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Expenditure of oil revenue: An optimal control approach with application to the Iranian economy
Book Reviews
381
slightly more substantive point, I feel that the insistence in the section on price aggregation that sectoral price indices depend only on prices is unnecessarily disabling. In particular, it means that the standard procedure in demand analysis (working with commodity groups and commodity prices, the inner product of ivhich is total expenditure) will only work if the subutility functions are homogeneous, with all goods which are grouped together required to have the same income elasticity. However, if the price and quantity indices are permitted to depend on total utility, implicit conjugate duality gives perfect (additive) price and quantity aggregation, while, if the indices can depend on the sectoral welfare level, such aggregation follows from the usual direct separability. Furthermore, in the latter case, the theoretical indices are likely to be closely approximated by the Laspeyres quantity and Paasche price indices which are used in practice. But these are minor, personal quibbles. As a whole, the book is an immensely valuable addition to the literature. The applications of separability spread out very widely; choice under uncertainty, the analysis of inequality and social choice theory are three obvious examples not covered here but employing. much the same mathematical structures. There will therefore be many economists and others who will find this an irreplaceable source of reference and who, like me, will feel that much more secure with this volume on their shelves. Angus DEATON University of Bristol
H. Motamen, Expenditure of oil revenue: An optimal control approach with application to the Iranian economy (Frances Pinter, London, 1979) pp. 189, E12.50. This book is a slightly extended and revised version of the author’s doctoral dissertation submitted to the University of Cambridge and is concerned with the application of control theory to development planning in the case of oilbased economies. Although the problem of optimal planning has attracted a great deal of attention in the literature of mathematical economics, its impact upon actual planning in developing countries has been minimal, to say the least. I am very doubtful as to whether the application of control techniques to the problems of developing countries should be emphasized at this point in time. Economic development is a complicated process which is invariably concerned with and involves structural change. Optimal control techniques that ignore the response of economic agents and institutions to the implementation of the optimal plan and the changing structure that it inevitably brings about can only be of limited practical relevance and it is
388
Book
Reoiews
comforting to note that even Dr. Motamen, enthusiastic advocate of the use of control techniques in economics as she is, does not recommend a full-scale application of the control theory to the actual planning of oil exporting countries. Her main aims are to use the control theory in order to highlight the policy options open to oil exporting countries faced with an exogenously given stream of earning in excess of their domestic absorptive capacities and to demonstrate how trajectories of the control and state variables can be efficiently calculated by the ‘method of feasible directions’. In Chapters 2 and 3, Dr. Motamen considers the problem of the optimal allocation of revenues obtained from an exhaustible resource such as oil, over a known planning horizon. She assumes that the stream of revenues from oil exports is given exogenously. This is a gross over-simplification. The most important problem faced by oil exporting countries is to determine their optimum rate of oil extraction given their domestic absorptive capacities, world demand and uncertainties concerning the future emergence of economically viable substitutes for oil. It is the simultaneous determination of the optimal rate of resource depletion and the optimal rates of domestic and foreign investment which lie at the heart of efficient development planning in oil exporting countries. Dr. Motamen’s arguments for assuming the exogeneity of the future oil revenues are two-fold. Firstly, she points out that since oil prices are determined by the Organization of Petroleum Exporting Countries (OPEC), thus no member country is at liberty to set its own export price unilaterally. Given the present oil price-setting mechanism this is reasonable. Secondly, she argues that for given export prices there will be an upper limit to the annual rate of oil extraction for OPEC as a whole which is set by world demand for OPEC exports. Therefore, she maintains that there is an upper limit to the rate of oil extraction for individual OPEC member countries. So far so good. But she goes on to argue that since the output of oil in OPEC member countries has generally been near the upper limit in the past, then it is valid to regard the rate of oil extraction, as well as oil prices, as being given exogenously. This argument is very unsatisfactory. Firstly, it is not true that all oil exporting countries have behaved in this way. Secondly, even if such an output policy has been followed by some of the OPEC member countries, it does not necessarily make it an optimal policy, whether viewed from the interests of the oil exporting countries or the world economy as a whole. Note, that as soon as the exogeneity of the rate of extraction is abandoned, we can no longer regard the planning horizon to be exogenous either. In the light of the recent political and social upheavals in Iran, it is becoming increasing clear that it is not appropriate to regard Iran’s future stream of oil revenues as exogenous. Furthermore, even in the case of a country like Saudi Arabia, it is not all obvious why on purely economic grounds an output policy based on a maximum possible rate of extraction should be followed. It is possible for a country such as Iran to
Book Reuiews
389
decide upon an optimal output policy within the lower extraction rate set by political considerations and the upper limit set by world demand for OPEC exports and the output policies of other OPEC member countries. Given the approach followed by Dr. Motamen, it is difficult to see how an endogenous extraction policy can be incorporated within her model. Other major features of the macro-economic framework adopted by the author are the assumptions of the unlimited supply of labour of whatever skill that might be required by the investment plans, the absence of capital depre.ciation and the exogenously given government consumption expenditure. The production function for the non-oil domestic income is specified to depend solely upon the stock of domestic capital, and the private sector consumption is assumed to be proportional to non-oil (or more generally non-export) incomes. Whilst admitting that any aggregative model inevitably has to involve some simplifying assumptions, the particular set of assumptions chosen by Dr. Motamen leaves a lot to be desired. Indigenous skilled labour is not in abundant supply in oil exporting countries and resort to the importation of the necessary skills is not without its socio-political costs as was witnessed in the pre-revolutionary situation in Iran. Inflow of foreign labour accentuates the shortages and bottlenecks that exist in the non-tradeable sector of the economy and often brings about a sense of alienation among the indigenous population. The assumption pf exogenously given government expenditure is also extremely unrealistic. As all oil revenues accrue to the government and it is the government that decides both the level and the pattern of government expenditure, one expects the level of government consumption expenditure to vary closely with the oil and non-oil incomes. Similarly the assumption that oil income only affects private consumption indirectly through raising non-oil incomes is unsubstantiated and no theoretical reasoning is advanced for such a specification. This assumption becomes particularly unsatisfactory when the basic model of Chapter 2 is extended in Chapter 3 where it is assumed that even income from non-oil exports has no direct impact upon private consumption. Taxation is singularly absent from the model. It is not clear how government expenditure is supposed to be financed when the oil runs out. The control problem considered by Dr. Motamen is the maximization of the terminal stock of capital subject to two constraints. Firstly that there should be no foreign debt at the terminal date and secondly, that a minimum level of imports should be met out of oil revenues in every period. By applying the Kuhn-Tucker theorem the author then shows that the intertemporal allocation of oil income should be carried out to the point where the marginal returns on foreign and domestic investments (the latter multiplied by the average propensity to save) is equalized. Even when the model is extended in Chapter 3 to include the non-oil export sector this basic result remains unaltered, although some complications arises when the
390
Book Reviews
minimum import constraint becomes binding. The major recommendation of Dr. Motamen’s analysis for the conduct of optimal planning in oil exporting countries, in her own words, is: ‘ . . . . accumulate reserves outside the economy during the early years of the resource’s life and invest internally only if the rate of return is higher than abroad. Conversely, invest more domestically during the later years of the resource’s life and accept a lower rate of return abroad.’ (p.39) Without disputing the fact that the above recommendation is the inevitable policy implication of Dr. Motamen’s control problem, it should, however, be emphasized that within limits oil exporting countries have other more attractive options when faced with limited absorptive capacities (i.e., low marginal rate of domestic investment). They can, so far as political considerations allow them, reduce the rate of exploitation of their exhaustible resources. Considering the technical difficulties and risks that are currently involved in foreign investment by a small oil producing country, it is not clear why expenditure of oil revenues abroad should be preferable to keeping the oil under the ground. The maximization of the terminal capital stock is only a viable strategy if the human resources that are needed for putting the capital stock iirto proper use are also developed before the exhaustion of the oil revenues. Long term planning strategies that do not pay due attention to the problems of manpower development should be viewed with extreme caution. The rest of the book is concerned with the application of the optimum control solution derived in Chapters 2 and 3 to determine the composition of the expenditure of oil revenues in pre-revolutionary Iran. A brief account of Iranian economic development over the 1970’s is given in Chapter 4. This chapter is intended for readers not familiar with the Iranian economy. The parameters of the basic macro-economic model are estimated for the Iranian economy in Chapter 5, where the author argues that since Iranian data is very unreliable one should avoid using sophisticated estimation techniques. It is difficult to see how the use of less sophisticated methods can help us overcome the problem of data deficiencies. Although I sympathize with Dr. Motamen’s distrust of Iranian data, I do not share her view that in these circumstances testing of economic relations should be abandoned. Furthermore, the import constraints specified by Dr. Motamen are difficult if not impossible, to test in the real world. To obtain ‘guess-estimates’ of the parameters of the constrained import funcllon the author implicitly assumes that all imports to Iran over the 1971-75 period can be classified as essential, which is a very doubtful presumption. The numerical computations of the optimum trajectories are implemented in Chapter 6 where the steps involved in the application of the ‘method of
Book Reviews
391
feasible directions’ are discussed in some detail. A number of useful and illuminating sensitivity analyses are carried out in Chapter 7. The book finishes with a short concluding chapter. Despite its shortcomings and the very preliminary nature of its findings this is a useful book. It is set out very clearly and all the major assumptions and the steps involved in the numerical computations are explicitly stated. Overall, I believe the book can be helpful both to economists who are interested in and insist on the application of control engineering techniques to economic planning and to control engineers who may wish to learn about some of the problems connected with the application of control techniques to solving economic problems. M.H. PESARAN Trinity College, Cambridge
G. Gandolfo, Economic dynamics: Methods Amsterdam, 1980) pp. xii + 571, $46.25.
and models (North-Holland,
This is an intermediate textbook on the solution of ordinary difference and differential equations and on stability theorems for nonlinear systems. In the course of the treatment the author discusses a variety of deterministic, dynamic models arising in analytical economics. This review concentrates on the mathematical aspects of the book and concludes with some remarks on the choice of economic applications. The first part of the volume gives a thorough treatment of the analytic solution of linear difference equations with constant coefficients. For the second order equation it shows what type of dynamic behaviour corresponds to a particular choice of parameter values. For higher order equations and linear systems the author provides a number of stability conditions in matrix form. The second part of the volume deals in the same manner with the solution of linear differential equations. It includes a brief discussion of the Routh-Hurwitz and LiCnard-Chipart stability criteria, some special results for non-negative systems and the assignment problem. The third part of the volume contains more advanced material and commences with a treatment of comparative statics and the correspondence principle and provides an interesting link with the stability properties of optimal states. It continues with a heuristic discussion of Lyapunov’s indirect test for stability of nonlinear systems, the Volterra-Lotka predator-prey equations and elements of the qualitative theory of nonlinear systems. The book concludes with the analysis of differential equations with time delay. Thus the mathematical content is fairly conventional, although well known techniques, such as the Laplace- or z-transforms, transfer functions in the
381
slightly more substantive point, I feel that the insistence in the section on price aggregation that sectoral price indices depend only on prices is unnecessarily disabling. In particular, it means that the standard procedure in demand analysis (working with commodity groups and commodity prices, the inner product of ivhich is total expenditure) will only work if the subutility functions are homogeneous, with all goods which are grouped together required to have the same income elasticity. However, if the price and quantity indices are permitted to depend on total utility, implicit conjugate duality gives perfect (additive) price and quantity aggregation, while, if the indices can depend on the sectoral welfare level, such aggregation follows from the usual direct separability. Furthermore, in the latter case, the theoretical indices are likely to be closely approximated by the Laspeyres quantity and Paasche price indices which are used in practice. But these are minor, personal quibbles. As a whole, the book is an immensely valuable addition to the literature. The applications of separability spread out very widely; choice under uncertainty, the analysis of inequality and social choice theory are three obvious examples not covered here but employing. much the same mathematical structures. There will therefore be many economists and others who will find this an irreplaceable source of reference and who, like me, will feel that much more secure with this volume on their shelves. Angus DEATON University of Bristol
H. Motamen, Expenditure of oil revenue: An optimal control approach with application to the Iranian economy (Frances Pinter, London, 1979) pp. 189, E12.50. This book is a slightly extended and revised version of the author’s doctoral dissertation submitted to the University of Cambridge and is concerned with the application of control theory to development planning in the case of oilbased economies. Although the problem of optimal planning has attracted a great deal of attention in the literature of mathematical economics, its impact upon actual planning in developing countries has been minimal, to say the least. I am very doubtful as to whether the application of control techniques to the problems of developing countries should be emphasized at this point in time. Economic development is a complicated process which is invariably concerned with and involves structural change. Optimal control techniques that ignore the response of economic agents and institutions to the implementation of the optimal plan and the changing structure that it inevitably brings about can only be of limited practical relevance and it is
388
Book
Reoiews
comforting to note that even Dr. Motamen, enthusiastic advocate of the use of control techniques in economics as she is, does not recommend a full-scale application of the control theory to the actual planning of oil exporting countries. Her main aims are to use the control theory in order to highlight the policy options open to oil exporting countries faced with an exogenously given stream of earning in excess of their domestic absorptive capacities and to demonstrate how trajectories of the control and state variables can be efficiently calculated by the ‘method of feasible directions’. In Chapters 2 and 3, Dr. Motamen considers the problem of the optimal allocation of revenues obtained from an exhaustible resource such as oil, over a known planning horizon. She assumes that the stream of revenues from oil exports is given exogenously. This is a gross over-simplification. The most important problem faced by oil exporting countries is to determine their optimum rate of oil extraction given their domestic absorptive capacities, world demand and uncertainties concerning the future emergence of economically viable substitutes for oil. It is the simultaneous determination of the optimal rate of resource depletion and the optimal rates of domestic and foreign investment which lie at the heart of efficient development planning in oil exporting countries. Dr. Motamen’s arguments for assuming the exogeneity of the future oil revenues are two-fold. Firstly, she points out that since oil prices are determined by the Organization of Petroleum Exporting Countries (OPEC), thus no member country is at liberty to set its own export price unilaterally. Given the present oil price-setting mechanism this is reasonable. Secondly, she argues that for given export prices there will be an upper limit to the annual rate of oil extraction for OPEC as a whole which is set by world demand for OPEC exports. Therefore, she maintains that there is an upper limit to the rate of oil extraction for individual OPEC member countries. So far so good. But she goes on to argue that since the output of oil in OPEC member countries has generally been near the upper limit in the past, then it is valid to regard the rate of oil extraction, as well as oil prices, as being given exogenously. This argument is very unsatisfactory. Firstly, it is not true that all oil exporting countries have behaved in this way. Secondly, even if such an output policy has been followed by some of the OPEC member countries, it does not necessarily make it an optimal policy, whether viewed from the interests of the oil exporting countries or the world economy as a whole. Note, that as soon as the exogeneity of the rate of extraction is abandoned, we can no longer regard the planning horizon to be exogenous either. In the light of the recent political and social upheavals in Iran, it is becoming increasing clear that it is not appropriate to regard Iran’s future stream of oil revenues as exogenous. Furthermore, even in the case of a country like Saudi Arabia, it is not all obvious why on purely economic grounds an output policy based on a maximum possible rate of extraction should be followed. It is possible for a country such as Iran to
Book Reuiews
389
decide upon an optimal output policy within the lower extraction rate set by political considerations and the upper limit set by world demand for OPEC exports and the output policies of other OPEC member countries. Given the approach followed by Dr. Motamen, it is difficult to see how an endogenous extraction policy can be incorporated within her model. Other major features of the macro-economic framework adopted by the author are the assumptions of the unlimited supply of labour of whatever skill that might be required by the investment plans, the absence of capital depre.ciation and the exogenously given government consumption expenditure. The production function for the non-oil domestic income is specified to depend solely upon the stock of domestic capital, and the private sector consumption is assumed to be proportional to non-oil (or more generally non-export) incomes. Whilst admitting that any aggregative model inevitably has to involve some simplifying assumptions, the particular set of assumptions chosen by Dr. Motamen leaves a lot to be desired. Indigenous skilled labour is not in abundant supply in oil exporting countries and resort to the importation of the necessary skills is not without its socio-political costs as was witnessed in the pre-revolutionary situation in Iran. Inflow of foreign labour accentuates the shortages and bottlenecks that exist in the non-tradeable sector of the economy and often brings about a sense of alienation among the indigenous population. The assumption pf exogenously given government expenditure is also extremely unrealistic. As all oil revenues accrue to the government and it is the government that decides both the level and the pattern of government expenditure, one expects the level of government consumption expenditure to vary closely with the oil and non-oil incomes. Similarly the assumption that oil income only affects private consumption indirectly through raising non-oil incomes is unsubstantiated and no theoretical reasoning is advanced for such a specification. This assumption becomes particularly unsatisfactory when the basic model of Chapter 2 is extended in Chapter 3 where it is assumed that even income from non-oil exports has no direct impact upon private consumption. Taxation is singularly absent from the model. It is not clear how government expenditure is supposed to be financed when the oil runs out. The control problem considered by Dr. Motamen is the maximization of the terminal stock of capital subject to two constraints. Firstly that there should be no foreign debt at the terminal date and secondly, that a minimum level of imports should be met out of oil revenues in every period. By applying the Kuhn-Tucker theorem the author then shows that the intertemporal allocation of oil income should be carried out to the point where the marginal returns on foreign and domestic investments (the latter multiplied by the average propensity to save) is equalized. Even when the model is extended in Chapter 3 to include the non-oil export sector this basic result remains unaltered, although some complications arises when the
390
Book Reviews
minimum import constraint becomes binding. The major recommendation of Dr. Motamen’s analysis for the conduct of optimal planning in oil exporting countries, in her own words, is: ‘ . . . . accumulate reserves outside the economy during the early years of the resource’s life and invest internally only if the rate of return is higher than abroad. Conversely, invest more domestically during the later years of the resource’s life and accept a lower rate of return abroad.’ (p.39) Without disputing the fact that the above recommendation is the inevitable policy implication of Dr. Motamen’s control problem, it should, however, be emphasized that within limits oil exporting countries have other more attractive options when faced with limited absorptive capacities (i.e., low marginal rate of domestic investment). They can, so far as political considerations allow them, reduce the rate of exploitation of their exhaustible resources. Considering the technical difficulties and risks that are currently involved in foreign investment by a small oil producing country, it is not clear why expenditure of oil revenues abroad should be preferable to keeping the oil under the ground. The maximization of the terminal capital stock is only a viable strategy if the human resources that are needed for putting the capital stock iirto proper use are also developed before the exhaustion of the oil revenues. Long term planning strategies that do not pay due attention to the problems of manpower development should be viewed with extreme caution. The rest of the book is concerned with the application of the optimum control solution derived in Chapters 2 and 3 to determine the composition of the expenditure of oil revenues in pre-revolutionary Iran. A brief account of Iranian economic development over the 1970’s is given in Chapter 4. This chapter is intended for readers not familiar with the Iranian economy. The parameters of the basic macro-economic model are estimated for the Iranian economy in Chapter 5, where the author argues that since Iranian data is very unreliable one should avoid using sophisticated estimation techniques. It is difficult to see how the use of less sophisticated methods can help us overcome the problem of data deficiencies. Although I sympathize with Dr. Motamen’s distrust of Iranian data, I do not share her view that in these circumstances testing of economic relations should be abandoned. Furthermore, the import constraints specified by Dr. Motamen are difficult if not impossible, to test in the real world. To obtain ‘guess-estimates’ of the parameters of the constrained import funcllon the author implicitly assumes that all imports to Iran over the 1971-75 period can be classified as essential, which is a very doubtful presumption. The numerical computations of the optimum trajectories are implemented in Chapter 6 where the steps involved in the application of the ‘method of
Book Reviews
391
feasible directions’ are discussed in some detail. A number of useful and illuminating sensitivity analyses are carried out in Chapter 7. The book finishes with a short concluding chapter. Despite its shortcomings and the very preliminary nature of its findings this is a useful book. It is set out very clearly and all the major assumptions and the steps involved in the numerical computations are explicitly stated. Overall, I believe the book can be helpful both to economists who are interested in and insist on the application of control engineering techniques to economic planning and to control engineers who may wish to learn about some of the problems connected with the application of control techniques to solving economic problems. M.H. PESARAN Trinity College, Cambridge
G. Gandolfo, Economic dynamics: Methods Amsterdam, 1980) pp. xii + 571, $46.25.
and models (North-Holland,
This is an intermediate textbook on the solution of ordinary difference and differential equations and on stability theorems for nonlinear systems. In the course of the treatment the author discusses a variety of deterministic, dynamic models arising in analytical economics. This review concentrates on the mathematical aspects of the book and concludes with some remarks on the choice of economic applications. The first part of the volume gives a thorough treatment of the analytic solution of linear difference equations with constant coefficients. For the second order equation it shows what type of dynamic behaviour corresponds to a particular choice of parameter values. For higher order equations and linear systems the author provides a number of stability conditions in matrix form. The second part of the volume deals in the same manner with the solution of linear differential equations. It includes a brief discussion of the Routh-Hurwitz and LiCnard-Chipart stability criteria, some special results for non-negative systems and the assignment problem. The third part of the volume contains more advanced material and commences with a treatment of comparative statics and the correspondence principle and provides an interesting link with the stability properties of optimal states. It continues with a heuristic discussion of Lyapunov’s indirect test for stability of nonlinear systems, the Volterra-Lotka predator-prey equations and elements of the qualitative theory of nonlinear systems. The book concludes with the analysis of differential equations with time delay. Thus the mathematical content is fairly conventional, although well known techniques, such as the Laplace- or z-transforms, transfer functions in the