a real options approach to the valuation of a forestry investment abstract the theory of real options is used to model the optimal tree harvesting decision the value of the option to harvest is estimated using a dynamic programming approach and a general numerical solution technique suitable for any type of stochastic process for prices the conditions under which the optimal harvest time is independent of price are examined in addition the impact of assuming future lumber prices are mean reverting is considered it is found that option value and optimal cutting time are significantly different under the mean reversion assumption compared to geometric brownian motion

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

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

forest valuation under the new zealand emissions trading scheme a real options binomial tree with stochastic carbon and timber prices under the new zealand emissions trading scheme forests planted on or after january 1 1990 earn carbon credits these credits have to be repaid when the forest is harvested this paper analyses the effects of this scheme on the value of bareland on which radiata pine is to be planted a real options method is developed and applied assuming stochastic carbon and timber prices we find that land value increases by about 73 with the optimal rotation age substantially lengthened the derived optimal harvest price thresholds are useful in deciding whether to harvest or to wait jel q23 q28

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

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

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

wicksellian theory of forest rotation under interest rate variability abstract we apply the wicksellian single rotation framework to cover the unexplored case of variable and stochastic interest rate we provide a mathematical characterization of the two dimensional optimal stopping problem and show in the presence of amenity valuation that increased interest rate volatility lengthens the optimal rotation period and increases the value of the optimal policy by modelling the interest rate as a mean reverting process and forest value as a geometric brownian motion and abstracting from amenity valuation we present an explicit solution for the problem numerical illustrations indicate that interest rate volatility has a significant and non linear impact on optimal rotation

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

good timing the economics of optimal stopping abstract this paper presents an economic interpretation of the optimal stopping of perpetual project opportunities under both certainty and uncertainty prior to stopping the expected rate of return from delay exceeds the rate of interest the expected rate of return from delay is the sum of the expected rate of change in project value and the expected rate of change in the option premium associated with waiting at stopping the expected rate of return from delay has fallen to the rate of interest viewing stopping in this way unifies the theoretical and practical insights of the theory of stopping under certainty and uncertainty

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

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

government debt government spending and private sector behavior a current period tax reduction financed by issuing government debt shifts the timing of tax collection from the current period to the future if the future taxes implied by government debt are not fully perceived and discounted by the private sector there will be a net wealth effect that increases private sector consumption thus reducing capital accumulation and growth if on the other hand the implied future taxes are perceived and discounted by the private sector the current period tax reduction will be used to increase private saving to pay for the future taxes and government debt will be absorbed without any real effects on the economy the effects of government spending financed by current period taxation also depend upon private sector perceptions 2 if the benefits of government spending are ignored private sector consumption will decrease in accordance with the reduction in permanent disposable income to the extent that government spending is on consumption type goods that are perceived as substitutes for privately provided consumption goods there will be a relatively greater reduction in private sector consumption to the extent that government spending is on investment type goods yielding future goods and services that are perceived as substitutes for future privately provided consumption goods there will be a relatively smaller reduction in private sector consumption the standard approach to modeling private sector consumption saving behavior involves a rather asymmetric set of assumptions as to how the private sector perceives the various elements of government fiscal policy 3 current period taxes are assumed to be fully perceived but current period government spending is implicitly assumed to be completely ignored by the private sector in considering permanent personal disposable income the private sector is assumed to be forward looking in its assessment of income and taxation the stock of government debt is nevertheless included as part of the stock of private wealth the implicit assumption associate professor of economics graduate school of business university of chicago 1101 east 58th street chicago il 60637 i thank eugene fama levis kochin michael mussa paul evans and an anonymous referee for helpful comments i am particularly grateful to daniel benjamin for contributing many hours of discussion and laura lahaye who was a research assistant and valuable adviser on earlier drafts the theoretical debate on the burden of the debt has been long standing gerald o driscoll 1977 documents ricardo s nineteenth century position robert barro 1974 reopened the debate by introducing the fundamental issue of intergenerational transfers also discussed in merton miller and charles upton 1974 the empirical side of the debate was initiated by levis kochin s 1974 attempt to test for the effects of deficits on consumption and by martin feldstein s 1974 attempt to test for the effects of social security wealth on consumption other empirical contributions include jess yawitz and laurence meyer 1976 myself 1978 and j earnest tanner 1978 1979 with respect to the effects of government deficits and debt and barro 1978 michael darby 1979 and dean leimer and selig lesnoy 1982 with respect to social security wealth see also interesting recent papers by john seater 1982 who generates detailed tests of the effects of deficits and debt on consumption charles plosser 1982 who explores the effects of government spending and debt shocks on interest rates and feldstein 1982 who attempts tests similar to some in this paper see fn 29 2martin bailey s 1962 1971 development of the effects of government spending on private consumption and aggregate economic activity is the seminal contribution paul david and john scadding 1974 extend bailey s ideas and provide some supporting empirical evidence more recently willem buiter 1977 and myself 1978 developed models based on bailey s earlier work barro 1981 has an interesting paper on related issues see also david aschauer 1982 3the standard approach incorporates fiscal policy through the concept of personal disposable income and by including the stock of government debt as part of personal wealth see for example the empirical specification of albert ando and franco modigliani 1963 which has been the basis of most empirical consumption studies since and feldstein 1974 for one of the more influential papers based on the ando modigliani specification

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

on the elasticities of harvesting rules abstract in this paper we rank the relative importance of the exogenous parameters upon the optimal harvesting size in a stochastic rotation problem we show that when the tree growth follows geometric brownian motion the harvesting size is most elastic to the harvesting cost followed by the interest rate and is least elastic to the parameters of tree growth similar ranking holds for the linear growth case in both cases the harvesting size is increasing and concave in the harvesting cost bounded between two parallel lines the harvesting decision is made according to a stochastic extension of the faustmann formula

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

welfare analysis when budget constraints are nonlinear the case of flood hazard reduction abstract nonlinear budget constraints occur when goods have a quality dimension or possess characteristics and the price of the composite good is a nonlinear function of its characteristics homogeneity is generally not characteristic of indirect utility functions and demand functions when budget constraints are nonlinear in this situation willingness to pay methods that impose homogeneity or fail to impose restrictions implied by nonlinear budget constraints on demands are inappropriate a straightforward method of estimating willingness to pay when budget constraints are nonlinear implements a direct utility approach exact and biased welfare measures are obtained without integration

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

the stochastic rotation problem a generalization of faustmann s formula to stochastic forest growth abstract in the present paper we study the optimal cutting strategy 1 2 for an ongoing forest by using stochastic impulse control we show how faustmann s formula can be generalized to stochastic growing forests the paper extends and clarifies previous studies by miller and voltaire 1983 clarke and reed 1989 and reed and clarke 1990