the tree cutting problem in a stochastic environment the case of age dependent growth abstract harvest policies are derived for growing biological assets e g forests livestock subject to stochastic age dependent growth and price uncertainty the task posed is analyzed as a continuous time optimal stopping problem for diffusion processes both single and ongoing rotation problems are considered qualitative comparative static and numerical results are provided

informational efficiency of markets for stumpage this paper examines the weak form informational efficiency of markets for pine sawtimber stumpage in the u s south analyses of annual and quarterly rates of price change generally indicate that stumpage markets are efficient when viewed over monthly intervals stumpage markets do not pass the tests for weak form efficiency this failure is attributed to friction in the market due to the time and cost involved in consumating timber sales the results have implications for price responsive timber harvest scheduling for the application of asset pricing models to forestry investments and for policies governing sales of timber from public lands

deep integration and production networks an empirical analysis this paper investigates the two way relationship between deep integration and production networks trade we capture deep integration with a set of indices constructed in terms of policy areas covered in preferential trade agreements we estimate an augmented gravity equation to investigate the impact of deep integration on production networks trade the results show that on average signing deeper agreements increases production networks trade between member countries by almost 12 percentage points in addition the impact of deep integration is higher for trade in automobile parts and information and technology products compared with textile products to analyse whether higher levels of network trade increase the likelihood of signing deeper agreements we follow the literature on the determinants of preferential trade agreements the estimation results show that after taking into account other pta determinants a ten percentage increase in the share of production network trade over total trade increases the depth of an agreement by approximately 6 percentage points in addition the probability of signing deeper agreements is higher for country pairs involved in north south production sharing and for countries belonging to the asia region

carbon subsidies taxes and optimal forest management we consider the effect of carbon credit payment schemes on forest owners land use and harvest decisions we study two possible credit allocation regimes one where credits are allocated according to the actual amount of carbon sequestered by the trees on a piece of land and another where credits are allocated according to the long run potential to sequester carbon on the land using a real options model with uncertain future timber prices we examine the effect on the timing of harvests and the replanting abandonment decision we show that both schemes discourage deforestation compensating growers for actual carbon sequestration leads to longer rotation periods between harvests while basing compensation only on the long run potential level of sequestration induces shorter rotation periods the former scheme leads to greater benefits of carbon sequestration at lower cost than the latter scheme although inducing moderate levels of sequestration is expensive under both schemes the cost falls dramatically when the level of payments climbs above some threshold indeed providing the payments are sufficiently generous carbon credit payment schemes offer an effective means of increasing carbon sequestration

timber price dynamics following a natural catastrophe catastrophic shocks to existing stocks of a renewable resource can cause long run price shifts with timber these long run price shifts may be accompanied by a short run price drop due to salvage hurricane hugo damaged 20 of southern pine timber in the south carolina coastal plain in 1989 to estimate the short and long run effects of the hurricane on the prices of timber stocks we estimated an intervention model of the residuals of cointegration of south carolina sawtimber and pulpwood stumpage prices with prices of similar products from other regions modeling revealed a 30 negative price spike due to salvage and a long run enhancement effect leading to prices that are 10 to 30 higher than they would have been had hugo not occurred

optimal adaptive price search consider the problem of a consumer desiring to buy a good which is sold at a variety of prices such a buyer will be able to obtain a sequence of price quotations from various sellers when should the buyer stop searching for a lower price if he continues he may obtain a lower price but he incurs additional time effort and expense in searching the optimal price search decision is one of balancing the expectation of a possibly lower price obtained by continued search against cumulative costs from search when the prices arise from a known probability distribution the optimal search strategy has certain well defined and desirable properties in the more realistic case that the buyer has only partial information about the price distribution and must update his beliefs after observing prices in the marketplace the problem becomes more complex and search strategies become less well behaved the major purpose of this article is to determine new conditions under which optimal policies have these desirable characteristics in the case where the consumer possesses only incomplete information about the distribution of prices price quotations he receives in addition to providing him with price possibilities provide him with information about that distribution rothschild 151 in citing an unpublished paper of gastwirth has noted that small specification errors for an assumed distribution can lead to substantial changes in expected number of searches and expected cost consequently the assumption of a known distribution of prices can have a profound effect on total cost 1 0022 053 l 8 l 040001 20 02 00 o

the impact of ftas on mena trade in agricultural and industrial products abstractthis article analyses the impact of free trade agreements ftas on middle east and north african countries mena trade for the period 1994 2010 the analysis distinguishes between industrial and agricultural trade to take into account the different liberalization schedules an augmented gravity model is estimated using up to date panel data techniques to control for all time invariant bilateral factors that influence bilateral trade as well as for the so called multilateral resistance factors we also control for the endogeneity of the agreements and test for self selection bias due to the presence of zero trade in our sample the main findings indicate that north south ftas and south south ftas have a differential impact in terms of increasing trade in mena countries with the former being more beneficial in terms of exports for mena countries but both showing greater global market integration we also find that ftas that include agricultural products in which mena countries have a clear comp

options uncertainty and sunk costs an empirical analysis of land use change abstract in a real option model of land conversion incorporating return uncertainty and sunk costs optimal conversion thresholds are significantly higher than those from expected net present value models not accounting for these factors empirical tests of conversion from agriculture to forest suggest that landowners value the option to convert when making conversion decisions higher uncertainty in returns to all potential uses and lower correlation between shocks to agricultural and forest returns decreases the likelihood of conversion estimates indicate a significant impact on conversion decisions with approximations of option values ranging from 7 to 81 of the expected value of the land asset

estimating gamma for tail hedge discount rates when project returns are cointegrated with gdp martin weitzman has suggested a method for calculating social discount rates for long term investments when project returns are covariant with consumption or other macroeconomic variables so calle

the optimal production of an exhaustible resource when price is exogenous and stochastic this paper examines the optimal production of a resource such as oil when its price is determined exogenously e g by a cartel such as opec and is subject to stochastic fluctuations away from an expected growth path we first examine the dependence of production on extraction cost and show that the conventional exponential decline curve is indeed optimal if marginal cost is constant with respect to the rate of extraction but is a hyperbolic function of the reserve level we next show that uncertainty about future price affects the optimal production rate in two ways first if marginal cost is a convex concave function of the rate of production stochastic fluctuations in price raise lower average cost over time so that there is an incentive to speed up slow down production second the option value of the reserve i e the ability to withhold production indefinitely and never incur the cost of extraction provides an incentive to slow down the rate of production

asset retirement with infinitely repeated alternative replacements harvest age and species choice in forestry abstract at what age should productive assets be retired how should replacements be chosen when they differ in their uncertain ability to generate future incomes as a particular version of that problem we study the tree harvesting decision with two possible replacement species whose values as timber are stochastic and whose growth functions are deterministic in the single rotation wicksell problem starting with a bare piece of land an empty shop it is optimal to choose and plant one species immediately if its current value is sufficiently high relative to that of the other species the alternative equipment however if the species are insufficiently price differentiated it is preferable to leave the land vacant the shop empty despite the opportunity cost of doing so in the repeated version of the problem it is never optimal to leave the land bare provided the cost of replacement is null furthermore the optimal harvest tree retirement age not only depends on the price and current productivity of the trees in place but also on the price and productivity of the other species because it may replace the current one the harvest age reaches a peak at some critical threshold of the relative price that signals the necessity to switch to the alternative species indeed this is when the opportunity cost of choosing one alternative replacement over the other is the highest the land value and also the value of the firm is similar to an american option with free boundary infinite expiry period and endogenous payoff the paper highlights the opportunity cost of alternative replacement options and the central role of their volatility in both asset retirement and replacement choice decisions all results are derived analytically a numerical treatment by the penalty method completes the resolution

taxation and rotation age under stochastic forest stand value abstract the paper uses both the single rotation and ongoing rotation framework to study the impact of yield tax lump sum tax and tax on interest rate earnings on the privately optimal rotation period when forest stand value is stochastic and forest owners are risk averse or risk neutral under risk aversion the optimal harvesting threshold is lower and therefore the expected rotation period shorter than under risk neutrality both in the single and ongoing rotation cases whether the forest owner is risk averse or risk neutral a higher yield tax a higher lump sum tax or a higher tax on interest rate earnings raise the optimal harvesting threshold numerical results indicate that the optimal harvesting threshold increases less rapidly under risk aversion than under risk neutrality with an increase in either a yield tax or the volatility of forest stand value

a stochastic analysis of the tree paradigm abstract the tree paradigm which is a problem in optimal stopping has important ramifications for human capital acquisition search behavior firm entry and in the theory of renewable resources our paper extends previous work in the stochastic literature on several fronts we exhibit a tractable solution to the rotation problem for the stochastic model analyze the effects of inputs which control the growth process and illustrate our results with a multi stage learning problem

non renewability in forest rotations implications for economic and ecosystem sustainability abstract the forest rotations problem has been considered by generations of economists fisher 1930 boulding 1966 samuelson 1976 traditionally the forest resource across all future harvest periods is assumed to grow without memory of past harvest periods this paper integrates economic theory and intertemporal ecological mechanics linking current harvest decisions with future forest growth financial value and ecosystem health results and implications of a non renewable forest resource and the influence of rotation length and number on forest recovery are reported cost estimates of moving from short term economic rotations to long term ecological rotations suggest the level of incentive required for one aspect of ecosystem management a net private cost of maintaining ecosystem health emerges and for public policy purposes can be compared with measures of non timber amenity values and social benefits exhibiting increasing returns to rotation length

a simple competitive model with production and storage we study a rational expectations partial equilibrium model of a market for a single storable commodity whose output each period is a function of previous period effort on production and a realization of a shock that affects equally all producers i he final demand is non random and depends only on each period s price risk neutral producers make production and storage decisions based on forecasts of future price distributions existence of equilibrium is proved and for the case of i i d shocks several comparative statics results are established as well as the existence and stability of a unique stationary distribution and whose output at each period is a multiplicative function of previous period s planting and of the realization of a shock that affects equally all producers the final demand for this good is non random and depends only on this period s price this describes approximately markets for agricultural products which are not traded internationally and where most of the price uncertainty stems from supply shocks risk neutral producers make their decisions based on forecasts of future price distributions and of known cost functions of storage and production to maximize their discounted profits in order to close the model an assumption on how such price forecasts are made is needed we assume that agents make equilibrium forecasts i e that their forecast is common and that when producers act taking the forecasted prices as given they make decisions that yield the forecasted prices as equilibrium prices this is of course what has been sometimes called rational expectations the assumption of equilibrium expectations and the presence of risk neutral pro ducers will imply that the equilibrium variables may be obtained by considering a related market surplus maximization problem 1 this places strong restriction on the stochastic process of equilibrium prices for the case where the basic shocks are assumed to be independently and identically distributed over time one may thus show that equilibrium prices are a function of a certain state variable the total stocks kept from last period plus this period s output and this allows us to derive properties of equilibrium solutions our main results concerning this case are a storage is a non increasing function of price and expected production a non decreasing one b the elasticity of expected future prices with respect to today s prices is positive and less than one c this elasticity is non constant being zero for high enough prices d the price process follows a renewal process if prices are low

the valuation of forestry resources under stochastic prices and inventories a contingent claims approach to capital budgeting may be preferable to traditional methods where uncertainty and managers strategic reactions to changing conditions are impor tant as an example of such a case we solve the classical problem of the duration of an investment in forestry resources i e when to cut down the trees in the general case of stochastic output prices and stochastic natural growth rate and timber inventories a con tingent claims approach is used to value the forestry resources as a function of 1 sto chastic prices and inventories and 2 an asymmetric optimal production policy that incorporates the option to halt timber production temporarily i introduction classical capital budgeting techniques are based on the assumption that fu ture cash flows follow a rigid pattern and can be accurately predicted far into the future on the basis of such cash flow predictions the project is either accepted or rejected the uncertainty in the project and management s strategic reactions to changing conditions are dealt with only superficially at best a risk adjusted interest rate is employed and various deterministic scenarios are plotted out in situations where uncertainty and management s strategic reactions to it are im portant the classical technique is apt to lead to wrong decisions the technology needed to deal with such problems more accurately is becoming available the purpose of this paper is to present a stylized example of how it can be used our example is a general solution to the classical duration problem of the optimal control of a long term renewable resource investment such as forestry resources i e when to chop down a tree 1 if the prices and the natural growth rate of the inventory of forest timber are assumed to be deterministic the optimal control is very simple to derive but when both the price and inventory of timber are stochastic the problem becomes both stochastic and asymmetric the asym

harvesting a renewable resource under uncertainty abstract this paper presents a theory of harvesting that allows for partial harvests and accounts for the risk of extinction for biological assets with size dependent stochastic growth the harvesting decision is formulated as a disinvestment problem in continuous time and generalized faustmann formulas are derived the probability of extinction is then analyzed for a wide class of growth functions an illustration based on the logistic brownian motion shows that both optimal biomass at harvest and harvest size do not vary monotonically with uncertainty more generally this paper illustrates the importance of properly accounting for barriers in stochastic investment problems

informational efficiency of markets for stumpage comment in a study of the information efficiency of markets for stumpage in the southern united states washburn and binkley found that time series data on stumpage price if given on annual or quarterly bases reveal weak form information efficiency for stumpage markets from this they conclude that there can be no gain from using past price movements to play the market in timing timber harvests p 403 specifically they infer that the reservation price rules derived for optimal forest harvesting by norstrom lohmander and brazee and mendelsohn are not applicable to the management of southern pine timberlands

an expository note on the valuation of foreign exchange options abstract this note describes the application of the binomial model to the valuation of foreign exchange options and reports simulated pricesof american as well as europen call and put options we find significant deviations of simulated call prices from those reported elsewhere this casts some doubt on empirical findings that american calls have significant pricing errors

tests of an american option pricing model on the foreign currency options market this paper tests the ability of the american option pricing model proposed by parkinson 18 or mason 14 to explain the pricing of the foreign currency options traded on the philadelphia stock exchange from february 28 1983 to march 26 1985 we find that the model underprices out of the money options relative to at the money and in the money options this relative underpricing is driven by an underpricing of out of the money call options of short maturity in addition the degree of relative mispricing for most categories of options is shown to be a decreasing function of the time to maturity of the options longer maturity options appear to trade at similar levels of implied volatility whether they are in at or out of the money most of these biases appear consistent with the fact that the underlying spot currency rate follows a mixed jump diffusion process as described in 17

assessing the trade impact of the european neighbourhood policy on the eu med free trade area the european neighbourhood policy enp set an additional objective for the southern mediterranean countries smcs the prospect of a stake in the internal market the launch of this new policy has been the occasion for a revival of empirical studies aimed at assessing the impact of the eu med partnership on bilateral trade the novelty of this work is twofold i to present nonparametric matching estimators besides gravity estimates ii to assume as a counterfactual of the treatment the ex post long run average treatment effects of the europe agreements by controlling for likely selection bias and country and time heterogeneity using both qualitative and quantitative measures of the policy variable we assess ex post the trade enhancing impact of the eu preferential agreements towards smcs and ex ante the actual efficacy of the enp

the pricing of call and put options on foreign exchange this paper derives pricing equations for european puts and calls on foreign exchange the call and put pricing formulas are unlike the black scholes equations for stock options in that there are two relevant interest rates interest rates are stochastic and boundary constraints differ in addition it is shown that both american call and put options have values larger than their european counterparts

harvest decisions and asset valuation for biological resources exhibiting size dependent stochastic growth optimal harvest rules and preharvest valuation procedures are derived for biological assets with stochastic size dependent growth in a stochastic price environment these issues are analyzed as continuous time optimal stopping problems both the single rotation and ongoing rotations problems are addressed the sensitivity of harvest and valuation rules is assessed the results are compared with those derived from a myopic look ahead procedure and with the corresponding findings for age dependent growth copyright 1990 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

a comparison of the ito and stratonovich formulations of problems in finance abstract a comparison of and the relationship between the ito and stratonovich formulations of stochastic integration is given it is argued that generally the ito formulation is appropriate for problems of finance and economics the black scholes option pricing problem is discussed in both frameworks with the ito formulation being shown to be clearly superior a finance example in which the stratonovich approach is simplest is also presented

optimal forest rotation when stumpage prices follow a diffusion process a key assumption in the faustmann rule for financial maturity is that stumpage prices are constant over time timber price series however exhibit wide fluctuations over time which this paper models as a lognormal diffusion process comparing the diffusion results modeled here to the fixed price faustmann results show 1 the prescribed rotation length is generally longer 2 computed stand values are higher using the diffusion model with the greatest divergence occurring when a stand is about the midpoint of a rotation 3 as the stumpage price volatility increases the gain in computed npv increases though in a nonlinear fashion

harvesting and recovery decisions under uncertainty abstract a stochastic forest rotation model in the faustmann tradition is presented and exemplified the model combines harvesting decisions with the potential to recover or clean up to restore the land after very unfavorable evolutions of the stochastic growth process uncertainty is shown to have a generally ambiguous effect on the optimal choice of investment strategy it is also shown how such models can be related to theory of optimal inventory control

on the pricing of european and american foreign currency call options abstract this study uses cox ross analysis and dynamic programming techniques to price foreign currency call options we show that under certain conditions the american call price will exceed its european counterpart while under other conditions the two prices will be identical we find that the american premium is a complex function of the degree to which an option is in or out of the money and that this premium is greatest when an option is near in or out we present empirical evidence which shows that the american model significantly improves upon a european model however significant pricing errors associated with the american model remain

the dynamic behavior of efficient timber prices a simple theoreticalmodel of a tim consist ing of faustmann rotations evalubermarket finds that there exists a rational expecta ated at the mean of the price process tions equilibrium in which prices evolve according the central question addressed in this to a stationary a r 1 process simulations analyz e study is what is the appropriate model of a model with a more general representation of tim timber prices this is an important quesber stock dynamics implications for the optimal tion given the prescriptive nature of the harvesting literature are 1 market efficiency pro timber harvesting literature3 vides little justification for random walk prices 2 and evidence unit root tests used in previous studies to analyz e that the form of the price process strongly the informational efficiency of timber markets do influences the performance of a reservanot distinguish between efficient and inefficient tion price rule relative to the faustmann markets and 3 failure to recognize asymmetric rotation haight and holmes 1991 plandisturbances in time series analyses of historical tinga 1998 nonetheless most authors aptimber prices can lead to sub optimal harvesting pear to select the form of the price process rules

the effect of catastrophic risk on forest investment decisions abstract we analyze the effect of catastrophic risk on forest investment decisions by employing a forest level model where the output price is specified to follow a stochastic process we then incorporate a poisson jump process to reflect the occurrence of catastrophic events it is found that the presence of catastrophic risk always results in a reduced production value but an increased investment threshold for a forestry project however depending on the assumption regarding the option whether the right to invest can be maintained after the occurrence of such an event the degree and pattern of the effect are different

on solving the multirotational timber harvesting problem with stochastic prices a linear complementarity formulation this article develops a two factor real options model of the harvesting decision over infinite rotations assuming a known stochastic price process and using a rigorous hamilton jacobi bellman methodology the harvesting problem is formulated as a linear complementarity problem that is solved numerically using a fully implicit finite difference method this approach is contrasted with the markov decision process models commonly used in the literature the model is used to estimate the value of a representative stand in ontario s boreal forest both when there is complete flexibility regarding harvesting time and when regulations dictate the harvesting date

informational efficiency of markets for stumpage reply we appreciate the opportunity to reply to hultkrantz s comment on our analysis of the informational efficiency of markets for pine sawtimber stumpage in the u s south washburn and binkley the efficiency or inefficiency of stumpage markets does indeed have important implications for forest management decisions and we are pleased by hultkrantz s interest in the subject his comment makes many valid points and furthers the debate on stumpage market efficiency there are however some issues raised by hultkrantz that require discussion clarification or correction our reply proceeds in five stages first we clarify the meaning of stumpage market efficiency and illustrate its consequences for the time series behavior of stumpage prices and for the profitability of priceresponsive timber harvesting strategies second we argue that the price elasticity of aggregate timber supply has little relevance to the question of stumpage market efficiency third we show that hultkrantz s analysis of the stationarity of southern pine stumpage prices and our analysis of the serial relationship between departures from equilibrium rates of stumpage price change are simply alternative means of testing the hypothesis that stumpage markets are weak form efficient fourth we argue that hultkrantz s results are largely consistent with those presented in washburn and binkley finally we interpret the results of tests of stumpage market efficiency to date and suggest a path forward

the long run decline in the share of agricultural and food products in international trade a gravity equation approach to its causes the objective of this study is to determine the causes of the loss of share of agricultural products and food in international trade the article compares using a gravity model the impact of various factors upon bilateral trade in agricultural products in manufactures and in total trade between 1963 and 2000 for a representative sample of 40 countries the results clearly demonstrate how the low demand elasticity for agricultural products and food the high degree of protectionism to which they were subjected and their meagre share in intra industrial trade are the principal causes of their relatively slow growth