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Efforts to increase wood mobilization have highlighted the need to appraise drivers of short-run timber supply. The current study aims to shed further light on harvesting decisions of private forest owners, by investigating optimal harvesting under uncertainty, when timber revenues are invested on financial markets and uncertainty is mitigated by news releases. By distinguishing between aggregate economic risk and sector specific risks, the model studies in great detail optimal harvesting-investment decisions, with particular emphasis on the non-trivial transmission of risk on optimal harvesting, and on the way private forest owners react to news and information. The analysis of the role played by information in harvesting decisions is a novelty in forest economic theory. The presented model is highly relevant from a policy—information is a commonly used forest policy instrument—as well as a practical perspective, since the mechanism of risk transmission is at the basis of timber pricing.

Forest ownership structure is known to have implications for forest management and the production of timber and other forest products and services [

Hence, building on previous partial equilibrium studies, the current model aims to shed further light on harvesting decisions of private forest owners. In particular, we study optimal consumption-saving and harvesting decisions of a risk-averse private forest owner that is allowed to invest harvest revenues on financial markets, when uncertainty is mitigated by news release. To the best of our knowledge, this model is the first in the literature to study the role of information in determining harvesting behavior. We believe that this is an important issue to be considered also from a policy perspective, since information can be a powerful tool to induce (socially) optimal behavior.

An important caveat is in order here: the present model follows a well-established direction in the existing literature [

Using the Fisherian two-period consumption-saving-harvesting model, optimal timber harvesting under uncertainty has been extensively investigated [

Johansson and Löfgren [

The analysis of Ollikainen [

The current study investigates optimal harvesting decisions under uncertainty, when forest owners are allowed to invest harvest revenues on financial markets and uncertainty is mitigated by news release. A model is developed that—albeit, like all theoretical frameworks, a simplification of reality—incorporates elements of realism worth considering to better understand forest owner behavior. In particular, we build on both Ollikainen [

For what concerns the correlation between the asset and timber price [

Following this idea, in our analysis we assume that the asset’s dividend and the future timber price both have two distinct components: A common aggregate economic component which is determined by a shock hitting the entire economy, including the forest sector and financial markets, and two separate idiosyncratic components. For the financial asset, the specific idiosyncratic component represents financial risk, while for future timber price it reflects risk specific to the forest sector. This particular structure is interesting since it allows studying how forest owners diversify between financial and timber markets in order to reduce idiosyncratic risk, and how risk is priced in timber markets.

The main innovative feature of our framework is that we consider the arrival of news concerning the future, by means of a signal received immediately before the harvesting decision. In particular, we assume that the news concerns the real economy and either the financial or the forest sector. This representation can shed light on how private forest owners react to news and information, modifying their harvesting schedule accordingly. In particular, when analyzing the reaction to news about financial markets, the model makes it possible to assess how financial specific risk impacts on the harvesting decision, independently from economic risk. This feature is relevant, as there are examples of financial risk affecting timber markets [

Alternatively, our framework could be used to model the response of private forest owners (

Finally, the arrival of information and the presence of distinct sources of risk render the way timber and financial markets co-move non-trivial, providing some theoretical support to the contrasting findings on correlation from the empirical literature [

We consider a two-period economy in which a risk-averse private landowner wants to maximize the utility deriving from final wealth, by choosing how much to harvest and how much to invest on financial markets [

Harvesting occurs in both periods, while financial investment made at time 1 returns its payoff at time 2. In particular, denoting by _{i}_{i}_{1}_{1} are invested at time 1 on the financial market.

Two assets are available: a risk-free bond with gross return (1 _{f}_{1}_{1} invested in the risk-free asset. Therefore, the investment portfolio will be generically indicated as (1 −

Finally, we denote by

Given the amount harvested at time 1, _{1}, the stock available at time 2 is uniquely defined by the growth function _{2} = (_{1}) + _{1})

When the landowner makes his harvesting-investment decision at time 1, the future timber price _{2} and the realized dividend of the asset _{a}_{i}_{2} = _{a}_{f} m_{a}_{a}^{2}), _{i}_{i}^{2}), _{f}_{f}^{2})

_{f}

The asset dividend _{2} have a common component _{a}_{a}_{a}^{2}, can be thought of as a measure of aggregate economic (or, equivalently, undiversifiable) risk.

The two shocks _{i}_{f}_{a}_{i}_{f}_{i}^{2} and _{f}^{2} can be thought of as measures of idiosyncratic risk: financial risk (_{i}^{2}), and forest sector risk (_{f}^{2}), respectively.

While uncertainty resolves by time 2, with the realizations of the asset dividend and the timber price, some news concerning the asset already arrives at time 1 through a signal _{a}_{i}_{s}

where _{s}_{s}_{s}^{2}). Notice that the signal in itself is a random variable, however its realization becomes known one period ahead with respect to the asset’s dividend and the timber price (that is, at time 1 instead of time 2). The signal is already partially informative about the asset’s price because of the two components _{i}_{a}._{s}_{s}^{2}.

_{s}^{2} is a measure of the precision of the signal, since higher _{s}^{2} induces also higher variability of the signal and, therefore, lower precision. _{a}_{2}. In contrast, if

The informativeness of the signal with respect to the dividend and the timber price respectively is defined usually as ^{p}^{2} = (_{2}))/(^{d}^{p}^{2} is also important to notice that an increase in aggregate economic risk _{a}^{2} makes the signal more informative (higher) for the forest price, while the opposite holds for an increase in financial specific risk _{i}^{2}.

Given our assumptions, _{2}|_{2}|^{d}s^{d}_{a}^{2} + (1 − ^{d}_{i}^{2})
_{2}|^{p2}^{p2})_{a}^{2} + _{f}^{2})
_{2}|^{d}_{a}^{2}

Notice that, when the signal is specific to the asset only, that is, when _{2}|_{2}] _{2}|_{a}^{2}, since _{i}_{f}

Also notice that conditional covariance increases as aggregate economic risk increases (_{a}^{2} is), while it reduces the signal becomes more precise (_{s}^{2} is, and/or less financially specific (_{a}_{s}_{s}^{2} is sufficiently low).

At the beginning of period 1, the forest owner is endowed with a forest stock _{1}, while the future price _{2} is known to be distributed according to _{2}~_{a}^{2} + _{f}^{2}).

The revenues _{1}_{1} from timbers harvested at time 1, _{1}, are invested on financial markets; more precisely, a fraction _{1}_{1} is invested in a risk-free bond with gross return 1 _{f}_{a}^{2} _{i}^{2}).

Hence the agent’s maximization problem consists in choosing optimal current timber supply _{1}, and the investment portfolio (

Given harvesting level _{1} and the portfolio (_{2}_{2} + _{1}_{1} (1 + _{f}_{1}_{1}_{2} is given by (1).

Before the harvesting and investment decisions are taken, the agent receives some news concerning the financial market by means of a signal _{a}_{i}_{s}_{2} and _{1} and the portfolio (_{ω,x1}E_{2}_{2} + _{1}_{1} (1 + _{f}_{1}_{1}

Since both _{2}|_{2} (^{d} s_{1}_{1} (1 + _{f}_{1}_{1}(^{d} s_{1}_{1})]^{2}[

The first order conditions associated to the maximization problem (7) yield:
_{2} is given by (1).

Notice that, _{2}/_{1} < 0, (9) holds only if

When analyzing the relationship between the optimal short-run supply of timber, _{1}, and the financial portfolio (_{1}_{1} is not affected by the specific level of current harvesting _{1}. Hence, if harvesting is increased at time 1, the extra-revenues from timber sales are invested into the risk-free asset, and not in the risky one. In a similar fashion, as long as the signal on the financial market is observable, even if the landowner was given the possibility to exclusively invest in the risk-free asset [_{1} solving (9) [

In general, there is a trade-off between investing in the risk-free asset and allowing the forest to grow to time 2. This immediately appears in the first order condition (9): If _{1} (harvesting in the first period) increases and the total investment in the risk-free asset increases as well. Similarly, if _{1} or _{f}_{1} and the investment in the risk-free asset.

The increase in aggregate economic risk and in the two idiosyncratic risks impacts the short-run supply of timber (_{1}), and therefore investment. In particular, if risk in the forest sector _{f}^{2} increases, so does current harvesting _{1} and the investment in the risk-free asset, as can be expected. Similarly, if risk-aversion _{1}. The investment in the risk-free asset increases as well, but this time also because the investment in the risky asset (1 −

Inspection of the first order condition (9) reveals an interesting result: when the asset specific risk _{i}^{2} increases, this is transmitted to the optimal harvested quantity through the signal ^{p2}. If the signal conveys good news, a higher financial risk _{i}^{2} unequivocally increases short-run timber supply,

The effect of financial risk _{i}^{2} on optimal harvesting is due to the presence of the common aggregate economic component _{a}_{i}^{2} affects optimal harvest as long as the agent observes the signal, no matter if he is given the actual possibility to invest in the risky asset or not. On the contrary, if no signal was received, and/or _{2}, _{i}^{2}.

To the best of our knowledge, our model is the first in the literature to suggest that financial idiosyncratic risk can have an impact on harvesting behavior. Despite the relative difficulty in providing an accurate empirical analysis of this claim, the observation of the patterns followed by timber markets during, in particular, the first phase of the recent financial downturn might support this idea, as discussed in more detail in

Finally, it is interesting to notice how harvesting and financial investment react differently to an increase in aggregate economic risk. For simplicity, consider the case _{a}^{2} will always reduce the investment in the risky asset (1 _{1} [

This result indicates that the forest owner is behaving differently when deciding about timber harvesting compared to the evaluation of financial assets. In particular, let us consider an alternative risky asset at the place of the forest, with dividend _{2}. The first order condition associated to this problem shows that, in case of a positive signal, the variation of the investment in the second asset in response to an increase in _{a}^{2}, is ambiguous, but in this case the sign of the reaction depends on the relative magnitude of variances, expected dividend, risk-free rate and signal realization, but not on the level of risk-aversion.

Even if it is beyond the scope of this paper to empirically evaluate the validity of the framework proposed, these findings seem to suggest that timber prices and financial markets co-move in quite a complicated manner, presenting both significant and negligible correlation; as empirical evidence from the literature also seems to suggest (see

We next investigate how harvesting is affected by the “positivity” of the information conveyed by the signal.

Suppose that _{2}|

Let us denote by _{1}

Next, we define the function _{1},_{1},_{1},_{f}^{p2}_{2}[_{1}(1 + _{f}_{1}°,_{1},_{f}

An increase of the signal to _{1}°,_{1},_{f}_{2}/_{1} < 0 and ^{2}_{2}/^{2}_{1} < 0, the new equilibrium requires a lower _{1}, so that the short-run supply of wood is reduced. As a consequence, also the total investment in the financial market _{1}_{1} is reduced. In addition, given the positivity of the signal, the investment portfolio (

Summarizing, the arrival of good news induces a reduction in current harvesting (which in turn translates in a decrease of current wealth) and in the proportion of current wealth invested in the risk-free bond in favor of the one in the risky investment. The opposite happens if the signal conveys bad news (that is if

The informativeness of the signal depends on risks _{a}^{2}, _{i}^{2}, precision _{s}^{2}, and the specificity parameter, _{s}^{2}) translates into higher informativeness for both the dividend and the price. Hence, the new equilibrium requires a lower _{1} and an investment portfolio more tilted towards the risky investment (that is, higher (1 − _{1}, but also because of the change in the optimal portfolio composition.

If good news arrives (

In the following we assume that the signal, _{a}_{f}_{s}

If _{2} is given by (1).

As before, since _{2}/_{1} < 0, the first order condition associated to optimal harvesting holds only if

Using this alternative formulation, one obtains that _{f}^{2} affects the optimal investment in the financial asset while the specific financial risk _{i}^{2} has no influence on the harvest level.

To facilitate the analysis, let us here assume that _{i}^{2} = _{f}^{2}. When comparing (9) and (11), the role played by the degree of informativeness of the signal immediately becomes apparent. In particular, as is intuitive, a positive signal induces a higher reduction in the short-run supply of wood when the signal itself is supposed to be informative about the forest sector, as it is in (11).

This does not immediately follow in the case of a negative signal: on the one hand a very trustable negative signal would induce an increase in the current-supply of wood. On the other hand, the high degree of informativeness is perceived as a reduction in risk and therefore it reduces current supply _{1}. In particular, for higher levels of risk aversion this second effect could prevail.

Comparative statics with respect to the parameters _{a}^{2}, _{f}^{2}, _{s}^{2}, _{f}

In this section, we briefly discuss the role played by the signal when the information conveyed does not add anything with respect to the initial expectations. This occurs when the realized signal (on the risky asset or on future timber price) takes value 0. In such an instance, the first order condition for optimal harvesting associated to the maximization problem will be:

We label the solution of the above equations _{1}^{A}_{1}^{B}_{1} the optimal solution if no signal is received, and, to facilitate the comparison, we assume _{i}^{2} = _{f}^{2}. Even if the updated expectations have not changed, the mere existence of the signal has strong impact on the optimal harvesting/investment quantities, through the reduced conditional variance, and therefore risk. In particular, _{1}^{B}_{1}^{A}_{1}, that is, the more the signal is specific to the forest sector, the more it reduces uncertainty. Notice that this implies that different landowners could react to the same signal in different ways, depending on whether they consider the signal more related to the forest sector or to financial markets. The difference |_{1}^{A}_{1}| reduces as _{i}^{2}, _{f}^{2} increase, while it increases as _{a}^{2} increase.

Therefore, the reply to the signal is stronger the higher the aggregate economic risk _{a}^{2} is, and the more informative the signal is. In contrast, _{f}^{2} and _{i}^{2} reduce the credibility of the signal. Indeed, when aggregate economic risk is high, it is relatively more important for the forest owner to receive a signal, so that he/she tends to “over-react” with respect to it. On the other hand, financial risk and the signal precision do not directly affect timber prices, which is why their increase simply adds disturbance to the interpretation of the signal, so that the forest owner becomes more cautious.

It is also worth noting that—even if in both cases considered above, the signals bring the same information about the economic component—the reaction to the signal of the second agent is stronger, simply because informativeness itself is stronger [

In this paper we have presented a theoretical model of optimal harvesting-investment decision for a private forest owner who invests the revenues from timber sale on financial markets. The framework has two main characteristics: (i) the role of information and (ii) the way uncertainty is modeled. As far as it has been possible to ascertain, this is the first theoretical paper investigating the effect of information on harvesting decisions. When modeling uncertainty, we explicitly allow for a distinction between aggregate economic risk and sector specific risk, such as financial and forestry risk respectively. Obviously it is beyond the scope of this paper to try to establish a direct linkage between concrete empirical facts and the results of our model. Nevertheless, the particular structure used here permits financial specific risk to influence harvesting behavior (see

For example, when the housing sector collapsed in US, timber prices in Sweden plummeted dramatically, as expected. However, they dropped even further after Lehman Brothers’ bankruptcy [

The presence of common aggregate economic risk (due to the potential occurrence of a shock, _{a}

Even if ours is not an equilibrium model, so that both financial and timber prices are exogenous, observing the conditional covariance between timber price and asset dividend one could partially accommodate these contrasting findings. Indeed, conditional covariance varies in value depending on the severity of aggregate economic risk and the specific information received (see

The accommodation of the role played by information/news in the model—particularly information specific to timber markets—is of relevance from a policy perspective. Hence, information is a frequently used policy tool, and the way information affects harvesting decisions is thus of interest, especially in light of the efforts to increase wood mobilization in many European countries. As an example, information about timber markets, coupled with recommendations not to postpone harvest, features frequently in forest owner associations membership magazines, presumably partly with the objective to increase the short-run supply of timber (see, e.g., [

Thus the model presented here can be used as a starting point for exploring an area of forest economics well worth considering, not least from a policy perspective and with very concrete applications. For example, departing from the approach proposed here, it is possible to develop an alternative framework suitable for analyzing how different degrees of information penetration affect the equilibrium price of timber. Alternatively, one could investigate how the release of information could be used as a policy tool to optimally induce higher/lower levels of timber supply among forest owners, depending on their specific characteristics (e.g., stand characteristics related to the extent of non-timber forest values). These topics will be part of our future research.

The authors declare no conflict of interest. The opinions expressed herein are those of the authors and do not necessarily reflect the views of the European Commission.

We emphasize that this is a key distinctive element between [

In what follows we will use the terms “agent”, “individual” and “landowner” interchangeably, without special or technical meanings, unless otherwise stated.

The case of a signal on the forest sector will be treated in a separate section.

CARA (constant absolute risk aversion) utility is a class of utility functions

In such an instance, final wealth would be _{2}_{2} + _{1}_{1} (1 + _{f}

We refer the Reader to the next section in order to obtain additional insight on this result.

Indeed higher risk makes the signal less credible and the absolute value of the variation in the short-run timber supply induced by an increase in financial risk is higher in case of good news.

Indeed

In the case of a negative signal, current harvesting always increases with economic risk.

Notice that we are implicitly assuming that ^{p2}/_{α}_{a}^{2}^{2} ≤ _{i}^{2} + _{s}^{2}, which is generally the case for realistic values of _{a}^{2}, _{i}^{2}, _{s}^{2}.

Here we are evaluating |_{1}^{A}_{1}^{B}