland i not an irreverible one. long a the reveribility o the deciion involve ome cot thi will rereent a diincentive to the wetland creation. Thi aer i the reult o a irt exloration on the iue o uncertainty and how it aect both the armer behavior and the olicy making related to ollution abatement to reduce eutrohication in the Baltic Sea.

32 3 tatic aroach to the role o rik averion in the deciion to convert land ue i reented and it i uggeted that either the roit certainty rom the wetland retoration or a negative correlation between cro rice and wetland ubidy could exlain a armer deciion to retore wetland. By uing rrow and Fiher ramework it i hown that the otential irreveribility o the wetland retoration together with the oibility o getting more inormation in the uture would either delay the armer deciion into converting land ue or make it more exenive rom the ocial lanner oint o view ince the armer would require a remium to engage in the irreverible activity thereore a higher wetland retoration ubidy. Beide it i hown that even when the deciion to retore wetland i not irreverible the rational armer will invet le in land converion a a irt te when there i uncertainty and with the oibility o receiving more inormation in the uture. The concluion i that to obtain more wetland retoration the olicy maker hould conider thee reult and deign an incentive mechanim that take uncertainty and inormation or the deciion into conideration.

33 3 endix - Rik Premium and Rik verion r c c i the certainty equivalent o the roit and it give a hown in the igure the ame utility a the exected utility o roit. The quetion here i to ind out what i r the rik remium that the armer i willing to ay or avoiding the uncertainty in roit and how it relate to the degree o rik averion o the agent. Through a irt order aroximation or the utility o the certainty equivalent roit c r r r c c c c c... and a econd order aroximation o the exected utility around the mean [ ].... [ ] i

34 33 Var nd taking into conideration the equality between c it i hown that. Var r. Var r.. Var r Since the rrow-pratt abolute rik averion coeicient i deined a r The rik remium or the dierence between the exected return and the certainty equivalent roit i.. Var r r

35 34 endix Proving the Prooition Ste - Showing under which condition the unction ϕ i concave in From the armer maximization roblem Max ϕ. From the irt order condition 0 I the area converted into wetland by the end o the econd eriod i a unction o the area converted in the irt eriod then and 0. ϕ The irt derivative i equal to: ϕ ϕ The econd derivative i ϕ. ϕ

36 35. ϕ.. For thi exreion to be negative which i the condition or the unction ϕ to be concave in the exreion. hould be greater than zero. I. wa equal to zero the exreion. would be equal to. For any other value o. 0. < <

37 36 In other word i > the unction ϕ i concave in. Thi condition i ulilled i 0 > i.e. i the determinant o the Heian matrix o the cot unction i oitive. Ste - nalyzing the relationhi between the two maximization roblem and comaring in both cae The main dierence between the two maximization roblem lie in the inormation aect. In the irt cae it i aumed that the armer ha no inormation whatoever to eed the deciion-making i.e. the deciion about converting agricultural roductive land into wetland i taken only on the bai o exected value o the relevant variable. In the econd cae there i inormation available or the deciion in the econd eriod. The ame unction ϕ o beore become here ψ or the robability vector o tate o the uncertain variable to be included in the analyi. 0 i i i Max ω ω ω ω ψ Perect inormation i deined here a a ituation where a given ignal y bring inormation on the behavior o the random variable : i y y P i i 0 i y y P i i ith erect inormation intead o taking the deciion on the bai o the rior belie about how the variable will behave exected value the armer take an inormed deciion in the econd eriod.

38 37 It i aumed that the armer would be in a better ituation with inormation rather than without i.e. ω ψ > ω ψ i ω i more inormative than ω. i In the no inormation cae q Max ω ψ. r Max. r r d d ψ r d d ii with orthcoming inormation erect inormation cae Max q ω ψ Max Max r ω ψ ω ψ d d ψ ω Since 0 i a irt order condition or the utility maximization in the econd eriod then:

39 38 ψ ω. Max r r d d ψ r d d The dierence between the two irt order condition i: r r ψ ψ r hat i needed now i to know which one i greater. To etablih the inequality between r and the marginal cot unction and it behavior in relation to the rice variable i analyzed in what ollow. 3

40 39 Since 0 < and 0 > it i now neceary to check the ign o the exreion. From the condition or otimization in the econd eriod 0 we can get the relationhi between and rice : 0 Deriving the reviou exreion with reect to give: 0 Since and are negative mut be maller than zero or the reviou equation to hold. Deriving again with reect to give: 0 0 Since the irt three term o the reviou exreion are oitive or the exreion to hold hould be oitive.

41 40 Thee lead to the concluion that < 0 which mean that the marginal cot unction thi i o then going back to the dierence between i concave with reect to. I ψ ψ and it i concluded that it i negative which mean that in the cae o erect inormation i maller than.

42 4 Reerence hreimer Berit and Han B. ittgren 00 Modelling nitrogen removal in otential wetland at the catchment cale cological ngineering 9: rrow Kenneth J. and nthony. Fiher 974 nvironmental Preervation ncertainty and Irreveribility The Quarterly Journal o conomic 88: Bocktael Nancy. and lena G. Irwin 000 conomic and the land ue-environment link The International Yearbook o nvironmental and Reource conomic 000/00: Survey o urrent Iue edited by Tom Tietenberg and Henk Folmer dward lgar -54. Bytröm Olo 000 The Relacement Value o etland in Sweden nvironmental and Reource conomic 64: réin nne-sohie 00 Incentive or wetland creation Tackling the economic o ecoytem Diertation in conomic 00:6 Deartment o conomic Stockholm niverity tein Larry G. 980 Deciion Making and the Temoral Reolution o ncertainty International conomic Review Volume Iue Jun Fernandez Linda 999 n analyi o economic incentive in wetland olicie addreing biodiverity The Science o the Total nvironment 40:07-. Folke arl and Åa Janon 000 etland a Nutrient Sink in Gren Ing-Marie Kerry Turner and Fredrik ul ed. Managing a Sea: The cological conomic o the Baltic arthcan Freixa Xavier and Jean-Jacque Laont 984 On the irreveribility eect hater 7 Bayeian Model in conomic Theory edited by M. Boyer and R.. Kihltrom levier Gren Ing-Marie 995 The Value o Inveting in etland or Nitrogen batement Beier Rerint Serie No. 47 rerinted rom uroean Review o gricultural conomic :57-7. Gren Ing-Marie Kerry Turner and Fredrik ul ed. 000 Managing a Sea: The cological conomic o the Baltic arthcan. Hamilton rmy irield etland Retoration Feaibility Study 998 Final IR/IS hater 7 Public Health December. vailable at: htt:// Heimlich Ralh. ot o an gricultural etland Reerve Land conomic 70: Henry laude 974 Invetment Deciion nder ncertainty: The Irreveribility ect The merican conomic Review 646:006-0.