Acquiring Information on the Environment
for Economic Decision Making
By
Carlisle A Pemberton
Department of Agricultural Economics and Extension
The University of the West Indies
St Augustine Trinidad and Tobago
INTRODUCTION
It is very common nowadays to consider environmental resources as giving rise to both market and non-market goods. Much of the literature on these resources is concerned with the damage caused by the indiscriminate actions of man. Such literature is concerned with how to reduce this damage, as well as the valuation of the resources themselves, so that we are aware of what we are losing when they are damaged or lost.
However, it has not been so long ago that a major interest in the environment concerned its role as an adversary to man. Notwithstanding the familiar name that was given to the environment as ‘Mother Nature’, the concern was that Mother Nature was responsible for causing floods, hurricanes, volcanoes, droughts, earthquakes etc., which caused untold damage to man. We want in this paper to return to this concern.
What we particularly want to return to here are problems associated with asymmetric information. In economic decision making, Mother Nature knows what it plans for the decision environment, which it does not share with the other economic players. Thus, particularly where the decisions of the other players depend heavily on environmental factors, these decision makers are placed in a decidedly disadvantageous position. In the language of the theory of asymmetric knowledge, Mother Nature is the agent, with knowledge, while the principal – man – wants the agent to reveal this knowledge, so that the principal can make the best decision.
Unable to induce the agent to take this best action from the viewpoint of the principal, in the past, attention focused on strategies that the principal could take to minimize the impact of the agent, Mother Nature, for example game theoretic strategies and insurance.
A consequence of the lack of knowledge of Mother Nature’s intended action not as frequently studied, is the attempt by some decision makers, especially farmers, to establish an advantage over other decision makers, by their presumed superior knowledge of the environment. These ‘knowledgeable’ decision makers, for example, would claim that because they can ‘predict’ the actions of Mother Nature, that they can make superior decisions, such as when the plant or to begin to harvest.
However, even if these knowledgeable decision makers exhibit higher profits, these profits could be due to other factors, such as better management or physical resources. However, once profits are not perfectly determined by the environment, the decision makers may be unable to tell whether the higher profits are due to superior knowledge or to better management or physical resources. Thus the presumed superior knowledge of the environment may be entirely baseless.
But such baseless, but presumed superior knowledge, may give rise to popular myths concerning the environment (such as the existence of unusual weather patterns). Thus when claims are made about the detection or existence of unusual knowledge of the environment, it is useful to determine whether such knowledge has any basis in reality. If indeed the presumed knowledge is factual, it may be quite useful in economic decision making.
One such presumed unusual weather pattern that may exist in Trinidad and Tobago in the Caribbean is a short dry period in the wet season, a phenomenon referred to as Petit Careme. If such a dry period occurs with a sufficiently high probability, then this knowledge, to a limited number of farmers and other decision makers would allow them to plan and implement their activities, which could put them in an advantageous position with respect to other decision makers.
This paper will examine this issue of the value to decision makers of asymmetric information on the environment, with particular emphasis the information on precipitation to agriculture.
The paper will first examine the optimality conditions for decision makers who maximize profits with respect to prices (rather than output), given that because of the risk associated with precipitation (and other factors) of the environment, output is considered more risky than prices. The paper will be particularly interested in determining whether under these optimality conditions, additional knowledge of the impact of the environment on output would be valuable, in terms of increasing the profit of the decision maker.
Then the paper will examine an approach that can be used to establish knowledge of the environment, by separating reality from presumption or myths. This will be done by establishing statistically, the presence of unusual environmental occurrences. The method of this approach is to treat the unusual environmental occurrences as outliners in a time series, so that the method proceeds to identify possible unusual events by the identification of outliners.
VALUE OF ENVIRONMENTAL KNOWLEDGE
Environmental factors are almost always considered to be highly risky or uncertain. Such environmental factors include precipitation, temperature, wind speed etc. We will consider here the case of a risk averse farmer under rain-fed conditions, thus totally dependent on precipitation as a source of water for farming. It is also assumed that the market for the output is perfectly competitive, or at any rate that the output of the farmer does not affect the price of the output and the farmer has no other way of controlling the price of the output. The farmer is in a typical tropical country, with temperature always suitable for crop growth, but with crop production highly dependent on precipitation because of a distinct seasonal pattern to rainfall. This is the typical pattern in the Caribbean, Latin America and West Africa. We further consider that the farmer is engaged in annual crop production e.g. vegetables or root crops, where it is possible to plant at any time during the year and achieve some output within 12 months.
The farmer has a choice as to what factor to base his decision on either: (i) to maximize expected utility by choosing the optimal level of output, on the assumption that output is less variable than price or (ii) to maximize expected utility by choosing the optimal time to plant and therefore the best price on the assumption that price is a function of time and is less variable than output.
We shall consider here that (ii) is more likely for the farmer, since he does not have ex ante knowledge of how output is affected by environmental variables especially precipitation.
For example, consider that the farmer receives profit (π) from the enterprise where (π) is: π = Py – C(y) …… (1)
The objective of the farmer is to maximize his expected utility. His utility function is:
U = U(π)
or U = U(Py – C(y)) … (2)
Then the unexpected utility is given by:
E(U) = Ф = ∫U (Py – C(y)) . G(y) . dG(y)….. (3)
where G(y) is the conditional probability distribution function given by
G(y) = F(yα) α ε [ α, ά] ….. (4)
where α is au environmental factor affecting the output y for example rainfall. (In some cases, α could indeed by a vector αih i = 1, …, m m environmental factors and h = 1, …, n where n farmers are involved in producing output y.
Then the objective of the farmer can be given as follows
ά
Max (Ф) = max ∫ U (Py – C(y)) G(y) d(G(y)) …. (5)
y α
However we argue that not knowing G(y) the farmer is not able to carry out the optimization in (5). We also assume that in the first instance, that he sees no value in a two stage process of attempting to determine G(y), (4) first then to carry out the optimization in (5).
Instead we assume that the farmer takes the ex post position of assuming that the price of the good P is precisely determined over time by a simple functional relationship:
P = μ t μ>o ….. (6)
where t is a time index defined over a continuous time interval (assumed here to be a year). Thus a higher value of t yields a higher price since μ = moment of the price variable usually the first moment or the mean. Thus in this formulation t does not necessarily increase consistently over the continuous time interval.
The ex post profit of the farmer is defined by
π = P y – C(y)
and ø = E[u] = E[U(Py – C(y))]
= E[U(μty – C(y))] …. (7)
The farmer now attempts to maximise expected utility by choosing the time to plant on the assumption of a good knowledge of the time index given by t.
So: δø = E[U′(μty – C(y))].μy] = 0 …. (8)
δt
δ2ø = E[U″(μty – C(y))].(μy)2] < 0 …. (9)
δt2
So it can be argued that the farmer attempts to maximize his expected utility by choosing the optimal time to plant.
We now consider the value of additional information on the environment to the farmer, even given that he has chosen the optimal time to plant t*.
Lemma:
Even where the optimal time t* has been selected by the farmer, obtaining additional knowledge on the environment via the nature of G(y) would allow an increase in the expected utility.
Proof:
Consider obtaining random values of y from repeated sampling from the known G(y) distribution and for each sample of y, its value is held fixed and the optimal time index t* is obtained as in equations (8) and (9).
From 8
μ E [U′(μty – C(y)).y] = 0
since μ is a constant and
E [U′(μty – C(y))y] = 0 since μ > 0 …. (10)
Also if we consider that we are holding y fixed to determine the optimal value of of t, t* then
y E[U′(μt*y – C(y))] = 0 and
E[U′(μt*y – C(y))] = 0 …. (11)
_
Subtract E[U′(μt*y – C(y)) y] from both sides of the equation (10).
_ _
E[U′(μt*y – C(y)) (y – y)] = - E[U′(μt*y – C(y) y] …. (12)
But if we consider equation (11) then the LHS of (12) is the covariance of marginal utility of profit with respect to output, given the optimal choice of time t*.
But this covariance is negative since as output increases profit increases given fixed prices to the farmer, and the marginal utility of profit will fall, as given risk aversion, greater profit will come with a diminishing marginal utility of this profit.
_
Hence E[U′(μty – C(y) y] < 0
_
or E[U′(μt*y – C(y) y] > 0 ….. (13)
or producing at the mean output and optimal price t* will mean that the expected utility of the farmer is not maximized, since at the maximum the expected marginal utility is zero in (10). Hence in the absence of knowledge of G(y), the farmer could be expected to obtain the mean output and therefore not maximize expected utility. However a knowledge of G(y) may allow the farmer to select values of y which will maximize expected utility.
Hence even where the optimal time t* has been selected by the farmer, there is still the incentive for the farmer to obtain additional information on G(y) to utilize (5) to obtain the maximum expected utility as:
ά
Max (Ф) = max ∫ U (μt*y – C(y)) G(y) d(G(y)) …. (5 a)
y α
ESTABLISHING KNOWLEDE ABOUT THE ENVIRONMENT
As was stated earlier, there is an incentive for decision makers to obtain additional information on the environment, which could allow them to maximize their expected utility and also given them an asymmetric knowledge advantage over their counterparts.
One way that decision makers can obtain this additional information on the environment is by detecting the existence of unusual events, and being able to predict their occurrence or at least knowing the probability of the occurrence.
In this paper, the unusual events will be detected as outlines in a time series of the random variable being considered. The environmental variable that the paper will focus on is precipitation or especially rainfall and the method will determine outliers in the time series on rainfall and be able to determine the probability of occurrence of these unusual events.
The method is due to Tsay and a derivation of the method for the case of additive outliers (AO case) will be considered in this paper, since this type of outlier is the type that presents the most opportunities for advantage by asymmetric information by decision makers.
Tsay (1988) however presents the five types of changes that can give rise to outliers and variance changes in time series of random variables.
AO Charge and Outlier Detection
Consider a time series for a random variable Zt for an environmental variable like precipitation. Such a time series can be given as an ARMA model approximation of the Wold representation by the Moving Average (MA) representation as follows (Diebold, 2001).
Ζt = θ(B) / Ф(B) at …. (14)
Where
(at) is a sequence of independent Gaussian variates with zero mean and variance σa2
θ(B) is a qth order lag operator polynomial,
Ф(B) is a pth order lag operator polynomial,
we assume that all of the roots of θ(B) and Ф(B) are on or outside the unit circle and that θ(B) and Ф(B) have no common factors (Tsay, 1988) and
B is the back shift operator and B-1 forward shift operator.
When outliers are present, Ζt is disturbed and unobservable. In this case it is assumed that the observed series {Yt} follows the model.
Yt = ƒ(t) + Ζt ..... (15)
For deterministic models such as we shall be concerned with in this paper
ƒ(t) is of the form
ƒ(t) = ω0 W(B). Єt(d) ….. (16)
δ(B)
where Єt(d) = l if t = d
= 0 if t ≠ d
is an indicator variable signifying the occurrence of an outlier at the time point (period) d.
ω (B) and δ(B) are polynomials of degree s and r and ω0 is a constant denoting the initial impact of the outlier at d.