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Optimum depletion of natural resources: Some general issues†
Socro-Econ. Plan Ser., Vol II, pp 233-234
Pergamon Press 1977
Printed in Great Britan
NOTES OPTIMUM
DEPLETION OF NATURAL RESOURCES: SOME GENERAL ISSUES’r
Institute for Social and Environmental
DIMITRIOS S. DENDRINOS Studies, The University of Kansas, Lawrence,
KS 66045, U.S.A.
(Received 29 October 1976)
The problem of intergenerational equity has long been an issue of concern. In the early seventies, renewed social emphasis on the energy question brought the problem of intergenerational equity back to the attention of economists interested in the area of optimum economic growth. For the lirst time, the possibility of complete depletion of resources within a living generation’s life span became a recognized threat. Therefore, it became important to determine how long these resources would last and what social welfare criterion could be used to weigh the effects of present decisions on future generations. With the exception of the seminal contribution by Hotelling[l] in the thirties, the basic theme for discussing this problem was laid out by Solow[2] in the 1974 symposium issue of the Review of Economic Studies. The excellent collections of papers resulting from this symposium was followed by another wave of publications, similar to the outburst of literary production on optimum economic growth experienced during the sixties, At the present, the most significant collection of papers on this topic can be found in The Economics of Natural Resources, edited by Pearse and Rose [3], in which the paper by Kay and Mirrlees is of special significance 141. Their paper and the Solow article will be the main focus of this discussion because of the social welfare criterion used, the conclusions drawn, and the type of issues raised. The following brief summary of the issues presented in these writings may be of some lasting interest to planners. Of course, the basic argument (independent of the specifics of the various models) evolves around a fundamental question: What criterion should be used to determine the optimum level of resource depletion for present and future generations? There is a tendency to show that market conditions will deplete a resource at an optimal rate if the social marginal rates of substitution between the opportunity costs of leaving in, or extracting the resource from the ground, are equal to the prices of the resource over time. Note that the above reasoning is consistent with the standard tradition encounter in the discussion on optimum economic growth which is now considered dated. In the standard tradition, the issue was to show the conditions for a steady state. It was felt that markets at equilibrium would always produce the optimum welfare if prices were set to correspond to marginal rates of substitution among the relevant production factors. According to Kay and Mirrlees, the extraction rate of the natural and nonreproducible resource that results in the maximum present value of the discounted profits from exploiting the resource also results in the maximum value of a social welfare function, as defined by the sum of social utilities over time. This criterion of a simple sum of utilities (or the sum of discounted utilities by an exogenous social discount rate) is also used by
tThe author would like to thank Profs. Britton Harris and Aaron Wildavsky for comments on an earlier version of this note. $The relevant assumption here is that no monopolistic resource owner manipulates prices. Kay and Mirrlees show that monopoly tends to deplete a resource at a lower than socially optimum pace. (It should be noted that Hotelling knew this.) Kay and Mirrlees conclude that, due to the prevailing monopolistic ownership structure, resources are most likely being depleted too
Weinstein and Zeckhauser [5], and Stiglitz[6], and their results are similar to those of Kay and Mirrlees. Solow adds another dimension by examining the impact of the Rawlsian criterion of maximizing the minimum (infimum) level of social welfare incurred over time. The use of the Rawlsian just criterion was lirst discussed by Dixit[7], in a paper on optimum continuous spatial allocation for a monocentric city, when absolute equality is imposed. Solow shows the difficulty of employing such a criterion for social optimization, as its use would tend to perpetuate poverty. The main point in the literature is that there is a built-in stabilizer in the economy (the market rate of interest) that regulates the depletion of the natural resource at its socially optimum levels. As the argument goes, if the price of the natural resource increases faster than the compounded market rate of interest, the owner of the resource will be motivated to deplete at a lower pace so he can accrue higher future benefits; whereas, if the price is increasing at a rate lower than the compound interest rate, the owner will be willing to put more into the market to avoid future higher losses. Several strong assumptions are made in order to derive the above: one of these is that under market equilibrium conditions, resource owners are assumed to have perfect foresight concerning future prices. Defending the possibility for such a foresight, Mirrlees, in the discussion following his paper@], argues that it is not absurd to assume that present owners may be motivated towards and capable of speculating how much future generations will be willing to pay for a resource 200 years hence. Independent of the feasibility of economic agents speculating near or far into the future, these agents have only a relatively short life span, whether they are governments, consuming agents or producing units. Furthermore, their learning from the past and their foresight are not identical, even under indicative planning. One may comfortably suggest that such speculation is not socially optimum and, thus, may result in inefficient depletion rates. However, one may point out further that if this sort of speculation provides a bias for depleting the resource too quickly, the counterforce of monopoly ownership balances this out by tending to deplete it too slowly, as shown by Kay and Mirrlees. Still, whether or not this depletion rate is socially optimum is an open questi0n.S A point that may be stimulating to planners and policy makers is related to the issue of planning horizon, an issue not of direct concern in this analysis. This issue is implicit in two comments found in the literature cited. Kay and Mirrlees, in criticizing the Club of Rome model of growth, stress that models with time horizon extending beyond a decade or so are worthless exercises for dealing with exhaustible resources. Solow writes that it is a mere trick of posterity that we can decide whether or not to make ourselves richer and, consequently, our descendants poorer, and there is an element of surprise only because of the time incongruity. These two points will be the focus of the discussion to follow. The time asymmetry that works forward (we can do things today that will affect the future, whereas the future can do nothing to affect us today on its own will-but only on ours) also works backwards; we cannot pass judgment on the future’s actions, 233
234
Notes Of course, nothing in the preceding suggests that we should do our best in the present by ignoring the future beyond our limited planning horizon. However, it is argued that perhaps the best thing for us, and the distant future, is to do what is best for us now, since we act alone. And in fact, will past or future historians really tell us that any generation has acted differently?
whereas the future can on ours. And this may be a concern in trying to derive optimum depletion rates, depending on our sensitivity and social awareness. Currently, discussion of the issue of intergenerational equity presents a pervasive sense of guilt; for a typical example see Meadows et aL[9]. However, it should be added that no longer are ueoole ureoccuuied with blaming the Huns for having high socialdiscount rates. infact, for the present, these are sunk cost/benefit events. A strong case can be made for a limited planning horizon since it is based not only on questions of uncertainty in the environment (technological change, risks. etc.), but also on the fact that within such a horizon, present generations can arrive at Pareto admissible decisions that, for the most part, will affect only the incongruity, since there would be a gradual transition among generations. Present generations can negotiate, whereas there is no negotiation possible between living and nonliving generati0ns.t In the long run, the resources will be depleted and the aggregate capital stock will be accumulated independently of the utility enjoyed by the different generations, of the specific correspondence between the paths of resource depletion and capital accumulation, and of the specific time unit presently used. The variety of the resources we presently utilize will decrease for future generations. However, the future technological stockpile will be a function of the knowledge developed today by our depleting the economic resources of today.
REFERENCES
1. H. Hotelling, The economics of exhaustible resources. J. P&t. Econ. XXXIX, 137-175 (1931) equity and exhaustible 2. R. M. Solow, Intergenerational resources. Rev. Econ. Studies Symposium issue, 29-46 (1974). 3. D. W. Pearse and 3. Rose (eds.), The Economics of Natural Resource Depletion. McMillan, London (1975). 4. J. Kay and .I. Miilees, The desirability of natural resource depletion, in The Economics of Natural Resource Depletion (Edited by D. W. Pearse and .I. Rose), pp. 140-176. McMillan, London (1975). 5. M. C. Weinstein and R. J. Zeckhauser, Use patterns for depletable and recycleable resources. Rev. Econ. Studies Symposium issue, 67-88 (1974). 6. J. E. Stiglitz, Growth with exhaustible natural resources; efficient and optimal growth paths. Rev. Econ. Studies Symposium issue, 29-46 (1974). 7. A. Dixit. The optimum factory town. The Bell J. Econ. Mangmt Sci. Autumn, 637-651 (1973). 8. D. W. Pearse and J. Rose (eds.), The Economics of Natural ResourceDepletion, Chap. 12, p. 204. McMillan, London (1975). 9. D. Meadowns et al., The Limits to Growth. Earth Island, London (1972).
tTechnically, this concern is not addressed if the final desired level of a resource is prespecitied and the time horizon is computed endogenously through the transversality conditions of the calculus of variations formulations of the optimum depletion problem.
Socm-Em
Plan. So., Vol 11, pp 234-231.
Pergamon Press 1977
Pnnted in Great Bntain
CANONICAL CORRELATION ANALYSIS VS SIMULTANEOUS EQUATION APPROACH: AN EMPIRICAL EXAMPLE EVALUATING CHILD HEALTH AND WELFARE PROGRAMS? TEH-WEI Institute for Research
on Human Resources,
HU
The Pennsylvania U.S.A.
State University,
University
Park, PA 16802.
(Received 21 October 1976; revised 21 January 1977)
INTRODUCTION
There have not been many empirical examples of canonical correlation analysis being applied to econometric studies. The most noticeable ones are those by Waugh[l], Tinter[2] and Hooper[3]. One of the reasons for little empirical work in the area is the difficulty of interpreting results from canonical correlation analysis in a meaningful economic way. However, there are arguments that canonical correlation and simultaneous equation are similar in the case of analyzing a set of simultaneous equations as suggested by Hopper[3] and Chow[4]. The objective of this paper is to investigate the effectiveness of child health and welfare programs using canonical correlation analysis as compared to the simultaneous equation approach. An earlier paper of the simultaneous equation approach was published in this journal[S].
tThe study was performed pursuant to a grant from the Governor’s Office,Commonwealthof Pennsylvania.Theauthorisgrateful to Ernst W. Stromsdorfer and Harold W. Watts for their comments and help in improving this article considerably. The views expressed are the responsibility of the author.
CANONICAL
CORRELATION EQUATION
VS SIMULTANROUS
APPROACH
In ordinary regression analysis, the objective is to obtain the regression coefficients which will maximize the correlation between a dependent (endogeneous) variable and a vector of independent (exogeneous) variables. In the case of more than one endogenous variable in the regression model, a simultaneous equation approach is often adopted. The drawback of a simultaneous equation approach is that each equation can treat only one endogenous variable as a regressand. Canonical correlation analysis is concerned with the relations between two sets of variables. In other words, the ordinary regression analysis becomes only a special case of canonical correlation analysis where one of a set contains only one variable. For the canonical correlation analysis, we can define that (Y,, Y2,. . . , Y,,,) and (X,, X,, . . X,) be vectors of endogeneous variables and exogenous variables, respectively. We further define that
Z=&,Y,=a'Y r=,
w=ep,x,=prx ,=I
Pergamon Press 1977
Printed in Great Britan
NOTES OPTIMUM
DEPLETION OF NATURAL RESOURCES: SOME GENERAL ISSUES’r
Institute for Social and Environmental
DIMITRIOS S. DENDRINOS Studies, The University of Kansas, Lawrence,
KS 66045, U.S.A.
(Received 29 October 1976)
The problem of intergenerational equity has long been an issue of concern. In the early seventies, renewed social emphasis on the energy question brought the problem of intergenerational equity back to the attention of economists interested in the area of optimum economic growth. For the lirst time, the possibility of complete depletion of resources within a living generation’s life span became a recognized threat. Therefore, it became important to determine how long these resources would last and what social welfare criterion could be used to weigh the effects of present decisions on future generations. With the exception of the seminal contribution by Hotelling[l] in the thirties, the basic theme for discussing this problem was laid out by Solow[2] in the 1974 symposium issue of the Review of Economic Studies. The excellent collections of papers resulting from this symposium was followed by another wave of publications, similar to the outburst of literary production on optimum economic growth experienced during the sixties, At the present, the most significant collection of papers on this topic can be found in The Economics of Natural Resources, edited by Pearse and Rose [3], in which the paper by Kay and Mirrlees is of special significance 141. Their paper and the Solow article will be the main focus of this discussion because of the social welfare criterion used, the conclusions drawn, and the type of issues raised. The following brief summary of the issues presented in these writings may be of some lasting interest to planners. Of course, the basic argument (independent of the specifics of the various models) evolves around a fundamental question: What criterion should be used to determine the optimum level of resource depletion for present and future generations? There is a tendency to show that market conditions will deplete a resource at an optimal rate if the social marginal rates of substitution between the opportunity costs of leaving in, or extracting the resource from the ground, are equal to the prices of the resource over time. Note that the above reasoning is consistent with the standard tradition encounter in the discussion on optimum economic growth which is now considered dated. In the standard tradition, the issue was to show the conditions for a steady state. It was felt that markets at equilibrium would always produce the optimum welfare if prices were set to correspond to marginal rates of substitution among the relevant production factors. According to Kay and Mirrlees, the extraction rate of the natural and nonreproducible resource that results in the maximum present value of the discounted profits from exploiting the resource also results in the maximum value of a social welfare function, as defined by the sum of social utilities over time. This criterion of a simple sum of utilities (or the sum of discounted utilities by an exogenous social discount rate) is also used by
tThe author would like to thank Profs. Britton Harris and Aaron Wildavsky for comments on an earlier version of this note. $The relevant assumption here is that no monopolistic resource owner manipulates prices. Kay and Mirrlees show that monopoly tends to deplete a resource at a lower than socially optimum pace. (It should be noted that Hotelling knew this.) Kay and Mirrlees conclude that, due to the prevailing monopolistic ownership structure, resources are most likely being depleted too
Weinstein and Zeckhauser [5], and Stiglitz[6], and their results are similar to those of Kay and Mirrlees. Solow adds another dimension by examining the impact of the Rawlsian criterion of maximizing the minimum (infimum) level of social welfare incurred over time. The use of the Rawlsian just criterion was lirst discussed by Dixit[7], in a paper on optimum continuous spatial allocation for a monocentric city, when absolute equality is imposed. Solow shows the difficulty of employing such a criterion for social optimization, as its use would tend to perpetuate poverty. The main point in the literature is that there is a built-in stabilizer in the economy (the market rate of interest) that regulates the depletion of the natural resource at its socially optimum levels. As the argument goes, if the price of the natural resource increases faster than the compounded market rate of interest, the owner of the resource will be motivated to deplete at a lower pace so he can accrue higher future benefits; whereas, if the price is increasing at a rate lower than the compound interest rate, the owner will be willing to put more into the market to avoid future higher losses. Several strong assumptions are made in order to derive the above: one of these is that under market equilibrium conditions, resource owners are assumed to have perfect foresight concerning future prices. Defending the possibility for such a foresight, Mirrlees, in the discussion following his paper@], argues that it is not absurd to assume that present owners may be motivated towards and capable of speculating how much future generations will be willing to pay for a resource 200 years hence. Independent of the feasibility of economic agents speculating near or far into the future, these agents have only a relatively short life span, whether they are governments, consuming agents or producing units. Furthermore, their learning from the past and their foresight are not identical, even under indicative planning. One may comfortably suggest that such speculation is not socially optimum and, thus, may result in inefficient depletion rates. However, one may point out further that if this sort of speculation provides a bias for depleting the resource too quickly, the counterforce of monopoly ownership balances this out by tending to deplete it too slowly, as shown by Kay and Mirrlees. Still, whether or not this depletion rate is socially optimum is an open questi0n.S A point that may be stimulating to planners and policy makers is related to the issue of planning horizon, an issue not of direct concern in this analysis. This issue is implicit in two comments found in the literature cited. Kay and Mirrlees, in criticizing the Club of Rome model of growth, stress that models with time horizon extending beyond a decade or so are worthless exercises for dealing with exhaustible resources. Solow writes that it is a mere trick of posterity that we can decide whether or not to make ourselves richer and, consequently, our descendants poorer, and there is an element of surprise only because of the time incongruity. These two points will be the focus of the discussion to follow. The time asymmetry that works forward (we can do things today that will affect the future, whereas the future can do nothing to affect us today on its own will-but only on ours) also works backwards; we cannot pass judgment on the future’s actions, 233
234
Notes Of course, nothing in the preceding suggests that we should do our best in the present by ignoring the future beyond our limited planning horizon. However, it is argued that perhaps the best thing for us, and the distant future, is to do what is best for us now, since we act alone. And in fact, will past or future historians really tell us that any generation has acted differently?
whereas the future can on ours. And this may be a concern in trying to derive optimum depletion rates, depending on our sensitivity and social awareness. Currently, discussion of the issue of intergenerational equity presents a pervasive sense of guilt; for a typical example see Meadows et aL[9]. However, it should be added that no longer are ueoole ureoccuuied with blaming the Huns for having high socialdiscount rates. infact, for the present, these are sunk cost/benefit events. A strong case can be made for a limited planning horizon since it is based not only on questions of uncertainty in the environment (technological change, risks. etc.), but also on the fact that within such a horizon, present generations can arrive at Pareto admissible decisions that, for the most part, will affect only the incongruity, since there would be a gradual transition among generations. Present generations can negotiate, whereas there is no negotiation possible between living and nonliving generati0ns.t In the long run, the resources will be depleted and the aggregate capital stock will be accumulated independently of the utility enjoyed by the different generations, of the specific correspondence between the paths of resource depletion and capital accumulation, and of the specific time unit presently used. The variety of the resources we presently utilize will decrease for future generations. However, the future technological stockpile will be a function of the knowledge developed today by our depleting the economic resources of today.
REFERENCES
1. H. Hotelling, The economics of exhaustible resources. J. P&t. Econ. XXXIX, 137-175 (1931) equity and exhaustible 2. R. M. Solow, Intergenerational resources. Rev. Econ. Studies Symposium issue, 29-46 (1974). 3. D. W. Pearse and 3. Rose (eds.), The Economics of Natural Resource Depletion. McMillan, London (1975). 4. J. Kay and .I. Miilees, The desirability of natural resource depletion, in The Economics of Natural Resource Depletion (Edited by D. W. Pearse and .I. Rose), pp. 140-176. McMillan, London (1975). 5. M. C. Weinstein and R. J. Zeckhauser, Use patterns for depletable and recycleable resources. Rev. Econ. Studies Symposium issue, 67-88 (1974). 6. J. E. Stiglitz, Growth with exhaustible natural resources; efficient and optimal growth paths. Rev. Econ. Studies Symposium issue, 29-46 (1974). 7. A. Dixit. The optimum factory town. The Bell J. Econ. Mangmt Sci. Autumn, 637-651 (1973). 8. D. W. Pearse and J. Rose (eds.), The Economics of Natural ResourceDepletion, Chap. 12, p. 204. McMillan, London (1975). 9. D. Meadowns et al., The Limits to Growth. Earth Island, London (1972).
tTechnically, this concern is not addressed if the final desired level of a resource is prespecitied and the time horizon is computed endogenously through the transversality conditions of the calculus of variations formulations of the optimum depletion problem.
Socm-Em
Plan. So., Vol 11, pp 234-231.
Pergamon Press 1977
Pnnted in Great Bntain
CANONICAL CORRELATION ANALYSIS VS SIMULTANEOUS EQUATION APPROACH: AN EMPIRICAL EXAMPLE EVALUATING CHILD HEALTH AND WELFARE PROGRAMS? TEH-WEI Institute for Research
on Human Resources,
HU
The Pennsylvania U.S.A.
State University,
University
Park, PA 16802.
(Received 21 October 1976; revised 21 January 1977)
INTRODUCTION
There have not been many empirical examples of canonical correlation analysis being applied to econometric studies. The most noticeable ones are those by Waugh[l], Tinter[2] and Hooper[3]. One of the reasons for little empirical work in the area is the difficulty of interpreting results from canonical correlation analysis in a meaningful economic way. However, there are arguments that canonical correlation and simultaneous equation are similar in the case of analyzing a set of simultaneous equations as suggested by Hopper[3] and Chow[4]. The objective of this paper is to investigate the effectiveness of child health and welfare programs using canonical correlation analysis as compared to the simultaneous equation approach. An earlier paper of the simultaneous equation approach was published in this journal[S].
tThe study was performed pursuant to a grant from the Governor’s Office,Commonwealthof Pennsylvania.Theauthorisgrateful to Ernst W. Stromsdorfer and Harold W. Watts for their comments and help in improving this article considerably. The views expressed are the responsibility of the author.
CANONICAL
CORRELATION EQUATION
VS SIMULTANROUS
APPROACH
In ordinary regression analysis, the objective is to obtain the regression coefficients which will maximize the correlation between a dependent (endogeneous) variable and a vector of independent (exogeneous) variables. In the case of more than one endogenous variable in the regression model, a simultaneous equation approach is often adopted. The drawback of a simultaneous equation approach is that each equation can treat only one endogenous variable as a regressand. Canonical correlation analysis is concerned with the relations between two sets of variables. In other words, the ordinary regression analysis becomes only a special case of canonical correlation analysis where one of a set contains only one variable. For the canonical correlation analysis, we can define that (Y,, Y2,. . . , Y,,,) and (X,, X,, . . X,) be vectors of endogeneous variables and exogenous variables, respectively. We further define that
Z=&,Y,=a'Y r=,
w=ep,x,=prx ,=I