the choice of a monetary instrument in a small open economy the case of korea abstract using a small macroeconometric model of korea this paper evaluates the correct choice of a monetary instrument either the money stock or the interest rate the optimal multiperiod policy and the value of current information on some monetary varialbles

option pricing and timberland s land use conversion option reply thomson s response to my recent article zinkhan 1991 in this journal proposes an alternative approach for valuing a timberland land use conversion option the most significant distinction between the zinkhan model zm and the thomson model tm is the selection of different analogies for two black scholes option pricing model parameters the underlying asset price and the exercise price thomson defines the adjusted price of the alternative land use s in his response to be the underlying asset price the sum of the land expectation value for continuous forest production lev and the physical costs associated with converting from timber to the alternative land use cc is treated as the exercise price x in contrast the gap sadj in zinkhan between the price of the alternative land use pal to after adjustment and the highest bid received for the given tract poffo after adjustment serves as the underlying asset price in the zm zinkhan assumes that the exercise price x is the sum of two values as of the time of expiration of the option t cc and the absolute value of the negative impact on lev resulting from a deviation if any from the optimal rotation age i there are several serious problems associated with the tm first the tm does not recognize the landowner s forfeiture of the land use conversion option from timber production to some alternative use if the tract is converted thus the opportunity cost associated with conversion is underestimated given thomson s framework for estimating the land use conversion option s value a solution to the problem would be indeterminable if the exercise price was simply modified through the addition of an estimate of the land use conversion option a solution would be unattainable since exercise price is an input in the process of calculating the same land use conversion option zinkhan partially avoids this problem by utilizing poffo rather than levo when estimating sadj where a bid is considered by the landowner only if poff levo poffo which is subtracted from palto after necessary adjustments in order to maintain the zm analogy for underlying asset price might at least partially reflect the value of the land use conversion option in contrast the tm s lev does not reflect this option value because of the possibility that the market clearing price of the cutover timberland tract at time 0 will

the effects of development constraints on forest management at the urban forest interface this article develops a model of a forest owner operating in a small open city environment where the rent for developed land is increasing concave in nearby preserved open space and is rising over time reflecting an upward trend in households income within this framework we examine how changes in nearby preserved open space and alternative development constraints affect an individual private landowner s decisions regarding both regeneration harvests and conversion dates we also examine how such policies affect development density once conversion from forestry to residential use occurs we show that when residential rents change over time the nature of the timber problem at the urban forest interface changes because it forces us to allow for the possibility of changes in land use from timber to residential use as a result the traditional faustmann setup is not suitable to study forest management decisions at this interface we also find that in the presence of rising income increases in permanently preserved open space hasten regeneration and conversion cuts of a neighboring parcel currently under forest use and leads to lower density development once conversion takes place compared to the case where income is constant we also find that both a binding development moratorium and a binding minimum lot size policy can postpone regeneration and conversion cut dates and thus help to protect open space even if only temporarily however the policies do not have the same effects on development density of converted forestland while the former leads to high density development the latter encourages low density development

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

combination monetary policies to stabilize price and output under rational expectations sargent and wallace 1 1 12 conclude that in a model with a lucas type supply curve and the assumption of rational expectations there is no sense in which the monetary authority has the option to conduct countercyclical policy 12 p 177 sargent and wallace confine their analysis to pure money stock or interest rate policies woglom 14 drawing on the earlier work of poole 10 leroy 5 and leroy and waud 6 examines the effectiveness of combination policies within a model where expectations are formed rationally and with a lucas type supply schedule within the poole or woglom models a combination policy amounts to setting a deterministic relationship between the money stock and the interest rate leroy and leroy and waud make clear that the ability to execute such combination policies depends on the current observability to the monetary authority of the interest rate and money stock or level of reserves in the leroywaud framework since the monetary authority s policy setting is conditioned on such current information while in woglom s framework private agents expectations are conditioned only on past information systematic policy actions the parameters of the combination policy will affect the distribution of real output the sargent wallace

evaluating natural resource investments notwithstanding impressive advances in the theory of finance over the past 2 decades practical procedures for capital budgeting have evolved only slowly the standard technique which has remained unchanged in essentials since it was originally proposed see dean 1951 bierman and smidt 1960 derives from a simple adaptation of the fisher 1907 model of valuation under certainty under this technique expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk and the resulting present value is compared with the cost of the project this standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory but see brennan 1973 bogue and roll 1974 turnbull 1977 constantinides 1978 the inadequacy of this approach to capital budgeting is widely acknowledged although not widely discussed its obvious deficiency is its the evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices it is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing and abandoning them the approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern

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

spatial interactions in multiple use forestry and substitution and wealth effects for the single stand abstract forestry models often ignore spatial relationships between forest stands this paper isolates the effects of stand interactions in multiple use forestry through a straightforward extension of the single stand model effects of stand interactions decompose into wealth and substitution effects and may cause time varying patterns of resource use for a forest stand simulations illustrate that a stand s role even in steady state may alternate an emphasis on timber with an emphasis on nontimber optimal management plans differ substantially depending on whether the manager values nonmarket goods from neighboring stands the model offers insights for improving heuristic forest level optimization models in current usage

how is the debt managed learning from fiscal stabilizations this paper provides evidence on the behavior of public debt managers during fiscal stabilizations such episodes provide valuable information on the way debt instruments are chosen because they allow to overcome the problem that policymakers expectations of interest rates are generally not observable we find that governments increase the share of fixed rate long term debt denominated in the domestic currency the higher is the conditional volatility of short term interest rates the lower are long term interest rates and the stronger is the fall in long term rates that follows the announcement of the stabilization program by contrast conventional measures of the relative cost of issuing long term debt such as the long short interest rate spread are not significant this evidence suggests that debt managers tend to prefer long to short maturity debt because they are concerned about the risk of refinancing at higher than expected interest rates however when long term rates are high relative to their expectations they issue short maturity debt to minimize borrowing costs

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

monetary and fiscal policies under two alternative types of rules abstract this paper considers the relative advantage of two types of monetary and fiscal feedback rules when the private agents have full current information the appropriate combination of monetary and fiscal feedback on past disturbances dominates the contemporaneous feedback in stabilizing the real output and the price level this dominancy however disappears when the exchange rate stability is included in the objective function or when the currently observable variables are limited in general there exist some tradeoffs among feedback parameters some of the policy coefficients can be set arbitrarily enabling the optimal policy rules to be specified in many equivalent ways

the value of adaption climate change and timberland management abstract adaptation to exogenous change occurs on both intensive and extensive margins whether and how one accounts for human adaptation directly affects estimates of the economic consequences of environmental change estimates that are both critical in informing policy decisions and notoriously difficult to value this paper introduces and applies an analytical framework for placing an economic value on adaptation we explore the issue first in a stylized model that facilitates making concrete generalizations about the kinds of adaptations that generate high or low economic value we then test the soundness of our insights by incorporating learning and adaptive decision making into a structural dynamic forestry model where climate change is imposed exogenously and agents respond optimally using downscaled climate projections integrated with site and species specific timber productivity data we estimate the economic value of adaptation to climate change within the california timber industry we find on the intensive margin changing the rotation intervals will yield a low value of adaptation but on the extensive margin replanting more suitable tree species can yield significant value

a balanced budget constraint in modern stochastic macromodels currently september 1985 a constitutional balanced budget amendment is pending in the u s senate thirty two states have passed resolutions calling for a constitutional convention to enact such an amendment in 1963 senator harry byrd sr asked budget director kermit gordon what balancing the budget would do for the country gordon replied that it probably would add about 2 5 million people to the rolls of the unemployed delay the recovery about four years and knock 10 percent off u s output 16 284 the keynesian conventional wisdom of the 1960s was that fiscal and monetary policy should focus on the benefit cost tradeoffs between inflation and unemployment stabilization along with tradeoffs implicit in resource allocation and the distribution of income given these objectives there should be no independent consideration of the budget deficit of the federal government 24 as abba lerner argued in his early statement of keynesian principles of functional finance the instruments to prevent unemployment and inflation are not available until it is recognized that the size of the national debt is relatively unimportant 17 302 as outlined by walter heller 15 and others the stabilization role of fiscal policy together with monetary policy in the 1960s was to provide the appropriate degree of stimulus or restraint to achieve a target level of real output since the mid 1960s such a role for fiscal policy has been challenged first by the friedman phelps 14 27 accelerationist hypothesis and then by the lucas sargent 19 29 policy ineffectiveness proposition the accelerationist or natural rate theory especially as advanced by milton friedman argues that stabilization policy should be geared toward rules and control of nominal variables such as the inflation rate friedman s analysis also implies the futility of using aggregate demand policy to achieve fixed output targets friedman s analysis suggests the possibility that with monetary policy geared to price stabilization and with sustainable real output gains not attainable via aggregate demand policy fiscal policy instruments may be adjusted to achieve a balanced budget without cost buchanan and wagner 7 rely on friedman s analysis to support their call for a constitutional balanced budget amendment

choosing a monetary instrument the case of supply side shocks abstract this paper examines the monetary instrument choice problem in models with an explicit supply sector and endogenous prices and price expectations we use the popular linear quadratic certainty equivalence framework to obtain analytic solutions the results indicate that interest rate policies generally are better able to insulate the real sector from unanticipated supply shocks we also show that at this level of abstraction the optimal choice of an instrument is independent of the specification of expectations e g rational vs adaptive price expectations the paper then reports empirical evidence from two experiments on the large nonlinear mit penn ssrc econometric model the evidence is consistent with the hypothesis that interest rate policies are preferable if the supply sector is the major source of uncertainty

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 decision to conserve or harvest old growth forest abstract the decision to harvest or conserve old growth forest is formulated as a stochastic decision problem in continuous time uncertainty in future amenity values for standing forest and in future timber revenues for harvested forest are included in the model along with the risk of catastrophic destruction by fire pest infestation etc it is shown how the decision problem can be expressed as an optimal stopping problem which can be solved analytically the optimal decision rule is shown to depend on how the ratio of current timber value to the current expected present value of amenity benefits foregone through harvesting compares with some critical level the effects of changes in uncertainty and other parameters on the optimal rule are discussed also it is shown how the cost benefit analysis and certainty equivalence procedures lead to premature harvesting and the expected loss in survival time for these sub optimal procedures is calculated

optimum forest rotation in an imperfect stumpage market with a changing demand function the purpose of this study is to determine the behavior of optimum lengths of forest rotation periods under conditions of imperfect markets and non constant real price behavior for stumpage the analysis expands on the previous work by nautiyal and fowler 1980 and newman gilbert and hyde 1985 determination of optimum forest rotations is an important problem facing forest managers there has been considerable debate as to which criterion should be used for this determination one criterion based on traditional forest management is production of maximum sustained yield per unit time other widely accepted criteria have been centered around maximum net

time consistency of fiscal and monetary policy a comment in an important recent contribution persson persson and svensson 1987 hereafter pps suggest that through careful restructuring of its nominal and real debt obligations a government may be able to induce future governments to follow the monetary and fiscal policies that it regards as optimal today the pps argument builds on lucas and stokey s 1983 demonstration that in a special nonmonetary setting the time inconsistency of optimal fiscal policy can be avoided through managing the term structure of real government obligations to the public the basic idea of the pps scheme for monetary economies is disarmingly intuitive in addition to continually restructuring nominal and real debt obligations a la lucas stokey each government must ensure that the next government inherits a stream of nominal claims on the public whose present discounted value equals the stock of money this equality pps argue removes the incentive for surprise inflation or deflation because such surprises would not affect the real net worth of the government this note shows that the pps prescription for avoiding time inconsistency appealing as it is is not generally sufficient even under the debt restructuring they recommend optimal policy is likely to be time inconsistent the main reason why their scheme fails is that the restrictions it imposes on government asset stocks satisfy first order but not second order conditions for an optimum because of the complex interactions between the current price level and future interest rates a government can raise its objective function by moving several variables at once away from the levels planned by the previous government even though price level changes alone would not affect government net worth we develop our argument using the model notation and equation numbers of pps to which the reader is referred for details the maximization problem associated with

simple binomial processes as diffusion approximations in financial models a binomial approximation to a diffusion is defined as computationally simple if the number of nodes grows at most linearly in the number of time intervals it is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models the convergence of the sequence of bond and european option prices from these processes to the corresponding values in the diffusion limit is also demonstrated numerical examples from the constant elasticity of variance stock price and the cox ingersoll and ross 1985 discount bond price are provided article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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

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

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

inflation and taxation with optimizing governments this paper examines the empirical validity of the predictions that if governments minimize the deadweight loss from raising revenue through inflation and tax finance there should be a positive contemporaneous association between inflation and the level of tax burdens the authors examine the empirical validity of this prediction using data from great britain france germany japan and the united states inflation and tax rates are as likely to be negatively as positively correlated so the results cast doubt on the empirical relevance of simple models in which governments with time invariant tastes choose monetary policy to equate the marginal deadweight burdens of inflation and taxes copyright 1990 by ohio state university press

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

searching for an optimal rotation age for forest stand management under stochastic log prices due to rapid change in timber prices in the japanese market most likely affected by imported timber from countries such as the u s canada and the nordic countries the domestic forest managers have been facing a large degree of future price uncertainty because of this it becomes necessary to take the future price uncertainty into account within the forest management framework in this paper the continuous time stochastic process i e the geometric brownian motion has been used to model the log price process the binomial option pricing approximation was then applied to value the sugi cryptomeria japonica and hinoki chamaecyparis obtusa forested land under stochastic log prices in order to search for an optimal rotation age our experiments with the proposed two state stochastic dynamic programming model showed that when the current log price is high enough to cover all costs an optimal rotation age from the stochastic price and deterministic price models coincides although the total expected present net value from management activities differs also it was shown that as the current log price decreases an optimal rotation age derived from the stochastic price model becomes longer than that from the deterministic price model if the current log price further decreases then forest management will be abandoned and the forest stand will be converted into alternative uses

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

achieving external and internal targets with exchange rate and interest rate intervention abstract this paper analyses how exchange rate and interest rate intervention rules can be computed so as to stabilize price and output and real exchange rate in the face of a variety of random shocks the major finding is that there exist a unique optimal intervention rule for both internal and external targets in the face of all random disturbances except for lm and foreign interest rate disturbances

optimal fiscal and monetary policy in an economy without capital abstract this paper is concerned with the structure and time consistency of optimal fiscal and monetary policy in an economy without capital in a dynamic context optimal taxation means distributing tax distortions over time in a welfare maximizing way for a barter economy our main finding is that with debt commitments of sufficiently rich maturity structure an optimal policy if one exists is time consistent in a monetary economy the idea of optimal taxation must be broadened to include an inflation tax and we find that time consistency does not carry over an optimal inflation tax requires commitment by rules in a sense that has no counterpart in the dynamic theory of ordinary excise taxes the reason time consistency fails in a monetary economy is that nominal assets should from a welfare maximizing point of view always be taxed away via an immediate inflation in a kind of capital levy this emerges as a new possibility when money is introduced into an economy without capital

regime switching in stochastic models of commodity prices an application to an optimal tree harvesting problem abstract this paper investigates whether a regime switching model of stochastic lumber prices is better for the analysis of optimal harvesting problems in forestry than a more traditional single regime model prices of lumber derivatives are used to calibrate a regime switching model with each of two regimes characterized by a different mean reverting process a single regime mean reverting process is also calibrated the value of a representative stand of trees and optimal harvesting prices are determined by specifying a hamilton jacobi bellman variational inequality which is solved for both pricing models using a implicit finite difference approach the regime switching model is found to more closely match the behavior of futures prices than the single regime model in addition analysis of a tree harvesting problem indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models

comment choosing a monetary instrument the case of supply side shocks abstract in a recent paper craine and havenner 1981 claim that an additional advantage of the linear quadratic framework which is not well known is that the basic forces affecting the instrument choice decision can be analyzed without an explicit specification for price expectations since the distribution of the error terms in a linear model is independent of the predetermined variables p 219 the aim of this note is to demonstrate that craine and havenner s claim does not generalize to models with expectations of future variables conditioned on present information such as turnovsky s 1980 model

irreversible investment under interest rate variability some generalizations we study the impact of interest rate and revenue variability on the decision to carry out irreversible investment we provide a mathematical characterization of the two dimensional optimal stopping problem and show that interest rate variability has a decelerating or accelerating impact on investment depending on whether the current interest rate is below or above the long run steady state allowing for interest rate volatility decelerates investment by raising both the required exercise premium of the investment opportunity and the value of waiting finally increased revenue volatility is shown to strengthen the negative impact of interest rate volatility and vice versa

optimal forest rotation and land values under a borrowing constraint abstract this study relaxes the assumption of perfect capital markets in the classical faustmann forest rotation model a constraint on borrowing changes all the basic properties of optimal forest harvesting instead of a constant rotation period an infinite chain of rotations is determined by a nonlinear difference equation the rotation period evolves over time and approaches a stationary rotation in finite or infinite time the length of optimal rotation timber supply and the value of forest land depend on forest owner specific factors that are normally nonexistent in rotation problems the model explains several empirical findings that cause problems for the classical versions of the faustmann model

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

an investigation of the harvest decision of timber firms in the south east united states in the forestry literature stochastic extensions of the classic faustmann model have become the predominant models of optimal harvesting on even aged timber stands a recent attempt to estimate a stochastic version of the faustmann model left several puzzling results unexplained provencher 1995 this paper reports on new estimation and analyses undertaken to resolve these puzzles of particular note is the result that the value of using correct price forecasts in the harvest decision is much lower than indicated by recent simulation studies perhaps because variability in convenience yield dampens the expected gain from exploiting stochastic variation in timber prices

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

seigniorage and tax smoothing in the united states 1914 1986 abstract when monetary and fiscal authorities cooperate to minimize the distortionary costs of financing an exogenous stream of government expenditures barro s tax smoothing model implies a long run relationship between tax revenues and inflation previous empirical tests of this relationship are reinterpreted in light of recent work on cointegration and are shown to hold only when stochastic temporal variation in the excess burden of taxes and seigniorage is transitory in nature a new test that holds in the presence of nonstationary disturbances is developed and applied annual u s data from the period 1914 to 1986 reject the revenue smoothing hypothesis

time consistency of fiscal and monetary policy the problem of time inconsistency arises from two different sources first as shown by guillermo a calvo 1978 the re is an incentive for each government to engage in an initial unanti cipated inflation second as discussed by robert e lucas and nancy l stokey 1983 there is an incentive for each government to deviat e from the path of taxes announced by the preceding government in th is paper it is shown that these two sources of time inconsistency ca n be removed by a particular method of debt management involving bot h nominal and indexed government bonds of various maturities copyright 1987 by the econometric society

bond and option pricing when short rates are lognormal this article describes a one factor model for bond and option pricing that is based on the short term interest rate and that allows the target rate mean reversion and local volatility to vary deterministically through time for any horizon the distribution of possible short rates is lognormal so the rate neither falls below zero nor reflects off a barrier at zero a model like this allows one to match the yield curve the volatility curve and the cap curve surprisingly adding to future local volatility lowers the volatility curve a conventional binary tree with probabilities of 0 5 but variable time spacing is used to value bonds and options when the inputs are constant the slope of the yield curve starts out positive and ends up negative while its curvature shifts from negative to positive even when mean reversion is zero the volatility curve has a negative slope the differential cap curve rises steeply through the effects of volatility and then falls steeply through the effects of discounting and a falling forward rate used as the strike price

forest taxation and rotation age under private amenity valuation new results abstract this paper studies the impact of harvesting property and profit taxes on private rotation age in an ongoing rotations model where the private landowner is interested not only in the present value of harvest revenue but also in the private amenity services provided by the forest stand the main finding of the paper is that conventional wisdom about the rotation effects of forest taxes distilled from the faustmann model predominantly ceases to hold this is because forest taxes distort the relative profitability of timber and amenity production in a way that is sensitive to the precise nature of amenity valuation therefore the design of forest tax policy necessitates good knowledge of the landowner s objective function concerning the type of amenity services

optimal maturity of nominal government debt abstract we report a first set of empirical results obtained from estimating on u s data a model of the optimal maturity structure of nominal government debt in a context where there is no full policy precommitment and markets are incomplete

the optimality of nominal income targeting when wages are indexed to price in the last decade there has been renewed interest in alternative monetary regimes institutions and policy procedures one policy proposal that has received increased attention is nominal income targeting this proposal has been suggested for instance by feldstein 9 gordon 13 hall 16 meade 21 and tobin 25 26 taylor 24 discusses this proposal in some detail and mccallum 20 presents a statistical analysis of a particular nominal income targeting rule in a variety of contexts bean 3 presents a theoretical analysis of nominal income targeting examining the properties of such a policy in a stochastic macro model in which rational agents sign nominal wage contracts given that the monetary authority s objective is to minimize the divergence of output from its full information level nominal income targeting is the optimal policy if labor supply is perfectly inelastic with an elastic labor supply however nominal income targeting provides the optimal response to demand side shocks but not to supply side shocks the problem of designing optimal policy in the face of both demand and supply side shocks is not new authors such as benavie and froyen 4 craine and havenner 8 parkin 22 and turnovsky 27 have stressed that pure policy rules such as a strict money rule or an interest rate peg are generally not the optimal policy response to both demand and supply shocks thus bean s result that nominal income targeting provides the optimal policy response to all shocks as long as labor supply is perfectly inelastic is rather impressive one avenue of research that attempts to provide a partial solution to the problem of suboptimal policy rules in the face of demand and supply shocks is the investigation of wage indexing work by gray 14 15 drew attention to the properties of nominal wage contracts indexed to the price level the relation between the monetary authority s choice of policy rule and the degree of indexing in the labor market has been investigated by fethke and policano 11 fethke and

waiting to invest investment and uncertainty the textbook analysis that accepts all projections with positive net present values as positive is quite generally wrong the ability to delay a project means that almost every project competes with itself postponed with uncertain interest rates even the simplest of projects has an option value the effect of interest rate uncertainty on the optimal delay of investment is sizable this implies that the rate of aggregate investment will depend on both the level of the real interest rate and the degree of interest rate uncertainty furthermore it is not necessarily true that investment rises with a fall in interest rates copyright 1992 by university of chicago press

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

on the use of period average stumpage prices to estimate forest asset pricing models several recent papers thomson 1987 zinkhan 1988 zinkhan and mitchell 1988 cubbage harris and redmond 1988 binkley and washburn 1988a 1988b including one in this journal redmond and cubbage 1988 use either sharpe s 1963 single index market model with returns to the overall market portfolio serving as the index or the capital asset pricing model capm sharpe 1964 lintner 1965 to measure the risk and evaluate the performance of timberland investments the capm specifies an equilibrium relationship between asset i s expected rate of return eri the risk free rate of return rf and the expected risk premium on the market portfolio of all assets in the economy the expected market rate of return erm minus the risk free rate rf

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

optimal maturity of nominal government debt an infinite horizon model the role of debt maturity is analyzed in a framework that blends tax smoothing with time inconsistency of optimal policy when policymakers have an incentive to use unanticipated inflation to reduce the real value of nominal government liabilities three conclusions emerge 1 nominal debt leads policymakers to resort to inflation even though in equilibrium inflation collects no revenue 2 when under full precommitment the optimal policy calls for complete tax smoothing and a constant debt level the equilibrium policy without precommitment calls for anticipating tax collection and early debt repayment and 3 management of debt maturity is an essential component of the equilibrium policy copyright 1992 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

thinning and harvesting in stochastic forest models abstract this paper analyzes a stochastic forest growth model in which the manager is able to first thin the forest to promote better growth before harvesting both wicksell single thinning and harvesting cycle and faustmann on going rotation problems are considered the wicksell problem is analyzed by first restricting the class of decision times to thinning harvesting pairs that bound the growth away from infinity and imbedding the problem in an infinite dimensional linear program on a space of triplets of measures these measures capture the thinning and harvesting decisions along with the behavior of the growth process prior to harvest an auxiliary linear program then leads to a nonlinear optimization problem for which an optimal value and solution are determined the values of all the problems are be related through a set of inequalities the solution of the nonlinear problem determines random thinning and harvesting times for the single thinning and harvesting cycle which demonstrate the equality of the values of these various problems finally for the wicksell problem the unrestricted class of thinning and harvest times is shown to give the same value as the restricted class the faustmann on going thinning and harvesting rotation problem is reduced to a wicksell problem which then allows for the characterization of the value as the solution to a different nonlinear optimization problem the effects of the opportunity to thin the forest are illustrated on a mean reverting stochastic model

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

planning timber production with evolving prices and costs the traditional faustmann solution to the timber harvesting problem was developed for an environment in which prices costs and technology were constant recent contributions recognizing the evolution of economic institutions have developed solutions to optimal harvesting problems under a variety of more realistic assumptions nautiyal and fowler 1980 show that the socially desirable rotation in a monopolistic situation is longer than that which maximizes the monopolist s present worth but is shorter than the atomistic rotation p 213 heaps and neher 1979 derive the optimal rotation when the rate of harvest is constrained bare and waggener 1980 investigate the value of timberland when timber prices change using a traditional faustmann model murphy fortson and bethune 1977 deal with an imperfect capital market one problem not addressed by recent contributions concerns the violation of the assumption of constant price and cost functions for timber production this assumption clearly does not hold stumpage prices exhibit substantial short run fluctuations and systematic long run trends for southern pine and douglas fir two species that are potential crops for timber plantations historical evidence demonstrates that stumpage prices relative to other price have grown steadily for the period 1913 1978 the ratio of southern pine stumpage price to prices paid by farmers increased at a 4 annual rate while the same ratio for douglas fir increased at an annual rate of 5 7 1 for douglas fir and southern pine forecasts of prices and costs based on his

the financial structure of government debt in oecd countries an examination of the time consistency issue abstract this paper analyzes the financial structure of government debt in the oecd countries from the perspective of time consistency problems with a focus on debt held by financial institutions testable implications from a theoretical time consistency model are derived and incorporated into the framework of a cost minimizing model for public debt service the approach is tested for a sample of 15 oecd countries over the period 1974 1989 the theoretical analysis and the empirical results show how in addition to maturity ownership of government debt in those oecd countries with debt accumulation problems can be related to time consistency considerations

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

general properties of option prices when the underlying price process is a one dimensional diffusion as well as in certain restricted stochastic volatility settings a contingent claim s delta is bounded by the infimum and supremum of its delta at maturity further if the claim s payoff is convex concave the claim s price is a convex concave function of the underlying asset s value however when volatility is less specialized or when the underlying process is discontinuous or non markovian a call s price can be a decreasing concave function of the underlying price over some range increasing with the passage of time and decreasing in the level of interest rates much of the financial options literature derives precise option prices when the underlying asset price process is completely specified since it is empirically difficult to ascertain what the true underlying process is another part of that literature is concerned with deriving general properties of option prices when the underlying price process is not fully specified but instead is assumed to belong to some general class of stochastic processes merton 1973 cox and ross 1976 jagannathan 1984 in particular in the absence of arbitrage opportunities and assuming that the risk neutralized stock price follows a proportional stochastic process a risk neutral return distribution independent of price merton 1973 and jagannathan 1984 show that a call option s price is an increasing convex function of the stock price cox and ross 1976

the optimal forest rotation with evolving prices timber is unique among natural resources in that its price shows a long term increasing trend relative to the price of other goods ruttan and callahan 1962 manthy 1978 adams and haynes 1980 in the best known forest econometric model project this trend to continue one explanation for this secular rise in price relates to the virtual mining of the standing stock of old growth mature timber and its positive effect on real stumpage prices hotelling s 1931 theory of the mine postulates that as a stock of nonrenewable re

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 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

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

measure twice cut once optimal inventory and harvest under volume uncertainty and stochastic price dynamics abstract natural resources are often subject to state uncertainty resource abundance is not known with certainty but can be measured measurements are typically imperfect and costly to obtain the decision of whether to invest in resource measurement may be influenced by other state variables for example a resource commodity price we introduce a mixed observability model of optimal forest management featuring a partially observable forest resource and perfectly observable stochastic price the decision maker optimizes the expected net present value of forest returns by choosing when to measure current forest volume conduct an inventory harvest and replant or delay action parameter values are obtained from numerous forestry data sources optimal investment in inventory reduces the cost of uncertainty about timber volume and increases the predictability of returns moreover price stochasticity interacts with inventory decisions to produce asymmetric effects of high and low prices on inventory timing we also produce the first graphical faustmann rule analogues for jointly optimal inventory and harvest