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Theoretical and empirical issues in the choice of exchange rate policy Price, Diana N. 1990

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THEORETICAL AND EMPIRICAL ISSUES IN THE CHOICE OF EXCHANGE RATE POLICY by DIANA N. PRICE B.A.(Hon.), Dalhousie University, 1978 M.A., Dalhousie University, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Economics) We accept this thesis as conforming to the required standard. THE UNIVERSITY OF BRITISH COLUMBIA NOVEMBER 1989 DIANA N. PRICE, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Economics The University of British Columbia Vancouver, Canada Date December 1 1 , 1989 DE-6 (2/88) Abstract Part I of this thesis is concerned with providing an explanation for the absence of an international monetary agreement since the breakdown of the Bretton Woods system. The analysis centers around the proposition that the potential gains are not sufficiently large to induce countries to engage in cooperative exchange rate management. The analysis is undertaken in the context of a two country model in which the monetary authorities of each country intervene in the foreign exchange market with the objective of stabilizing domestic consumption and prices. Non-cooperative behaviour is characterized in terms of the equilibrium intervention strategies associated with Cournot and Stackelberg games, as well as a game in which each player correctly anticipates the responses of his opponent; the principal form of cooperative behaviour considered is the agreement to participate in joint loss minimization. The results of the numerical simulations, used to compare the losses associated with cooperative and non-cooperative intervention strategies, support the proposition that countries behave non-cooperatively because the gains from policy coordination are too small to extract a cooperative effort. The primary objective of Part II is to formulate a quantitative measure of exchange market intervention that- can be used to classify exchange rate practices and to conduct empirical studies of exchange rate policy. The measure that is proposed in this study is an index of exchange market intervention which characterizes exchange rate policy as the proportion of exchange market pressure that is alleviated by an endogenous change in the domestic money supply. Exchange market pressure is measured using a model-consistent generalization of the Girton and Roper (1977) formulation. In order to provide a basis of comparison for future empirical work, the proposed measures of exchange market pressure and exchange ii market intervention are calculated quarterly for Canada, Germany, Japan, United Kingdom, and the United States over the period 1973(1) - 1984(IV). Estimates are obtained for each country on the basis of a multiple-partner small open economy model as well as a model in which interdependence among trading partners is explicitly incorporated. i i i CONTENTS Abstract ii Tables vii Figures viii Preface • \ 1 PART I OPTIMAL EXCHANGE RATE POLICY IN INTERDEPENDENT ECONOMIES 3 Chapter 1 Optimal Exchange Rate Policy 1.1 Introduction 4 1.2 Optimal Exchange Market Intervention 6 1.3 Policy Coordination 10 1.4 Conclusion 16 Chapter 2 Optimal Exchange Market Intervention in the Small Open Economy 2.1 Introduction 19 2.2 The Small Open Economy Model 20 2.3 The Objective Function 22 2.4 Optimal Exchange Market Intervention 27 2.5 Intervention and Monetary Policy 30 2.6 Conclusion 31 Chapter 3 Optimal Exchange Market Intervention in Interdependent Economies 3.1 Introduction 33 3.2 The Two Country Model 36 3.3 Intervention and Monetary Policy 42 3.4 Loss Minimization 44 3.5 Cournot Game 45 3.6 Stackelberg Game 49 3.7 Consistent Conjectural Variations 51 3.8 Numerical Procedures 54 iv PART I continued 3.9 Cooperative Exchange Market Intervention 61 3.10 Conclusion 68 Appendix 3.1 78 PART II QUANTITATIVE MEASURES OF EXCHANGE RATE POLICY 92 Chapter 4 The Empirical Analysis of Exchange Rate Policy 4.1 Introduction 93 4.2 A Brief Overview 93 4.3 Quantitative Measures of Exchange Rate Policy 99 4.4 Conclusion 111 Appendix 4.1 113 Chapter 5 Measuring Exchange Market Intervention and Exchange Market Pressure 5.1 Introduction 115 5.2 Exchange Market Intervention 116 5.3 Measuring Exchange Market Intervention 119 5.4 Measuring Exchange Market Pressure 121 5.5 The Small Open Economy 122 5.6 Money Market Adjustment 129 5.7 Solving the Small Open Economy Model 134 5.8 Small Open Economy with Multiple Trading Partners 138 5.9 Two Interdependent Economies 142 5.10 Interdependence with Multiple Trading Partners 146 5.11 Conclusion 148 Appendix 5.1 150 Appendix 5.2 152 Chapter 6 Estimation and Testing: A Preliminary Exploration 6.1 Introduction 153 v PART II continued 6.2 Preliminary Estimation 154 6.3 Small Open Economy Estimation 165 6.4 Exchange Market Pressure and Intervention 172 6.5 Interdependent Economies 180 ; 6.6 Model Misspecification - Causes and Implications 190 6.7 Conclusion 192 Appendix 6.1 195 Appendix 6.2 196 Appendix 6.3 197 Appendix 6.4 201 Appendix 6.5 206 Appendix 6.6 212 Bibliography 214 v i TABLES Chapter 3 3.1(a) Real Disturbances: p(u) = - 0.75 71 3.1(b) Real Disturbances: p(u) = 0.75 72 3.2 Monetary Disturbances: b = 0 73 3.3(a) Real Disturbances: p(u) = - 0.75 74 3.3(b) Real Disturbances: p(u) = 0.75 75 Chapter 6 6.1 Small Open Economy: ^ A 6.2 Small Open Economy: p 6.3 Estimates of &2 and B using 2SLS-A 6.4 Small Open Economy: Final Estimates of a2, P and TJ 6.5 Interdependent Economies: Final Estimates of &2> P and if 163 164 167 171 182 vii FIGURES Chapter 3 3.1 Losses Real Disturbances: p(u) = - 0.75; b = 0 76 3.2 Losses Real Disturbances: p(u) = 0.75; b = 0.75 76 3.3 Losses Monetary Disturbances: p(u) = - 0.75; b = 0 77 3.4 Losses Monetary Disturbances: p(u) = 0.75; b = 0.75 77 Chapter 5 5.1 Money Market Adjustment 133 5.2 Exchange Market Pressure 137 Chapter 6 6.1(a) Canada: Exchange Market Pressure 175 6.1(b) Canada: Exchange Market Intervention 175 6.2(a) Germany. Exchange Market Pressure 176 6.2(b) Germany: Exchange Market Intervention 176 6.3(a) Japan: Exchange Market Pressure 177 6.3(b) Japan: Exchange Market Intervention 177 6.4(a) United Kingdom: Exchange Market Pressure 178 6.4(b) United Kingdom: Exchange Market Intervention 178 6.5(a) United States: Exchange Market Pressure 179 6.5(b) United States: Exchange Market Intervention 179 6.6(a) Canada: Exchange Market Pressure 185 j 6.6(b) Canada: Exchange Market Intervention 185 j 6.7(a) Germany: Exchange Market Pressure 186 i 6.7(b) Germany: Exchange Market Intervention 186 6.8(a) Japan: Exchange Market Pressure 187 6.8(b) Japan: Exchange Market Intervention 187 6.9(a) United Kingdom: Exchange Market Pressure 188 6.9(b) United Kingdom: Exchange Market Intervention 188 6.10(a) United States: Exchange Market Pressure 189 6.10(b) United States: Exchange Market Intervention 189 viii PREFACE This project deals with theoretical and empirical issues in the study of optimal exchange rate management. The first three chapters, which together comprise Part I, are concerned with providing an explanation for the absence of an international monetary agreement since the breakdown of the Bretton Woods system. The analysis centers around the proposition that the potential gains are not sufficiently large to induce countries to engage in cooperative exchange rate management. The analysis is undertaken in the context of a two country model in which the monetary authorities of each country intervene in the foreign exchange market with the objective of stabilizing domestic consumption and prices. Non-cooperative behaviour is characterized in terms of the equilibrium intervention strategies associated with Cournot and Stackelberg games, as well as a game in which each player correctly anticipates the responses of his opponent; the principal form of cooperative behaviour considered is the agreement to participate in joint loss minimization. The results of the numerical simulations, used to compare the losses associated with cooperative and non-cooperative intervention strategies, support the proposition that countries behave non-cooperatively because the gains from policy coordination are too small to extract a cooperative effort. Despite the proliferation of theoretical studies on the subject of optimal exchange rate management, empirical work in this area has been relatively scarce. One of the main reasons for this is that there has existed no generally accepted method of characterizing the wide variety of exchange rate practices that have developed over the past fifteen years. The primary objective of Part II is to formulate 1 a quantitative measure of exchange market intervention that can be used to classify exchange rate practices and to conduct empirical studies of exchange rate policy. The measure that is proposed in this study is an index of exchange market intervention which characterizes exchange rate policy in terms of the proportion of exchange market pressure that is alleviated by a change in the domestic money supply. With changes in the domestic money supply readily observable, the problem of representing exchange rate policy quantitatively, on the basis of this intervention index, becomes one of measuring exchange market pressure. The measure of exchange market pressure that is developed in this analysis is a model-consistent generalization of the measure introduced by Girton and Roper (1977). In order to provide a basis of comparison for future empirical work, the proposed measures of exchange market pressure and exchange market intervention are calculated quarterly for Canada, Germany, Japan, United Kingdom, and the United States over the period 1973(1) - 1984(IV). Estimates are obtained for each country on the basis of a multiple-partner small open economy model as well as a model in which interdependence among trading partners is explicitly incorporated. A comparison of the estimated obtained under these alternative models shows that the empirical results are fairly sensitive to changes in the model specification, indicating that further empirical investigation is required in order to determine whether it is possible to obtain quantitative measures of exchange market pressure and exchange market intervention that are robust to a relatively large class of models. PART I OPTIMAL EXCHANGE RATE POLICY IN INTERDEPENDENT ECONOMIES 3 CHAPTER 1 OPTIMAL EXCHANGE RATE POLICY 1.1 Introduction Despite the considerable attention that has been devoted to the subject of exchange rate management, the question of whether policy authorities should maintain exchange rates at some target level, or allow the rate at which currencies are traded internationally to be determined by private market forces, remains largely unresolved. In the absence of a consensus of opinion, the practical necessity of implementing an exchange rate policy has led policy authorities to experiment with a variety of exchange rate systems. The longest running and perhaps the most successful of these experiments was the Bretton Woods system, which was adopted in 1944. Although the Bretton Woods system is most often characterized solely as an exchange rate regime under which exchange rates were held relatively fixed, it had a second, equally important, characteristic. Namely, it represented a formal agreement under which the policies of participating countries were coordinated according to well defined rules and with the expectation that all participants wished to achieve full employment. When the Bretton Woods system collapsed in 1973, countries gained the freedom to choose their exchange rate policies as they saw fit, but at the same time, they lost whatever gains might have accrued to them as participants in a cooperative game. The debate over whether exchange rates should be held fixed or allowed to float freely continued throughout the period during which the Bretton Woods system 4 5 was in force. Consequently, with the breakdown of the Bretton Woods system, a policy of freely floating exchange rates appeared to be the natural alternative. The observation that freely floating exchange rates offered alternatives that were no better, and indeed sometimes worse, than those available under the Bretton Woods system, gave rise to the suspicion that choosing between fixed and flexible exchange rates is an exercise in the theory of the second best; a hypothesis that is bom out by the numerous studies that now exist on the subject of optimal exchange rate policy. The failure of both fixed and freely floating exchange rate systems to provide the universal means by which the various ends desired by national policy authorities could be obtained, brought about a new era of independent policy experimentation. The result of this has been the development of a wide variety of intervention practices. One of the reasons that the Bretton Woods system was abandoned was that the participants judged the potential gains from that agreement to be too small to sustain their cooperative effort. In the intervening years, international monetary relations have continued to be characterized by the absence of a formal agreement governing the conduct of monetary policy and exchange market intervention. There are indications, however, that several countries may be in the process of revising their estimates of the size of potential gains from cooperation.1 The need to explain the observed diversity of exchange rate practices and the persistent absence of an international monetary agreement has produced an extensive literature dealing with the determinants of optimal exchange rate policy and the related issue of the potential gains from international policy coordination. A brief survey of this literature is provided in the following two sections. 1 Evidence of this is to be found in the form of the Group of Five Agreement, adopted in September 1985, and the communique issued at the Louvre meeting of the G-7 countries in February 1987, both of which called for greater policy coordination among member countries. 6 1.2 Optimal Exchange Market Intervention At its most fundamental level, the question of whether exchange rates should be fixed or floating is concerned with the choice of the correct monetary policy instrument in an open economy. In the absence of risk or uncertainty, there is no basis for choosing between the two policies because, in a deterministic world, the costs of adjustment associated with external imbalances are identical under fixed and flexible exchange rates. This point, which was made by Poole (1970) in a study of the proper choice Of monetary policy instrument in a closed economy, was recognized in earlier work concerned with the choice of exchange rate policy. Beginning with Mundell's original contribution in 1961, the optimum currency area literature argued that the costs of adjustment associated with economic disturbances should be the principal determinant of exchange rate policy.2 It was also pointed out that costs of adjustment associated with any given disturbance will vary, depending on the structure of the economy. By incorporating stochastic disturbances into the basic IS-LM model, Poole was able to conduct a formal comparison between the costs associated with economic disturbances of varying origin, under interest rate and money supply targeting. In his analysis, the cost associated with each policy is measured in terms of a quadratic loss function representing the deviation of actual output from the full employment level. The policy instrument is then chosen with the objective of minimizing the value of this loss function. The results of Poole's analysis support the position, taken by contributors to the optimum currency area literature, that the choice of policy instrument is jointly dependent on the structure of the economy and the source and magnitude of economic disturbances. Poole's analysis has a number of distinguishing characteristics: (i) the formal inclusion of stochastic disturbances in the underlying structural model, (ii) the 2 Other contributors are Kenen (1969) and Tower and Willett (1976); Ishiyama (1975) provides a useful survey of the optimum currency area literature. 7 evaluation of alternative policy instruments in terms of a specific policy objective, (iii) the explicit representation of this policy objective in terms of a quadratic loss function, and (iv) the assumption that monetary policy is properly directed towards the maintenance of economic stability. The fact that almost all of the subsequent literature on the choice of exchange rate policy employs a similar methodology is evidence of the considerable debt that this literature owes to Poole's original contribution. One of the first applications of Poole's analytical framework to the problem of the choice of monetary policy instrument in an open economy was undertaken by Fischer (1977). In the context of a stochastic monetarist model, in which capital is assumed to be immobile and output fixed, Fischer compares fixed and flexible exchange rate policies on the basis of their implications for the stability of real consumption. Fischer finds that, for the small open economy specified, floating rates minimize the variance of real consumption when shocks originate as money demand disturbances or as changes in the foreign price level. When disturbances originate in the real sector of the domestic economy, fixed rates are preferable because they allow some of the domestic disturbance to be transmitted to the rest of the world. In related studies, Turnovsky (1976) and Flood (1979) included capital flows and allowed price prediction errors to have real effects through an expectations-augmented Phillips Curve. The studies differ, however, in the assumptions that are made about the nature of capital flows and the objective function. Turnovsky chooses output stability as the objective function and allows the degree of capital mobility to vary, while Flood assumes perfect capital mobility and makes the minimization of domestic price prediction errors the policy objective. As a result, the studies come to different conclusions regarding the choice of exchange rate policy. Turnovsky concurs with Fischer that flexible exchange rates insulate the economy against foreign price disturbances, but finds that fixed exchange rates are preferable when disturbances 8 originate in the monetary sector. He also concludes that in the case of output disturbances the degree of capital mobility determines the choice of exchange rate policy, floating rates being preferred to fixed when capital is very mobile. Flood's analysis is less conclusive. He is able to show that when capital is mobile, floating exchange rates no longer insulate the small open economy from foreign disturbances, but is forced to admit that the choice of optimal policy is an empirical matter. The lesson to be learned from this is that the optimal exchange rate policy is country specific, depending jointly on the relationship between economic structure, social objectives and the nature of the disturbances to which the economy is subjected.3 In their studies, Fischer, Flood, and Turnovsky restricted the choice of exchange rate policy to fixed and flexible exchange rates. The need to explain the preference that developed, after the breakdown of the Bretton Woods system, for exchange rate regimes in which currencies are neither completely fixed nor allowed to float freely, led subsequent contributors to adopt a more general optimizing framework. The resulting literature, which is now extensive, is represented by two main methods of analysis. The first, employed by Boyer (1978), Buiter (1979), Buiter and Eaton (1985) and Turnovsky (1983,1984,1985,1987), describes exchange market intervention in terms of a money supply rule which reflects the response of the policy authority to observed changes in selected endogenous variables. In its simplest form, this contemporaneous feedback rule is given by: Am t = k Ae t, where A m t denotes the change in the money supply and Ae t the observed change in the exchange rate to which the policy authority responds. In more general specification of this type of rule, the policy authority may also respond to other signals such as the domestic interest rate and price level. The value of the coefficient k indicates the 3 Other extensions are provided by Flood and Marion (1982), and Aizenman (1983) who consider the effects of wage indexation and commercial policy, respectively, on the choice of exchange rate policy. nature of the exchange rate policy. When k = 0, the policy authority holds the money supply constant regardless of the observed change in exchange rates indicating that the exchange rate is freely floating; under perfectly fixed exchange rates k = - 0 0 . Values of k between 0 and - 0 0 , are representative of intermediate exchange rate systems. Positive values of k indicate that the optimal change in domestic credit is one that moves the exchange rate in the opposite direction to the change that would have occurred had quantity of domestic credit been held constant. In the second approach, developed by Frenkel (1980) and Frenkel and Aizenman (1982), the degree of exchange market intervention itself, rather than the resulting change in the domestic money supply, is viewed as the policy instrument. Frenkel and Aizenman measure the degree of exchange market intervention on the basis of an intervention index, y't,. defined as : y't = Aet/Ae(f)t, where Ae t denotes the observed exchange rate change and Ae(f) t the change in the exchange rate that would have occurred under freely floating exchange rates. In the model employed by Frenkel and Aizenman, the extent of money market disequilibrium can be measured as the exchange rate change that is required to restore equilibrium under a system of freely floating exchange rates. The intervention .index therefore describes exchange rate policy in terms of the proportion of money market disequilibrium removed by a change in the exchange rate. When y' = 1, exchange rates are freely floating; y' = 0 indicates that exchange rates are held fixed. Values between 0 and 1 represent intermediate exchange rate systems. Although Frenkel and Aizenman do not consider the possibility, values of y' that are greater than 1 can be interpreted as "leaning with the wind", while negative values of y' are analogous to the situation in which k > 0. It is clear that, from a theoretical point of view, the two methods of analysis are equivalent and that in both cases domestic monetary policy is, by definition, indistinguishable from direct intervention in the exchange market. From an 10 empirical point of view, the intervention index y' has the advantage that it assigns finite values to both of the extreme exchange rate systems. While the precise characteristics of the optimal intervention policy remain sensitive to both the structure of the underlying model and the choice of objective function, there is one point of perfect unanimity.4 All of the studies clearly demonstrate that neither perfectly fixed nor freely floating exchange rates will, in general, be optimal. 1.3 Policy Coordination It is not a coincidence that the existing diversity of exchange rate practices has been accompanied by the persistent absence of international monetary policy coordination. The fact that countries choose a wide variety of intervention policies is evidence of the differences that exist with respect to their social objectives and economic circumstances. The problems that arise when the policy authorities in interdependent economies pursue independent policies have been studied by a number of authors. Early contributors to this literature analyzed the problem of strategic policy formation in the context of deterministic models. Examples of this approach are found in the contributions of Cooper (1969), Hamada (1976), Kydland (1976), McFadden (1969), Patrick (1973), and Pindyck (1976). Although these studies focus on a variety of different aspects of decentralized policy formation, they reach the common conclusion that there exist gains from policy coordination. The existence of such gains is usually established by comparing the outcome of various non-cooperative strategies with a cooperative alternative on the basis some specified policy objective.5 In this respect the methodology used in the analysis of policy 4 Melvin (1985) provides a useful summary of the sensitivity of optimal exchange rate policy to the choice of objective function. 5 Throughout this study, the distinction between cooperative and non-cooperative games follows the definitions used by Aumann (1988). That is, a game is considered 11 coordination is similar to that employed in the studies on optimal exchange rate policy. Recently, Buiter and Eaton (1985) have introduced stochastic elements into the analysis of strategic policy formation. The authors consider the problem of optimal exchange market intervention in the context of a two country model in which the only contemporaneous variable observed by each policy authority is the exchange rate.6 As disturbances to the economy cannot be observed directly, policy authorities must infer the nature of destabilizing shocks from the observed changes in the exchange rate. The task facing each policy authority is to stabilize domestic output and the exchange rate using an optimal monetary policy and taking into account the fact that the foreign policy authority is engaged in the same exercise. A comparison of the result of non-cooperative behaviour, represented in terms of a Cournot game, and the cooperative, joint loss minimizing solution, leads to the conclusion that the Nash equilibrium is not Pareto optimal. In this particular case, gains from cooperation exist because coordinated monetary policy leads to greater exchange rate stability than can be achieved with decentralized policy formation. In related studies, Canzeroni (1982), Canzeroni and Gray (1983), Oudiz and Sachs (1984), and Turnovsky and d'Orey (1985), reach the same conclusion. In view of these results, the observed reluctance of national policy authorities to engage in cooperative policy formation requires explanation. The studies of Oudiz and Sachs (1984) and also Turnovsky and d'Orey (1985) offer one possible explanation. Using numerical simulations to evaluate the outcomes of various forms of cooperative and non-cooperative behaviour in a static model, these studies cooperative if commitments, in the form of agreements, promises, or threats, are fully binding and enforceable. A game is non-cooperative if commitments are not enforceable, even if pre-play communication between the players is possible. 6 Their analysis also incorporates rational expectations, a Lucas supply function and an uncovered interest parity condition. 12 conclude that the gains from cooperation, where they are found to exist, are small.7 The implication of this result is that countries may not cooperate because the perceived gains from cooperation are too small to compensate them for the costs associated with reaching an agreement. Given that this conclusion is obtained on the basis of static analyses, the question that naturally arises is whether dynamic analyses would generate a similar result. There is now a growing interest in employing dynamic game theory in the analysis of international policy formation. There appear to be two main reasons for this. The most obvious of these is that economic policy is conducted in a dynamic environment. That is, policy authorities interact with each other repeatedly over time so that their current actions as well as the current state of the world must inevitably be a function of all past actions. Secondly, in the absence of a global agency capable of enforcing binding commitments between sovereign nations, only self-enforcing or incentive compatible agreements are credible. Since dynamic games open up the possibility of collusive equilibria, they provide a convenient vehicle for analyzing non-cooperative policy coordination. At present, one of two approaches is used to conduct macroeconomic analyses involving multi-period dynamic interaction among players. The first of these takes the form of a repeated game. In repeated games there are no structural dynamics and the relationship between the games played in each period arises because players condition their strategies on their own past actions as well as those of their opponents. Repeated games take place in discrete time and are often referred to as supergames or games of reputation. One well known example of a reputational game is provided by Barro and Gordon (1983). However, such applications of repeated games are rare. This is largely because the absence of structural dynamics in 7 Owing to the specification of their theoretical model, they are able to identify only constrained optima and therefore, in a few instances, obtain the result that non-cooperative solutions are superior to joint loss minimization. 13 repeated games makes them unsuitable for analyzing macroeconomic issues in which asset and price dynamics are central. An alternative approach is to use difference or differential games. These games, which may be formulated in discrete or continuous time, naturally incorporate structural dynamics. In both formulations, the pay-off in each period is a function of the actions taken in preceeding periods so that the game that is played changes endogenously over time. The main difficulty with games of this sort is that the problem of interest must always be formulated in such a way as to produce difference or differential equations for which known solutions exist.8 Consequently, although the framework is, in principle, flexible enough to accomodate structural, behavioural and informational dynamics, practical considerations limit the degree to which this flexibility may be advantageously employed. As differential equations are often easier to solve than difference equations, most of the recent work on dynamic policy coordination employs continuous-time games which incorporate only structural dynamics.9 Differential games have been employed by Curry and Levine (1985), Curry, Levine and Vidalis (1987) and Turnovsky, Basar and d'Orey (1988), to study the existence and potential magnitude of gains from cooperation in a dynamic framework. These studies, which assume that policy authorities know the structure of the economy, reach the general conclusion that cooperation does improve welfare measured in terms of a potential increase in GNP. While the potential gains from cooperation estimated on the basis of these dynamic models are generally larger than those obtained in static analyses, they remain modest promising GNP increases 8 See Fudenberg and Tirole (1986). 9 It should be pointed out, however, that game theorists are not happy about this development and would prefer to see the games modeled in discrete time. The reason for this is that continuous time formulations imply that the observation of the state variables, the actions taken by players, and the motion of state variables resulting from these actions all occur simultaneously so that the game cannot be described in extensive form. 14 between 0.5% and 1.5%. The results obtained in these studies also suggest that the magnitudes of potential gains are model specific, depending jointly on the structure of the model, the form of the objective function, and the persistence of the shocks to which economies are subjected.10 Holtham and Hughes Hallett (1987) have studied the variation in the potential gains from cooperation across a range of widely used empirical multicountry models. The general conclusion reached on the basis of this study is that cooperative policies that are optimal with respect to one model frequently lead to welfare losses when compared to the non-cooperative outcomes associated with alternative models. Holtham and Hughes Hallett also find that Nash equilibrium strategies tend to be more robust to changes in model specification, and therefore less risky, than optimal cooperative policies. The implication of this result is that risk-averse policy authorities who are aware of the possibility of model misspecification may have little incentive to cooperate. Frankel and Rockett (1988) have explored the implications of model uncertainty from a different perspective. The question they address is whether cooperation is beneficial when policy authorities have different views of the world. Frankel and Rockett's simulations of ten large-scale econometric models indicate that when policy makers do not agree on the underlying structures of their economies, cooperation may not be beneficial and may even leave at least one participant worse off relative to the non-cooperative outcome. Much of the recent political debate over policy coordination has been concerned with exchange rate management. Analytical studies of optimal exchange rate management in interdependent economies have focused on the strategic choice of monetary policy under floating exchange rates. In these studies, a monetary policy rule is used as the strategic variable rather than some measure of the degree 1 0 Some authors, notably Rogoff (1985) and Miller and Salmon (1985) have found cooperation to be counterproductive. As Rogoff has pointed out, this outcome depends heavily on the precise formulation of the analytical model employed. 15 of exchange market intervention. While nobody has previously used exchange market intervention as a strategic variable, Holtham and Hughes Hallett (1987) use the exchange rate as a target of economic policy. With the exchange rate as a target, the degree of exchange market intervention is a residual. The addition of the exchange rate as a variable in the objective function was found to increase the gains from cooperation significantly, with the gains falling between 3% and 6% of GNP. This indicates that countries pursuing exchange rate stability have a greater incentive to cooperate than those who do not pursue this objective. It is not clear, however, that exchange rate stability is an appropriate target for government policy, particularly since the one point that all studies of optimal intervention policy agree on is that fixed exchange rates will not, in general, be optimal. The exchange rate cannot be used as a strategic variable because the value of the exchange rate is jointly determined by the actions of domestic and foreign policy authorities. To qualify as a strategic variable, an instrument must be completely under the control of a single policy authority. The degree of exchange market intervention is such a policy instrument since policy authorities are always free, reserve stocks permitting, to choose the extent to which they intervene in the foreign exchange market. In this study the degree of exchange market intervention is defined as the proportion of domestic money market disequilibrium removed by intervention in the exchange market by the domestic policy authority.11 The choice of a level of exchange market intervention on the part of each authority jointly determines the exchange rate. In terms of game forms, strategies are degrees of exchange market intervention and the exchange rate is part of the description of the outcome. 1 1 Disequilibrium, in the context of the market-clearing models employed throughout this study, refers to an initial imbalance between the demand and supply sides in the domestic money market caused by an exogenous disturbance to the economy. 16 Consider fixing the level of the foreign country's strategic variable and making a small change in that of the domestic country. One can think of the impact of this change as being decomposed into two parts: the direct impact on the domestic economy and the indirect, or spillover, effect on the foreign economy. For most monetary and fiscal policy instruments, one would expect the former effect to be greater than the latter. In contrast, with the degree of exchange market intervention as the strategic variable, the spillover effect can be expected to be substantially stronger. The reason for this is that the impact of exchange market intervention on the level of the exchange rate is the same regardless of whether the intervention is undertaken by a domestic or foreign policy authority. This line of reasoning suggests that the potential gains from cooperatively coordinating exchange market intervention may be quite large. The subsequent analysis shows that this conclusion is correct for Cournot-Nash non-cooperative equilibria using the degree of exchange market intervention as the strategic variable. However, it is also shown that the potential gains from cooperation are small when other non-cooperative solution concepts are employed, 1.4 Conclusion This chapter has provided a brief summary of the main developments in the study of optimal exchange rate policy and policy coordination. The extensive literature concerned with optimal exchange rate policy suggests that the reason for the observed diversity in exchange rate practices among countries is to be found in their differing economic circumstances and social objectives, and in the fact that neither fixed not flexible rates will, in general, be optimal. Given that the existence of gains from cooperation is well established in the literature on policy coordination, the persistent absence of an international monetary agreement is more difficult to 17 explain. Recent attempts to measure the potential gains from cooperation suggest that one reason for the lack of cooperative policy formation may be that the gains are too small to extract a cooperative effort. The foregoing discussion has suggested that cooperative gains might in fact be large when the degree of exchange market intervention is the strategic variable. Nevertheless, we do not observe cooperative exchange rate management. The purpose of this analysis is to reconcile these apparently conflicting observations. The analytical framework employed is very simple and is based on the monetary model introduced by Fischer (1977) and later used by Frenkel and Aizenman (1982). The main reason for employing this model is that it is simple enough to produce reasonably tractable game theoretic solutions and, at the same time, contains the essential elements required to characterize strategic exchange rate policy in terms of the degree of exchange market intervention practised by domestic and foreign policy authorities. In Chapter 2 the basic analytical framework is introduced and used to analyze the problem of optimal intervention policy in the small open economy. Strategic aspects of intervention policy in interdependent economies are analyzed in Chapter 3 in the context of a two country model in which the exchange rate and price level are jointly determined by the exchange rate policies of the two national policy authorities. In order to simplify the game theoretic analysis, a static framework is initially employed to study the potential gains from cooperative exchange market intervention. The implications of conducting the analysis in the context of a repeated game are subsequently considered. The strategic variable used by the policy authorities in each country is an index of exchange market intervention. This index is a measure of the proportion of money market disequilibrium removed by endogenous changes in the money supply. While this concept is independent of the model specification, the functional form of the index is not. Given the model specification, the functional form of the index is 18 completely determined. This is not to say that the value of the index is completely determined by the model specification as the model will contain parameters whose values must be determined empirically. In order to calculate the value of an exchange market intervention index, one must first specify a structural model of the economy; second, derive the corresponding functional form for the index; and third, estimate the parameters of the model. In the second part of this study, this procedure is illustrated using one particular model of the economy. CHAPTER 2 OPTIMAL EXCHANGE MARKET INTERVENTION IN THE SMALL OPEN ECONOMY 2.1 Introduction This chapter studies the choice of optimal exchange rate policy in a small open economy that is subject to stochastic output, money demand, and foreign price disturbances which cannot be observed directly. It is assumed that the policy authority is concerned with stabilizing real consumption and prices and that exchange rate policy is formulated on the basis of the known distributions of the various disturbances in order to achieve this objective. Following the example of Frenkel and Aizenman (1982), exchange rate policy is defined in terms of an index of exchange market intervention. The problem of the policy authority is to choose the degree of exchange market intervention that minimizes the effects of the disturbances on the domestic economy. The analysis is conducted on the basis of a simple version of the class of structural models most frequently employed in studies of optimal intervention policy. The assumptions that output is exogenous, capital immobile and that private agents do not exhibit forward looking behaviour are employed in order to make the solutions to the strategic games, presented in Chapter 3, more tractable. 19 20 2.2 The Small Open Economy Model The structure of the small open economy is given by equations (2.1) - (2.5). The model is adapted from Fischer (1977) and is expressed here in terms of logarithms as an analytical convenience. yt= y + ut lt= k + pt +yt + vt pt= (p* + et) + et Ar^ = m^  - m^ . \ mt = l t where: y is domestic output, y the mean level of domestic output, 1 the demand for money, p the domestic price level, p* the foreign price level, e the exchange rate (i.e., number of domestic currency units per unit of foreign currency), Ar the balance of payments (i.e., change in reserves), m the supply of money - all expressed in logarithms. Lower case letters represent the logarithms of their upper case counterparts except in case of Art which is defined as the change in reserves as a percentage of the initial money supply so that Art = (R^  - R^.^/M^j. It is assumed that the random variables ut, vt, and ej, representing real, money demand and foreign price shocks respectively, are independently distributed and serially uncorrected, each with zero mean and constant variance.1 It is assumed also that each country is endowed with some initial stock of reserves, R Q , and that the stock of reserves at any time, t, is determined by R T = RQ + X Ar tM t.i. (2.1) (2.2) (23) (2.4) (2.5) 1 It is worth noting that in the context of this model, real disturbances are analogous to general supply disturbances and nominal disturbances to demand shocks. 21 The equations above describe a small open economy that is subject to three distinct and serially uncorrected types of stochastic disturbance. Output is exogenously determined, homogeneous, and freely traded. It is also assumed that domestic residents do not hold money balances denominated in foreign currencies and obtain such currencies only for the purpose of acquiring foreign goods which are always purchased in the currency of the seller. The link between the real and monetary sectors is established through equation (2.2) which specifies the desired and nominal money stock as a function of price and output levels and random disturbances to money demand. The foreign price level, p*t = p* + et, is exogenous to the small open economy and subject to a random disturbance et. The relationship between foreign and domestic price levels is established by the purchasing power parity condition, equation (2.3). Equation (2.4) reflects the fact that, in the absence of sterilization, changes in the foreign exchange holdings of the policy authority have a direct impact on the size of the domestic money supply. Equation (2.5) incorporates into the model the assumption of continuous money market clearing. In Fischer's original formulation of this model, the short run change in the money supply was the result of a stock adjustment process where the change in the money supply observed in any period was a constant fraction of stock disequilibrium in the money market.^  When exchange rates are flexible, the money supply is exogenous and the exchange rate adjusts to remove any money market disequilibrium within one period 2 This type of formulation is common in the empirical literature dealing with estimation of money demand functions. See for example, Chow (1966) and Ooldfeld (1973, 1976) . A good review of such money demand functions is provided by Hetzel (1984). Fischer's original formulation of equation (2.5) is given by m t- mt_i= a(l t - mt_i). In this framework, the assumption that the money market clears continuously implies that a = 1. 22 so that substituting equations (2.1), (2.2), (2.3), and (2.5) into (2.4) and then setting equation (2.4) equal to zero determines the exchange rate as: et = mt.i - k - p* - et - y - ut - vt (2.6). Under fixed exchange rates, the elimination of disequilibria is accomplished through changes in the endogenous money stock as private agents trade goods for money in order to restore portfolio balance. Subtracting m t.j from both sides of equation (2.5) yields an expression of the money market clearing condition in terms of changes in the quantity of money supplied and demanded m t - mt.j = lj - mt_j (2.5'). Substitution of equations (2.1), (2.2), and (2.3) into equation (2.5') shows that under fixed exchange rates the change in the nominal money supply is given by: mt- mt.i = k + (p* + et) + e + (y + ut) + vt - mt_\ where e indicates that the exchange rate is fixed. 2.3 The Objective Function Studies of optimal exchange rate policy have attributed a variety of objectives to the policy authority, the most common of these being the stabilization of some linear combination of output and prices or the stabilization of real consumption.3 In this analysis, the policy authority is primarily concerned with employing exchange 3 The sensitivity of the optimal policy rules to these various policy objectives is discussed in Chapter 1. 23 rate policy in order to stabilize real consumption and the price level. It is assumed that the policy authority cannot directly observe contemporaneous shocks to the economy and must therefore choose its stabilization policy based on the known distributions of the various disturbances. The simple, non-optimizing structure of the model presented in section 2.2 implicitly assumes that there exists no conflict of interest between the policy authority and the private agents in the economy. For consistency, it is therefore necessary to interpret the policy objectives as arguments in a social welfare function. The inclusion of consumption stability in the social welfare function can generally be justified on the basis of intertemporal utility maximization.4 However, in the context of this analysis, a question arises regarding the appropriate target of consumption stabilization in an economy that is subject to demand as well as supply disturbances. In the absence of demand disturbances, and with output exogenous, it can be reasonably argued that stabilizing real consumption about y is welfare improving from the point of view of the private agent. If, on the other hand, transitory demand disturbances cause the aggregate desired consumption level to differ from y, a conflict of interest will arise between the policy authority and private individuals whenever the policy authority pursues policies that stabilize consumption relative to y. In this model, income is allocated between goods and money so that an increase in the demand for money, at a given level of income, indicates that there has been a decrease in the demand for goods. The stochastic money demand disturbance, v., can therefore be interpreted as evidence of an unanticipated change 4 Some studies which demonstrate this under uncertainty are Leland (1968), Sandmo (1970) and Dreze and Modigliani (1972). 24 in the consumption plans of private individuals. In order to ensure that no conflict of interest arises in the context of this model, such changes in preferences must be accommodated by the policy authority. Consequently, in this analysis the objective of the policy authority is to stabilize real consumption about (y - vt) rather than y. The inclusion of price stability as an argument in the social welfare function can be justified on the grounds that existing contracts for goods and services are fixed in nominal terms. The source of the welfare loss associated with unanticipated changes in the price level is that agents who are pre-committed to nominal contracts are forced to trade at distorted relative prices in the current period.5 Welfare losses associated with consumption and price stability are represented by the policy authority's loss function, L t : L t = var [byt + (l-b)pt] (2.7). In the small open economy, the policies that maintain price stability simultaneously ensure that real consumption is stabilized at (y - vt). The reason for this is that the demand for small open economy goods by the rest of the world, and the supply of foreign goods to the small open economy are, by assumption, perfectly elastic at the prevailing world price level so that consumption in the small open economy can be stabilized through trade in goods when disturbances originate in the monetary and output sectors. When foreign price shocks are the source of disturbance, policies that hold domestic prices constant prevent foreign price changes from affecting real consumption in the small open economy. Since the policy objectives of price and output stability coincide perfectly, the loss function 5 Discussions of the welfare costs associated with unanticipated inflation are to be found in Fischer and Modigliani (1978) and Fischer (1981). 25 appropriate for policy evaluation in the small open economy, obtained by setting b=0 in equation (2.7), is simply given by: L t = var (pt) (2.7*). A more general form of the loss function, obtained by allowing 0 b < 1, is appropriate for the evaluation of stabilization policy among interdependent economies whose activities jointly determine the world price level.6 The problem of the policy authority is to minimize this loss function with respect to the degree of exchange market intervention, y, which is defined in a manner similar to that proposed by Frenkel and Aizenman:7 m t - mt.1 — - — (2.8). k + p*'+et+e + y + ut+ vt - mt-i The parameter y characterizes the whole range of possible degrees of exchange market intervention, exchange rates being completely flexible or perfectly fixed when y takes on the values of 0 and 1, respectively. In principle, y can take on any value from minus to plus infinity; when 0 z.ys.1, the intervention index simply reflects the proportion of money market disequilibrium that is eliminated through changes in the nominal money supply. Values of y outside this range are associated with a floating exchange rate and a change in domestic credit, Ad t . In particular, it can be shown that when Y<0 the optimal monetary policy associated with a real disturbance u t, is given by Ad t=yu t which exacerbates the change in the exchange 6 This point is discussed in greater detail in Chapter 3. 7 Frenkel and Aizenman actually use (I-?). 26 rate that would have occurred in the absence of active monetary policy.8 Wheny>l, the policy authority intervenes to move the exchange rate in a direction opposite to that which a freely floating rate would have taken. Substituting equation (2.3) into equation (2.8) and solving for pt as a function of y, gives rise to the loss function, L t | expressed in terms of y : Lt(y) = [(2b-l) + (l-b)y]2a2u + (l-b)2(l-y)2a2v + (l-b)2Y2c2e (2.9). With b=0, the policy authority's period-by-period loss minimization problem is therefore given by: min L.(Y) = min (1-Y)2[ c2 + c2 i + y2c2 (2.10). {y} ii) Clearly, neither individuals nor policy authorities can be assumed only to be concerned with the losses incurred in the current period. In general, it is more reasonable to assume that individuals and policy authorities have some notion of minimizing losses over some longer time period. Formally the loss minimization problem of a policy authority concerned with losses over an infinite time horizon can be given in discrete form by: oo min Y(l+8)-t Lt(y) (2.11) W to 8 Algebraically, it must be the case that mt-mt-i= y[k+p*+e+y+ut+vt- mt-i] = [k+p*+e+Aet+y+ut+vt-mt-i]. Under floating exchange rates with a passive monetary policy, Aet=-ut. But the monetary authority wants Aep (y-l)ut. If the monetary authority alters the existing money stock so that mt_i=m't_i+Adt, then the optimal monetary policy under floating rates is given by Adt=yut. 27 where 8 is the discount rate Lt(y) is as defined in equation (2.9). As the single period loss function depends only on the level of intervention, y, and the variance of the economic disturbances which are, by assumption, constant from period to period, Lt(y) = L(y) for all t. A representation of the policy authority's loss minimization problem that is equivalent to (2.11) is therefore given by min L(Y)£(l+8)-t = min j L(y) ( "^T^ } (2.12). M t=0 M 1 8 J Since the discount rate, 8, is exogenously determined, the problem of intertemporal loss minimization described by equations (2.11) and (2.12) is identical to the period-by-period minimization problem, (2.10). 2.4 Optimal Exchange Market Intervention Minimizing the loss function, Lt(y), with respect to y yields the optimal degree of exchange market intervention <r2u + <*2V Y(opt) = - r - = r- (2.13) o2u + a 2 y + a 2 £ Since d2L(y)/dY2 = 2(a2u+ a2v+ o 2 e) >0, second order conditions confirm this to be a minimum. It is clear from equation (2.13) that managed floating, which is defined as 0 < Y(opt) < 1, will be optimal whenever foreign price shocks are accompanied by money demand and/or output disturbances. The change in reserves reqired to achieve the optimal degree of intervention is obtained from equation (2.8) as: 28 Art(opt) = y(opt)[k + p* + e t + e + y + Ut + vt - mt-i] (2.14). 1. Foreign price disturbances - (a2u=o-2v=0 ; a2e>0): When disturbances originate as foreign price shocks, flexible exchange rates are the only way to insulate the economy against losses so that y(opt)=0. At the prevailing exchange rate, an increase in the foreign price level p*t would cause the small country's goods to be relatively more attractive to foreign purchasers, causing an increase in the quantity of small country currency demanded. Under floating exchange rates, this causes the exchange rate to appreciate in the same proportion as increase in the foreign price which insulates the small economy from the disturbance. 9 Using the framework introduced by Salant and Henderson (1978), Krugman (1979) studied the nature of balance of payments crises under a fixed exchange rate system. Recently, Buiter (1987) extended the analysis to study the viability of exchange rate targets given the possibility of speculative attacks. These analyses all conclude that price stabilization schemes, of which exchange rate management is an example, are subject to speculative attack when the administered price persistently exceeds the price that the market would determine in the absence of intervention. Under these circumstances, if stocks of the asset used to effect price stabilization are limited, a crisis of confidence will inevitably occur. At such time, speculators, acting on the expectation that the administered price cannot be maintained, launch a speculative attack on the administered price which absorbes all of the remaining intervention asset. The policy authority, unable to maintain the administered price, is forced to allow the price to float. In the context of the current study, the conclusions reached by Salant and Henderson, Krugman, and Buiter, seem to suggest that exchange rate targeting cannot be successful in the long run. In order for this to be true, however, the analysis would have to be concerned with the possibility of persistent reserve drains. This is not the case in this analysis. Reserve drains occur, whenever Y * 0, in response to unanticipated disturbances which have mean zero. That is, speculative attacks will not occur within this framework because private agents do not expect observed reserve drains to persist. In addition, according to equation (2.IS), the policy authority always has the option of employing domestic credit changes to support an exchange rate target in the event of a temporary reserve shortage. 29 2. Money demand disturbances - ( a 2 u = a2E=0 ; a 2 v >0): When the small country is subject to monetary disturbances, the adjustment process, from the point of view of the small economy is best accommodated by means of the purchase or sale of an appropriate quantity of domestic output under fixed exchange rates and y(opt)=l. A positive disturbance to money demand (vt>0) for example, indicates that economic agents prefer a higher proportion of money balances (i.e., future consumption) relative to current consumption. Under fixed exchange rates, the small economy can alter the composition of its aggregate portfolio of goods and financial assets simply by selling some additional output at the prevailing world price. As the domestic price level is unchanged, total loss, as measured by the loss function, remains unaffected, the burden of adjustment having successfully been shifted to the rest of the world. 3. Real disturbances - ( a 2 v = a 2 e=0 ; o 2 u >0): When disturbances originate in the real sector of the economy, perfectly fixed exchange rates simultaneously maintain price stability and ensure that the equilibrium level of real consumption is held constant at y so that y(opt)=l. The reason for this is that, as a price taker, the small open economy can trade goods at prevailing world prices in order to stabilize domestic consumption in the presence of output shocks. As long as the world price level remains stable, the small open economy can achieve its dual goals of price and consumption stability simply by maintaining a fixed exchange rate. 30 2.5 Intervention and Monetary Policy Although the optimal degree of exchange market intervention defined by equation (2.3) is unique, the optimal exchange rate and monetary policy combinations implied by the optimal degree of intervention are not. It is relatively easy to show that there is a well defined correspondence between the optimal degree of exchange market intervention and a continuum of optimal exchange rate and monetary policy combinations. Substituting equations (2.1), (2.2) and (2.3) into equation (2.5') shows that the change in the nominal money supply is determined by: mt- mt_i = k + (p* + et) + et + (y + ut) + vt - mt.j = k + (p* + et) + e + Aet + (y + ut) + vt - mt_i (2.5"). Substituting mt- mt.j = y[k + (p* + et) + e + (y + ut) + vt - mt_i] from equation (2.6) into the left hand side of equation (2.5") and defining m t.j = + Ad t such that (k + p* + e + y - m't_i) = 0, yields the following relationship: Y = Aet "\ {(*t + ut + v t * A d t > J + 1 (2.15). Equation (2.15) implies that changes in domestic credit and direct intervention in the exchange market are perfect substitutes. Since the breakdown of the Bretton Woods system, most of the literature dealing with the management of monetary policy in open economies has focused on the choice of the optimal money supply (that is, on the optimal change in domestic credit) conditional on the assumption that exchange rates are fully floating. Equation (2.15) indicates that the problem of identifying the optimal monetary policy under a system of floating exchange rates is a special case of the more general problem of determining the optimal degree of exchange market 31 intervention. Furthermore, for all 7*1. there exist an infinite number of combinations of exchange rate and domestic credit changes that can be employed to achieve a desired degree of intervention.10 2.6 Conclusion The results of this chapter suggest that small open economies subject to a combination of real, money demand, and foreign price shocks can be expected to engage in some intermediate degree of exchange rate management. It is interesting that the theoretical results have an upper bound of y(opt)=l since, as a practical matter, one would expect the abilities of small economies to effect currency revaluations in opposition to prevailing market forces to be severely limited by the size of their foreign exchange reserves although the framework employed in this paper ignores such considerations. It was pointed out in Chapter 1 that the choice of optimal intervention strategy is sensitive to the specification of the structural model and the nature of the objective function. The assumptions made about the degree of capital mobility and whether price stability is treated as a policy objective, are particularly important. With output fixed, capital immobile, and the stability of real consumption as the policy objective, Fischer (1977) concludes that a flexible exchange rate is best when economies are subject to money demand shocks while fixed rates are preferable when economic disturbances originate in the real sector. This result is corroborated by Frenkel and Aizenman (1982), in the context of a formal optimizing framework. They also find that capital mobility reduces the optimal degree of exchange rate 1 0 Note that while Aet= 0 by definition when 7=1, there exist an infinite number of combinations of reserve and domestic credit changes that will hold the exchange rate fixed. Specifically, the exchange rate will remain fixed for all Art = et + + vt - Adt. 32 fixity associated with real shocks.11 Flood (1979) and Aizenman (1983) focus on price stability and obtain the result that fixed exchange rates are best when the economy is subject to domestic monetary disturbances. The results obtained in this chapter are in agreement with those generally obtained when price variation is included as an argument in the loss function of the policy authority. 1 1 The reason for this is that higher degrees of capital mobility imply that a larger fraction of the money supply change needed to accommodate the real shock is supplied by private international capital flows, reducing the need to use exchange market intervention to alter the monetary base. CHAPTER 3 OPTIMAL EXCHANGE MARKET INTERVENTION IN INTERDEPENDENT ECONOMIES 3.1 Introduction The distinguishing feature of the small open economy is that its policy actions have no significant impact on the rest of the world and therefore initiate no retaliatory responses. It is for this reason that the small open economy is free to choose its degree of exchange market intervention without having to consider the effects that its policy actions might have on other nations. In this section, the small open economy model is extended to incorporate two interdependent countries in which the monetary authorities intervene in the foreign exchange market with the objective of stabilizing real consumption and prices. Economic interdependence is reflected in the fact that the level of the exchange rate, and therefore also the domestic price level in each country, is jointly determined by the exchange rate policies that the two policy authorities choose to employ. As a consequence, it is necessary to make a clear distinction between the exchange rate policy employed by each policy authority and the joint outcome of these policy choices. In the two country model, the choice of exchange rate policy is reflected in the degree of exchange market intervention, while the observed exchange rate is the joint outcome of the intervention practices of the two policy authorities. Policy authorities are therefore free to choose different exchange rate policies; it is the resulting exchange rate that must be common to both countries. 33 34 This chapter focuses on the proposition that countries behave non-cooperatively because the gains from cooperation are too small to provide sufficient incentive to engage in cooperative exchange market intervention. Following the example of Turnovsky and d'Orey, a static game theoretic framework is used to characterize non-cooperative exchange market intervention. The three non-cooperative games considered are Cournot, Stackelberg, and one in which players correctly anticipate the responses of their opponents. The examples of cooperative behaviour considered are agreements under which policy authorities intervene fully in the exchange market, refrain from all exchange market intervention, and participate in joint loss minimization. Numerical simulations are used to compute representative optimal intervention strategies and the associated losses for each of the non-cooperative games as well as for the cooperative alternatives considered. One of the main differences between the study conducted by Turnovsky and d'Orey (1985) and the analysis presented here is the choice of strategic variable. In all of their non-cooperative games, Turnovsky and d'Orey treat the exchange rate as endogenous. Consequently, in these games policy authorities choose their nominal money supplies conditional on the assumption that the exchange rate is freely floating. In this chapter, an index of exchange market intervention, analogous to the one developed in Chapter 2, is the strategic policy instrument. The analysis of the previous chapter indicates that, in the small open economy, domestic money supply or direct intervention in the exchange market can be used equally successfully to achieve a given policy objective. If this were true in the case of interdependent economies also, the choice of strategic variable would be a matter of indifference. Recent work in duopoly theory, which demonstrates that Cournot and Bertrand solutions coincide only under special conditions, suggests that this is not the case.1 In fact, the choice of strategic variable could potentially have a profound 1 Cheng (1985). 35 impact on the outcomes of the various strategic games. The reason for this is that with the degree of exchange market intervention as the strategic variable, the players make assumptions about their opponent's responses in terms of a linear combination of exchange rate and domestic credit changes rather than domestic credit changes alone. For example, in the Cournot game presented in this chapter, each player takes the linear combination of exchange rate and domestic credit changes employed by his opponent as given. By contrast, each of Turnovsky and d'Orey's Cournot players assumes that his actions will not provoke a change in the domestic credit policies of his opponent. These assumptions are clearly not the same and have the potential of providing quite different solutions to the Cournot game. The same can be said of the assumptions made by the players participating in Stackelberg and Cournot games so that the non-cooperative games presented in this analysis differ in substance, though not in form, from those employed by Turnovsky and d'Orey. A second important difference between the analysis presented in this chapter and that conducted by Turnovsky and d'Orey is that, unlike Turnovsky and d'Orey's policy authorities, the players in this analysis cannot observe economic disturbances contemporaneously. Since the various types of non-cooperative behaviour considered in this chapter are not identical to those studied by Turnovsky and d'Orey, a comparison of the results obtained in each case can be used to assess whether the magnitude of gains from cooperation depend on the precise nature of the. alternative non-cooperative games available. The simulation results obtained by Turnovsky and d'Orey show that there is very little difference between the outcomes of the three non-cooperative games considered and that the gains from cooperation are quite small relative to each of the three non-cooperative alternatives. Given the very different characteristics of the non-cooperative games employed, it is surprising that the non-cooperative losses are relatively constant across games. The results of 36 the simulations conducted in the course of this analysis concur with those of Turnovsky and d'Orey insofar as they show that at least one of the three non^  cooperative games will lead to losses that are not substantially larger than those associated with joint loss minimization. The results here differ from those of Turnovsky and d'Orey in that the Cournot game always leads to extremely large welfare losses while the losses associated with the CCV game, though considerably smaller than Cournot losses, are relatively small only when disturbances are negatively correlated. The results of this analysis suggest that the potential gains from policy coordination are too small to encourage cooperation whenever the alternative of playing a non-cooperative Stackelberg game exists. 3.2 The Two Country Model The analysis of this chapter assumes that the world is composed of two economic entities. In order to distinguish between the two, one is referred to as the domestic or home country and the other as the foreign country. Equations (2.1), (2.2), (2.4), and (2.5) from the small open economy model are retained to describe the economy of the home country. For ease of reference these equations are reproduced below as equations (3.1) - (3.5): yt= y + «t (3.1) lt= k + pt +yt + vt (3.2) Afj= mt - mt_j (3.3) (3.4). The corresponding equations representing the economic structure of the foreign economy are given by: 37 y*t=y* + u*t (3.1*) l*t= k + p*t +y*t + v*t (3.2*) Ar*t= m*t - m*t_i (3.3*) m*t = l* t (3.4*). Throughout this chapter, asterisks (*) refer to foreign variables. Since capital is assumed to be immobile, trade in goods provides the primary link between the two economies. In this analysis, it is assumed that all goods are freely traded between the two economies and that purchasing power parity, reflected by equation (3.5), is maintained through international goods market arbitrage. Pt = P*t + et (3.5). In the small open economy model, the foreign price level was treated as exogenous so that domestic prices were determined by the purchasing power parity relationship. In this model, in which neither country is assumed to be a price taker, the price levels of both countries are endogenous and cannot be determined on the basis of equation (3.5) alone. An additional equation is needed in order to close the two country model and allow the world price level to be determined endogenously. This is achieved by imposing the requirement that, in any given time period, the payments balances of the two countries sum to zero. This requirement can be expressed as:2 2 Consistency requires that the trade balances of the two countries sun to zero in any given period so that Rt + E tR* t = 0 (3.6.1) where Rt and R*t represent the balance of payments in period t of the home and foreign countries, respectively, and E t is the exchange rate expressed in units of domestic currency per unit of foreign currency. Equation (3.6.1) can be expressed as R t + (Mt_i- M M ) + E,R*t + E t(M* t . 1- M* M ) = 0 (3.6.2). Rearranging (3.6.2) yields { M t _i[R t /M M + 1] - 1} + {EtM*t.i[R*t/M*t.i + 1] -1} = 0 which, in this model, is equivalent to 38 M t_i Art + E tM* t_ 1Ar* t = 0 which is the same as Mt.^mt-m t.1) + E tM* t. 1(m* t-m* t.l) = 0 (3.6). As in the case of the small open economy, it is assumed that the policy authorities of both countries are concerned with stabilizing their domestic income and price levels. The importance of consumption stability relative to price stability is reflected for the domestic and foreign economies in the loss functions L t and L* t , respectively. The loss function for the two countries are given by equations (3.7) and (3.7*): L t = var [byt + (l-b)pt ] (3.7) L * t = var [ b*y*t + (l-b*)p*t ] (3.7*) where 0 _ b < 1 and 0 <. b* < 1. It was pointed out in Chapter 2 that for the small open economy, the stability of real consumption is ensured whenever price stability is maintained. Under the assumptions of the present model, this is also true for interdependent economies when disturbances originate as money demand or foreign price shocks.^  However, this is not generally the case when interdependent economies are subject to output shocks. The reason for this is that as long as output disturbances are not perfectly negatively correlated, attempts by the policy authorities to remove the effects of output disturbances on real consumption through • Mt_i[expAr(t) - 1 ] + EtM*t_1[expAr*(t) -1] = 0 (3.6.3). The first order Taylor approximation of Mt_i(expAr(t)-l) and E tM* t.i(expA r*( t)-l) about Art=0 and Ar*t=0, respectively, yields : Mt_!Art + EtM*t_iAr*t = 0 (3.6). 3 In the two country model, the degree to which consumption plans can be accommodated through trade at a stable world price level when vt £ 0 and/or v*t £ 0 depends on the correlation of domestic and foreign money demand disturbances. 39 trade in goods will initiate changes in the world price level, creating a conflict between the simultaneous achievement of price and consumption stability. When disturbances in the domestic country originate in the real sector and 0 < b < 1, equation (3.7) gives rise to the covariance term b(l-b)cov(yt, p t). In the two country model, therefore, the welfare losses associated with output disturbances are reduced when output and prices move in opposite directions. This will occur whenever output shocks occur and domestic agents, in an attempt to maintain the desired consumption level y, engage in trade that, at prevailing prices, is not beneficial to foreign residents. As a result, in the context of the two country model, the covariance term associated with equation (3.7) captures the welfare gains associated with consumption stability. The same is true of the covariance term in the foreign loss function, (3.7*). The magnitude of b reflects the concern of domestic and foreign policy authorities with price stability relative to the stabilization of real consumption. It is assumed that each policy authority employs exchange market intervention as the instrument of stabilization policy. Each policy authority therefore chooses its degree of exchange market intervention with the objective of minimizing the value of its loss function. In the context of the two country model, the intervention index for the domestic economy is defined as: k + p t (f) + e + y + u t + v t - m t where pt(f) is defined as the price level that would prevail in the domestic economy under a policy of full exchange market intervention. The analogous intervention index for the foreign country is given by: 4 0 T* = m* t-1 (3.8*) k + p*t(f) - e + y* +. u* t + v* t - m* t where p*.(f) is the foreign full intervention price level. Full intervention is defined strictly defined as the ratio of actual money supply change to the change that would have taken place under full intervention. The assumptions of the small open economy model ensure the existence of a one-to-one correspondence between the degree of exchange market intervention and observed exchange rate changes. This allows the denominator of the small open economy intervention index to be interpreted as the magnitude of the money supply change that would be necessary to restore money market equilibrium under a system of perfectly fixed exchange rates. In the two country model, exchange rate fixity can be achieved through an infinite number of appropriate combinations of y and y*, one of which is y = y* =1. In order to avoid introducing circularity into definitions of y and y*. it is necessary to choose from among the many possibilities a single unit of measurement. Under the assumptions of the small open economy model, y = 1 reflects the intention of the policy authority to allow money market disequilibria to be fully removed through endogenous money supply changes. In the context of the two country model, the same policy stance is reflected on the part of the policy authorities of both countries by the intervention pair y = y* = 1. Full intervention in the two country model is therefore analogous to exchange rate fixity in the small open economy model making the intervention pair y = y* = 1 the natural unit of measurement in the two country model. Under the assumption that purchasing power parity is maintained between the two economies, and noting that, by definition full exchange market intervention on the part of both monetary as the policy pair y = y* = 1. In the two country model, the intervention index is 4 1 authorities requires Y=Y*=1> we can solve for pt(f) by substituting equations ( 3 . 8 ) and ( 3 . 8 * ) into ( 3 . 6 ) to obtain: pt(f) = M(mt.i-k - y - ut - vt) + M^m*^!-k* -y* - u*t - v*t + e) ( 3 . 9 ) where: M= Mt-i and M*=M*t„i, and e is the full intervention exchange rate and is therefore fixed. Substituting equation ( 3 . 4 ) into ( 3 . 8 ) , equation ( 3 . 4 * ) into ( 3 . 8 * ) , and the resultant expressions into equation ( 3 . 9 ) , the price level in each country is obtained as a function of y and y*: For the home country Pt(Y.Y*) = [l/(M+M*)][{(y-r*)M*M + (l-y)M* + M}(mM-k - y - urv t) + {(Y-Y*)(M*)2 +Y*M*}(m*t.!- k*- y* - u*t - v*t) + M*(yk + Ye - Y*k*)] ( 3 . 1 0 ) and for the foreign country P*t(Y.Y*) = [1/(M+M*)][{(Y*-Y)M*M + (1-Y*)M + M*}(m*t_i-k*-y *-u*rv*t) + [(Y*-Y)M2 + YM}(mt.!- k - y - ut - vt) .+ M(y*k* - yt - yk)] ( 3 . 1 0 * ) . Then, under purchasing power parity, the exchange rate is determined as et(Y.Y*) = Pt(Y.Y*) - P*t(Y.Y*) = (Y-Y*)[M(mt.1- k - y - ut- vt) +M*(m*t.!- k*- y*- u*t - v*t)] + (Y-l)(y + ut + vt - mt_!) - (Y*-l)Cy* + u*t + v*t - m*t.!) +Y*e ( 3 . 1 1 ) . Equation ( 3 . 1 1 ) indicates that the exchange rate is jointly determined by the intervention policies of the two countries. Furthermore, while it is true that full intervention by both countries will result in a fixed exchange rate, Y = Y * = 1 is o n i y o n e 42 of a continuum of intervention pairs for which et-e = 0. In particular, the exchange rate will remain fixed in the two country model whenever y = [(B - B*)/A] + [A*/A]v* (3.12) where: A =[(M+l)(mt.1-k->ut-vt) + M*(m*t.l-k*-y*-u*rv*t)] A*= [M(mt_i-k-y-ut-vt) + (M*+l)(m*t_i-k*-y*-u*t-v*t- e)] B =[y + ut + vt - mt_i] B*= [y* + u*t + v*t - m*t.i+ e] . It is clear that the relationship between domestic and foreign intervention needed to sustain any given exchange rate level can be derived on the basis of equation (3.11). 3.3 Intervention and Monetary Policy The majority of studies analyze the choice of exchange rate policy in terms of the identification of an optimal monetary policy conditional on the assumption that exchange rates are freely floating. In principle, any equilibrium exchange market intervention policy can be decomposed into equivalent combinations of intervention and active monetary policy. The objective of this section is to derive formally the relationship between optimal monetary policy and optimal intervention policy in the context of the two country model. Since countries effectively choose the equilibrium money stock change when they choose their optimal intervention policies, two policy combinations are equivalent if they result in the same equilibrium money stock change. The price level that prevails at any given point in time can be expressed as pt= Pt-i+ Apt(y,Y*). Beginning from a position of initial equilibrium in which (mt.j- k - y - Pt-i) = 0, and 43 substituting pt= Pt-i+ Apt(y>Y*) into equation (2.5') of the previous chapter, the change in the nominal money stock can be represented as Amt(y,y*) = A P I ( Y , Y * ) + u t + v t (3.13). In general therefore, a policy combination equivalent to (y, y*) is any exchange rate/monetary policy combination, ( Y 0 , Y * 0 ) / A d ( Y 0 , y * 0 ) , such that A m t ( Y 0 . Y * 0 ) +Ad T (Y 0 ,Y* 0 ) = Am T (Y,Y*) (3.14) where Ad t is the change in domestic credit. Since the endogenous money stock change, given the disturbances u t and v t, is determined by the price change A Pt(Y>Y*). equation (3.14) can be expressed as A P t ( Y 0 . Y * 0 ) + "t + vt + A d t ( Y 0 ' T * 0 ) = Ap T (Y,Y*) + u t + vt (3.15) so that A d T ( Y 0 , Y * 0 ) = ApT(Y>Y*) - A P t ( Y 0 » Y * 0 ) is the required change in domestic credit. Given the existence of a well defined relationship between the degree of exchange market intervention and changes in exchange rates and domestic credit, it follows that an exchange rate regime can be fully characterized on the basis of any equivalent exchange rate/active monetary policy combination. The zero intervention/active monetary policy combination provides a useful way of characterizing the intervention solutions associated with the various games. The zero intervention/active monetary policy combination that is equivalent to the intervention policy A e T ( Y > Y * ) / A d T ( Y , Y * ) is characterized by the policy pair Aet(0,0) and Adt(0,0) = Ap T (Y,Y*) - Apt(0,0). Two observations can be made in connection with the equivalence of various intervention/monetary policy combinations. First, since the choice of optimal 44 exchange rate policy always involves an optimal intervention/monetary policy combination, the domestic monetary policy must always be chosen conditional upon the intervention policy (or vice versa) if losses are to be minimized. Consequently, although under a system of flexible exchange rates the money supply does become exogenous, it cannot be manipulated independently for the purpose of achieving other economic targets without adversely affecting economic stability (if, as we assume here, exchange rate policy is directed towards stabilization). Second, the correspondence between intervention and monetary policy implies that international monetary rules must govern not only exchange market intervention, but also domestic monetary policy if they are to achieve the distribution of losses expected at the time the agreement was made. 3.4 Loss Minimization Having solved for domestic and foreign prices in terms of y and y*, the loss function of the domestic policy authority can be obtained by substituting equation (3.8) into equation (3.7). After some manipulation, the objective function of the domestic policy authority is obtained as: Lt(y,Y*)= {b + [(l-b)/(M+M*)][-M + M*({l-M}y- 1 + My*)]2a2u + [(l-b)/(M+M*)]2[-M + M*({l-M}y-1 + My*)]2a2v +[(l-b)/(M+M*)]2[-M*Y*]2[a2u*+a2v*] + 2p(u){b + [(l-b)/(M+M*)][-M+M*({l-M)Y- l+MY*)]}[(l-b)/(M+M*)][-M*Y*]ou°u* + 2p(v)[(l-b)/(M+M*)]2[-M+M*({l-M)Y-l + MY*)][-M*Y*]avov* (3.16) where p (u) and p (v) reflect the correlation between domestic and foreign disturbances originating in the real and monetary sectors, respectively. 45 The foreign loss function, L*t(Y,Y*). is analogous. It is apparent that the domestic policy authority's loss function is jointly dependent on two variables of which only one is subject to its direct control. The same is true of the foreign country. Given that the policy authorities in both countries are aware of this, each will want to choose some "best" intervention strategy taking into account the conjectured response of the opponent. To begin with, three types of non-cooperative games, that can be distinguished from one another on the basis of the conjectures that the players make about the responses of their opponents, are considered. In particular, Cournot, Stackelberg and consistent conjectural variation games are solved for equilibrium intervention levels. In order to simplify the analysis it is assumed throughout that the two countries are symmetric in preferences and size so that b=b* and M=M*. The analytical solutions to the non-cooperative games are given first, followed by a discussion of the results of the numerical simulations. A general result of the analysis is that for all games intervention equilibria depend on relative rather than absolute disturbance size. 3.5 Cournot Game Under the assumptions of the Cournot game, each policy maker chooses his degree of exchange market intervention so as to minimize his own loss function taking the behaviour of his opponent as given. Each policy authority sets the conjectured response of his opponent equal to zero and minimizes his loss function by solving the appropriate equation; (3.17) for the domestic policy authority and (3.17*) for that of the foreign country: 3Lt(T.Y*) = [2/(i-b)]e0 + e 2n+e 1 1Y* = o (3.17) 46 9LVJ,Y*) _ [ 2 / ( 1. 5 ) ]e* 0 + e 1 1 Y + e12Y*= o (3.n*) where 60, 6*0, 8i 2, 0 2j, and Q\\ are defined as: 6 0 = (2b-l)(l-M)a2u + (b-l)(l-M)a2v - p(u)(2b-l)Mauo*u* - p(v)(b-l)Movov* 6*0= (2b-l)(l-M)a2u* + (b-l)(l-M)a2v* - p(u)(2b-l)Mouou*- p(v)(b-l)Movav* 6 1 2 = M2(a2 u+ o 2 v) + (l-M)2(o2u*+ a2v*) - 2M(1-M)[p(u)auau* + p(v)ovav*] 6 2 i = (1-M)2(CT 2 u + a 2 v) + M 2 (a 2 u * + a2v*) - 2M(l-M)[p(u)ouau* + p(v)avav*] 6 1 1 = (l-M)M[a2u + o 2 v + a 2 u * + a2v*] - [(1-M)2 + M2][p(u)auau* + p(v)ovov*] Note that 6 1 2 _ 0 and 6 2 1 ^ 0.4 Rearranging (3.17) and (3.16*) yields the reaction functions for the domestic and foreign countries, respectively: T(R) = [-2/o-b)][60/e21] + [-en/e 2 1]Y* 0.18) Y*(R*) = [-2/(i-b)][9*0/e12] + t - e n / e 1 2 ] Y o.is*). Since 0 j 2 and 6 2 j are both positive, the sign of the reaction function slope coefficient for both countries will be determined by the sign of G j j . When disturbances are positively correlated 8 j \ < 0 and both reaction functions will be positively sloped. When disturbances are negatively correlated the sign of B \ \ depends on relative disturbance size. For example, given real disturbances such that au*= s(u)au, where s(u) is some constant reflecting relative disturbance size, G J J is less than zero whenever p(u) < (l-M)M[l+s2(u)][(l-M)2+ M2]s(u). It is clear from 4 To see that sign 9 j 2 £ 0 and 6 2 i _ 0 we need only note that 6 i 2 = var[M(ut + vt) - (1-M)(u*t + v*t)] £ 0 6 2 1 = var[(l-M)(ut + vt) - M(u*t + v*t)] ^ 0. 47 equations (3.18) and (3.18*) that both reaction functions must have slopes of the same sign so that the direction of response to changes in the intervention policy of the opposing player is the same for both countries. Owing to the linearity of the model, multiplying all disturbances by some constant k has no effect on the reaction functions (3.18) and (3.18*) so that the optimal degree of exchange market intervention depends on relative rather than absolute disturbances. This result does not depend on the symmetry assumptions and holds for all games considered in this paper. Solving equations (3.18) and (3.18*) simultaneously for y and y*, yields the Cournot equilibrium intervention pair (yc,y*c): _ [2/(i-b)][(-e 0e 1 2-He* 0e n )] . Y c " ( e 1 2 e 2 1 -e2 n ) ( 3 1 9 ) _ [2/(i-b)]((-e* pe 2 1 +e pe n)]  Y c " ( e 1 2 e 2 1 -e2„) ( 3- 1 9 ) t As 9i2>0 and 92i>0, 32Lt(Y.Y*)/dy2 > 0 and 32L*t(Y.Y*)/dY*2 > 0 so that second order conditions confirm the equilibrium described by equations (3.19) and (3.19*) to be a minimum. Since the reaction functions are linear in y and y*, a unique Cournot equilibrium exists whenever [6 i 2 8 2 i -8 2 i 1] $ 0. This equilibrium is stable when [dY/dY*]y*(R*) > [dY/dY*]y(R). This implies that [- e 2 i / 6 n ] > [-611/61 2] so that the stability requirement becomes [ 6 1 2 6 2 i - 8 2 i 1 ]/611< 0. It is easily verified that the simulated equilibrium solutions as reported in Appendix 3.1 all meet this stability condition. When [ 6 i 2 9 2 i - 6 2 j j] = 0, the reaction functions of the two countries have the same slope and must be either parallel or coincident in (y,Y*) space. In general, the reaction functions will be coincident whenever the reaction functions have the same intercept so that [6 * 0 /811 ] = [ 6 0 / 6 2 1 ]. Whether this condition is satisfied 48 depends on the origin, correlation and relative sizes of disturbances in the two countries.5 When disturbances originating in the monetary sector are perfectly negatively correlated so that o v = o v * and p(v)=-l, the equilibrium combinations o f y and y* lie along the negatively sloped line y=2 - y*. Clearly, y<=y*=l is an element o f this set. The numerical simulations indicate that y=y*=l dominates other intervention pairs in the sense that both countries have the smallest losses (and these losses are symmetrically distributed) when both countries practise full exchange market intervention. When money demand disturbances are perfectly negatively correlated, the best solution for interdependent countries playing a Cournot game is the same as that of the small open economy. Under these circumstances, each country would welcome the attempts of the other to rid itself of its disturbance so that prices would remain invariant and each country could behave as if it faced a perfectly elastic demand curve for its product at some exogenous price. The situation is analogous when real disturbances among symmetric countries are perfectly negatively correlated. In this case the Pareto optimal intervention pair is given by y=y* = (l-2b)/(l-b) which, when b=0, is clearly identical to the optimal degree of exchange market intervention derived for the small open economy in Chapter 2. When [6i2®21"®^ll ] = u —d 5 When symmetric countries have identical negatively correlated real disturbances so that au= a u* and p(u)= -1, there exists a continuum of equilibrium intervention pairs along the negatively sloped line y = [2(l-2b)/(l-b)] -y \ Notice that the two polar exchange rate regimes y=y* = 1 and y=y*=0 are equilibrium solutions only under very special conditions. In particular, y=y*=1 is an element of the set of equilibrium solutions only if b=0 while y=y*=0 is the unique equilibrium solution when b=0.S. The set of equilibrium intervention pairs that corresponds to perfectly symmetric, perfectly positively correlated real disturbances is given by y = [2(l-2b)/(l-2M)(l-b)] + y*. It is clear that under these conditions y=Y*=1 and Y=y*=0 comprise a subset of the set of equilibrium solutions only if b=0.5. 49 [0*o/0 j i] it [8o/021 ]. the reaction functions of the two countries are parallel and a Cournot equilibrium does not exist.6 3.6 Stackelberg Game The Cournot game is symmetric in that both players set their conjectural variations equal to zero and are assumed to choose their intervention strategies simultaneously. The Stackelberg game is asymmetric with respect to the player's conjectural variations as well as the timing of intervention strategy. Under the rules of the Stackelberg game the follower, as in the Cournot game, sets his conjectural variation equal to zero while the leader, who has the first move, correctly incorporates the response of the follower into his reaction function. Under the assumption that the domestic policy authority is the leader and the foreign policy authority the follower, the optimization problems of the follower and leader are given by equations (3.20) and (3.20*), respectively: i t i g i i + i k f e Q i £ p . 0 a 2 0 ) dy dy* dy dL*t(y,y*) dy* = 0 (3-20*) 6 In this model, one condition that generates this result is when only one of the two countries experiences domestic disturbances. It can be shown however that the conditions generating parallel Cournot reaction functions differ depending on the choice of strategic variable. In this model, attempts to play a Cournot game when only one of the two countries is subject to domestic disturbances will, according to equation (3.10), result in the exchange rate increasing or decreasing (depending on the direction of the disturbance) without bound as y and y* increase or decrease without bound. This suggests that decisions concerning the choice of strategic variable may significantly affect the variablility of exchange rates and the losses countries must ultimately accept. 50 where dy*(R*)/d7 denotes the response of the follower to the policy actions of the leader as measured along the follower's reaction function. The optimizing conditions corresponding to (3.20) and (3.20*) are then obtained as 8 0 + [(l-b)/2][82iY+ enY*] + {6 + [(l-b)/2][8nY+ 6 1 2 Y*]}dY*(R*)/dY=0 (3.21) e*0 + [(l-b)/2][enY+e12Y*] =0 (3.21*). Equation (3.21*) implies that the conjectural variation for the leader is dY*(R*)/dY =-6j 1/61 2. Substituting this expression into (3.21) and solving for the Stackelberg equilibrium (Ys>Y*s) yields, for the leader: Y s _ [2/(i-b)][(-e12e0 + e n e)] ( . ^ ( e 1 2 8 2 i - e 2 n ) and for the follower: [2/(i-b)]{(-e*0/e12) - (e 1i/e 1 2)[(-e 1 2e 0 + e n e)] _ ( e 1 2 e 2 i - e 2 n ) where: 9 = (2b-l)Ma 2 u + (b-l)Ma2v - p(u)(2b-l)(l-M)auau* - p(v)(b-l)(l-M)avav * and 6 i 2 » ® 2 1 > ^ l l ,^0' —d 6*o a r e a s previously defined. Second order conditions for the Stackelberg game are given by: B^/dy2 = [(l-b)/2] { 6 2 1 + e 2 n / e 1 2 } >0 for the leader and d2L*t/dy*2 = [(l-b)/2)] 0 j 2 > 0 for the follower, confirming that Ys m & T* s are loss minimizing solutions. Whether a country will be willing to take on the role of Stackelberg leader or would prefer to be the follower is determined by the relative weights assigned to output relative to price disturbances in the loss functions of the policy authorities as well as the relative size, origin, and correlation of disturbances. It is worth noting that the absolute value of the equilibrium degree of exchange market intervention 51 becomes arbitrarily large as [812®21*®21 l l - approaches zero. One interpretation of this observation, given that [612^ 21 "^211^ = 0 whenever disturbances are perfectly negatively or perfectly positively correlated between symmetric countries, is that the Stackelberg game is feasible only if there exists some critical degree of asymmetry either in the underlying economic structures or in the incidence of disturbances. As in the case of the Cournot game and for the same reasons, the value of the intervention index is higher when disturbances originate in the real sector than for money demand disturbances of equal magnitude. The results of the simulated Stackelberg game indicate that in the case of both real and monetary disturbances, the country with the larger disturbance is always better off taking on the role as leader. Whether or not the country with the smaller disturbance is better off as the leader or follower however, depends on the correlation of disturbances. In the simulated game in which the home country was assumed to suffer disturbances such that 0= 0.5 and the foreign country disturbances were characterized by 0*=1, the home country is better off as a follower as long as p £ 0.25.7 3.7 Consistent Conjectural Variations Under the rules of the Cournot game, each policy authority assumes that the other is unresponsive to changes in the intervention policy of his opponent.8 Since each policy authority in fact responds in accordance with his reaction function so that dy/dy*= - 611/621 for the home country and dyVdy = - 8j 1/8^ 2 f ° r th*5 foreign 7 When monetary disturbances are positively correlated with p2 0.5, both countries prefer to be Stackelberg leaders. It is possible to solve simultaneously for a leader-leader equilibrium, but there is some question as to whether it makes any sense to do so since it is difficult to imagine how both parties could be perceived to have the first move - see Friedman (1983), page 116. 8 The CCV game was developed by Bresnahan (1981), Perry (1982), and Kamien and Schwartz (1983). 52 country, the conjecture of the Cournot player will be incorrect except under the very special circumstances ih which 8n=0. The CCV equilibrium is obtained under the assumption that each player correctly anticipates the response of his opponent and takes this response into account in choosing his own strategy. The optimizing problems facing the two policy authorities under the CCV assumptions give rise to the following first order conditions: 3L*t(Y,y*) 9L*t(Y,Y') /dyV aV + ly WJl = 0 (3.23*) which, in terms of the model presented here, can be expressed as e 0 +[(i-b)/2j[e2iY+env*]+ te + [(i-b)/2][e11Y + e12Y*]id2 = o (3.24) 6*o + [(l-b)/2][6nY+ 612Y*] + {6* + [(l-b)/2]t6nY* + e21Y]}di =0 (3.24*) for home and foreign countries, respectively. Note that di = (dy/dY*)i .d2= (dY*/dy)2 and 6* = (2b-l)Ma2u* + (b-l)Ma2v*- p(u)(2b-l)(l-M)ou<ru* - p(v)(b-l)(l M)a vc v*. Rearranging (3.24) and (3.24*) results in the CCV reaction functions: _ [-2/(l-b)](6Q + 6d2) ( 6 u + 6^d2) Yccv(R) - , F I J . A H \ ' " ta A A \ Y ( 3 ' 2 5 ) _ _ [-2/(i-b)](e*p-fe*dl) (e 1 1 + e 2 1 d l )  Y c c v ( R ) " (e 1 2 + e n ) • (e 1 2 + e n ) a 2 5 >• Solving (3.25) and (3.25*) simultaneously for y and y* yields the CCV equilibrium: 53 _ [2/(i-b)]((e12 + e n di ) (e 0 + 9 d 2 ) - ( e n + 9 1 2 d 2 x 9 * 0 + 9*d,)}  7 c c v = (62 1 1 - e 1 2 e 2 1 ) ( i - d 1 d 2 ) ( 3 2 6 ) . [2/(i-b)]{(9n + e 2 1 di)(e 0 + ed2) - (e 2 1 + e n d 2 )(e* 0 + e*d!)} Y c c v = (^n-Bl2B2lKiii2- 1 ) where: d!=-(e 1 1+9 1 2d 2)/(6 2 1+e 1 1d 2) and d2= -(0ii+e21d1)/(012+011d1). Note that Cournot reaction functions and optimal intervention indices can be obtained by setting di=d2=0 in equations (3.25),(3.25*),(3.26), and (3.26*). It is apparent from equations (3.25) and (3.25*) that the slope of the reaction function of each policy maker is dependent on the slope of the reaction function of his opponent. Since the reaction functions are linear in the strategic variables yand Y*. the CCV equilibrium exists and is unique when [9 2j i - 9j 2 9 2 i ]*0 and di* l /d 2 . When the first, but not the second, of these conditions is satisfied, the reaction functions have the same slope and will be coincident whenever [9 0di+ 9] = [9*0+ 9*di]. When [9 2n- 9 1 2 9 2 J = 0, the CCV equilibrium does not exist. One situation in which one might expect d^ =d2=d is in the case of countries that are identical in size and economic structure. Consequently, in the simulations of the CCV game, two countries are assumed to have symmetric conjectural variations. The conjectural variations are then found as the solution to the quadratic polynomial 6 j jd 2 + (9 2 p9 1 2 )d + 9j j= 0. Second order conditions for a minimum require that 3 2 L t /3Y 2 = [0-b)/2] { 9 1 2 d 2 + 29ud + 9 2 1 } > 0 for the domestic economy and 9 2 L* t /3Y* 2 = [(l-b)/2] { 9 2 i d 2 + 2 9 n d + 012) > 0 for the foreign country. For symmetric countries, the conjectural variations represented by the positive root, d = {- (9 2 1 - 9 1 2 ) + [(9 2 1 - 9 1 2 ) 2 - 4 e 2 1 1 ] 1 / 2 }/26 1 j , result in loss minimizing CCV intervention indices. The numerical procedures confirm that, for the conditions specified, the positive root leads to lower losses. 54 3.8 Numerical Procedures As the complexity of the optimal intervention solutions makes it difficult to obtain analytical results, numerical simulations were employed to characterize the various strategic equilibria. The simulations were performed for symmetric countries using the 1983 Canadian Ml money stock so that M = M* = $42.86 billion. A representative sample of simulation results are provided in Appendix 3.1. The numerical procedures, which were performed for a wide variety of real and monetary disturbances, lead to the following propositions:9 (a) For both real and money demand disturbances, I y I increases as the correlation, of disturbances becomes more positive. The reason for this is that as disturbances become more positively correlated, the two monetary authorities find themselves engaged in increasingly more competitive intervention policies as they try to minimize their individual loss functions. (b) Monetary disturbances require less exchange market intervention and smaller money supply changes than real disturbances of the same size. This is because real disturbances have both a direct impact in the form of income variation as well as generating induced price variation during the adjustment process. Money demand disturbances, on the other hand, have associated with them only induced price effects so that losses as perceived by the policy authorities are smaller for monetary disturbances than for real disturbances of equal magnitude (for b^O).1^ 9 Conclusions (a), (c), and (d) are model specific. They do, however, appear to hold for changes in the size of the initial money stock. 1 0 This result corresponds to Turnovsky and d'Orey's finding that the welfare losses associated with demand disturbances are smaller than those resulting from supply disturbances of equal magnitude. 55 (c) For all games, the equilibrium degree of intervention depends on relative rather than absolute disturbance size . (d) For any disturbance of given size and correlation, non-cooperative losses are larger for both countries when policy authorities employ Cournot strategies rather than CCV strategies. Simulated intervention indices and associated losses for disturbances having the distribution a=0.5 and a*=l are illustrated in Tables 3.1(a), 3.1(b), 3.2, 3.3(a) and 3.3(b) for the alternative weights b=0 and b=0.75 and under the alternative assumptions that these disturbances are negatively, (p =-0.75), and positively, (p=0.75), correlated. In order to calculate the equilibrating changes in endogenous variables, it is necessary to choose some arbitrary magnitude for the realized (but unobservable) disturbances u t, u*t, vt, and v*t - absolute magnitudes of 0.5 and 1 for the home and foreign countries respectively seemed as good as any.11 In each table, lines 5-9 give the equilibrating changes in prices, money supplies and the exchange rate associated with the intervention equilibria for each game.12 Lines 10 and 11 reflect the equivalent zero intervention monetary policies and line 12, the exchange rate adjustment that would occur if both policy authorities refrained from exchange market intervention under the assumed conditions. The argument that the gains from cooperation are small requires that the outcomes of the various games be evaluated and compared in some meaningful way. 1 1 Calculations of the equilibrating endogenous changes associated with a variety of realized disturbances showed the qualitative results to be relatively insensitive to changes in the size of realized disturbances. 1 2 Under the assumptions that (mt.j- k- y- Pt-i) = 0, [y(k+e) + y*k*] = 0, and with M=M*, changes in domestic endogenous variables are calculated as Amt = Apt(y,Y*)+ut+vt and Apt = l/2{[(7-Y*)M-Y+2][-ut-vt]+[(Y-y*)M+Y*][-u*t-v*t]; Am*t and Ap*t are obtained in a similar manner and Aet = Apt - Ap* t. The equivalent zero intervention money supply change is obtained as Adt = Apt(Y,Y*) - Apt(0,0). 56 In the context of this chapter, one way of doing this is to use the loss function, evaluated at the equilibrium solution to each game, as a basis for comparison. The problem with such a cardinal interpretation of the loss function is that it is difficult to determine what constitutes a large or small difference in the losses suffered under the various games since such differences can be altered simply by means of appropriate monotonic transformations of the loss function. One way of dealing with this problem is to interpret the losses associated with each of the games as percentage deviations from target. In general terms, the loss function for the domestic economy can be expressed as defined as: L t = var[ byt + (l-b)pt] = lb(yt-y) + (l-b)(pt -p)]2 (3.27) where y and p are the mean values of yt and pt, respectively. In the context of this analysis, in which policy authorities are assumed to minimize consumption and price variations, y and p can be interpreted as the target values. Letting T represent the composite target such that T = by + (l-b)p and substituting this expression into equation (3.27) yields L t = [ byt + (l-b)pt - T ] 2 (3.28). Since the loss function is expressed in terms of logarithms, the square root of the loss function, L t = byt + (l-b)pt - T, measures the percent deviation from target as a weighted average of the percent deviations from target consumption and price levels. 57 1. Real Disturbances Tables 3.1(a) and 3.1(b) report the equilibrating changes in endogenous variables that occur under Cournot, Stackelberg, and CCV games when domestic and foreign countries are subject to 0.5 and 1 unit disturbances, respectively. It is evident that the Cournot game leads to the greatest losses and the CCV game to the smallest regardless of whether disturbances are positively or negatively correlated. In general, the intervention equilibrium achieved depends on the nature o f the game played by the policy authorities, the size and correlation of disturbances and the relative weights assigned output and price variation in the policy authority's loss function. When b=0, both policy authorities are primarily concerned with price variation. If each policy authority were able to observe the disturbances directly, the best course of action would be a fully accommodating monetary policy (i.e., some combination of intervention and active monetary policy that fully accommodates the disturbance to money demand in each country). Table 3.1(a) indicates that while Stackelberg and CCV games do result in accommodating monetary policies, neither game reduces losses to zero owing to the imperfect knowledge of the policy authorities. It is also apparent that the Cournot game results in an outcome far worse than either of the other games. In particular, the Cournot game results in an intervention equilibrium that is characterized by larger price and output variations than would have occurred in the absence of an active monetary policy under zero intervention. This is a direct consequence of the Cournot player's erroneous assumption that his opponent will remain unresponsive. In the CCV solution, each policy authority correctly takes account o f his opponent's response. Comparing the slope of the domestic country's Cournot reaction function (forau=0.5; a u * = l ; p(u)=-0.75), - 6i i /021 = 0-96. with the slope of the (symmetric) consistently conjectured reaction, d = 0.95, indicates that in the CCV 58 game the domestic policy authority correctly expects a larger degree of intervention on the part of the foreign authority and therefore intervenes less than in the Cournot game. Similarly, the foreign policy authority's Cournot response is given by -811/612 = 104 whereas the CCV reaction is d = 0.95. The foreign authority, as a CCV player, anticipates a larger degree of intervention on the part of the domestic authority and therefore intervenes less than in the Cournot game. As lines 10 and 11 of Table 3.1(a) indicate, the net result of the Cournot strategies is equivalent to offsetting rather than accommodating monetary policies which exacerbate rather than ameliorate the price variation associated with the real disturbances in both countries. In the Stackelberg game, the leader correctly anticipates the response of the follower and is able to choose a degree of intervention that reduces the losses of both players as compared to the Cournot game. Comparing lines 9 and 12 of Table 3.1(a) shows that the Cournot game leads to a flexible exchange rate regime accompanied by offsetting monetary policy, the Stackelberg game to a flexible exchange rate with accommodating monetary policy, while the CCV game leads to an intermediate exchange rate system. When b=0.75, both policy authorities are primarily concerned with the variation of real consumption.13 Given that disturbances are assumed to be negatively correlated, there exists some mutually beneficial trade which can be facilitated through exchange market intervention by one or both of the policy authorities. Eventually however, a conflict of interest must arise because of the difference in disturbance size. That is, once the initial 0.5 unit disturbance to consumption is removed from the domestic economy, the domestic policy authority will want to insulate the economy to prevent any of the remaining foreign 1 3 It will be recalled, from the discussion in Chapter 2, that the domestic and foreign policy authorities stabilize consumption with respect to (y - vt) and (y - v*t), respectively. 59 disturbance from being imported. The foreign policy authority, wishing to shift as much of the remaining foreign disturbance as possible to its opponent, has the opposite objective. When the two countries engage in a Cournot game, each policy authority underestimates the intervention response of his opponent. Consequently, the domestic authority, attempting to prevent domestic residents from selling goods in excess of the initial disturbance size as goods prices rise, engages in too large a monetary expansion. Similarly, the foreign authority, in an attempt to facilitate the purchase of domestic goods, supplies too much domestic currency to foreign residents. The net effect is a depreciation of the domestic currency. As the foreign authority underestimates the domestic response by 96% while the domestic authority underestimates the foreign response by 104%, the foreign policy authority is able to shift some of the disturbance remaining after the completion of the mutually beneficial trade to the domestic economy. It is apparent that both players suffer smaller losses in the Stackelberg and CCV games than in the Cournot game. A comparison of the price changes reported on lines 5 and 6 of Table 3.1(a) suggests that the magnitude of the Cournot losses may be due to the large price variations associated with competitive intervention policies. Although a weight of b=0.75 indicates that policy authorities are primarily concerned with consumption disturbances, there must come a point at which the benefits associated with reducing disturbances to real consumption are outweighed by the cost of large price variations. In the Cournot game, the assumption that the opponent will not react, causes each player to underestimate the price change associated with his intervention policy. In the CCV game, the correct anticipation of the opponent's response leads the domestic policy authority (which has the smaller disturbance and therefore also the smaller tolerance for price variation) to encourage domestic residents to sell goods beyond the initial disturbance size by 60 contracting the domestic money stock. The upward pressure on prices is reduced along with the losses of both players. The foreign policy authority, having a greater tolerance for price variation, expands the foreign money supply in order to accommodate the rise in goods prices thereby inducing foreign residents to buy more domestic goods and shift a larger portion of the foreign consumption disturbance to the domestic economy. The rationale behind the monetary contraction of the Stackelberg follower is the same as for the CCV game. However, as a result of the leader's choice of intervention policy in the Stackelberg game, the follower contracts his money supply less than he would as a CCV player causing the Stackelberg losses of the follower to exceed those of the CCV game. The leader, on the other hand, is better off playing the Stackelberg game than the CCV game when disturbances are negatively correlated and b=0.75 When real disturbances are positively correlated, the argument is much the same as for negatively correlated disturbances except that there is no initial mutually beneficial exchange of goods at existing prices so that the equilibrating changes in prices, money stocks, and the exchange rate are larger than when disturbances are negatively correlated. 2. Monetary Disturbances. When disturbances originate in the monetary sector, the degree of exchange market intervention is invariant with respect to the relative weights assigned to output and price disturbances in the loss functions of the policy authorities.14 The reason for this is that a disturbance to money demand brings about an induced real 1 4 The results of the numerical simulations provided in Appendix 3.1, show that the optimal degree of exchange market intervention does vary slightly with changes in the relative weights assigned to output and price disturbances in the loss function. These variations, which diminish as disturbance size increases, are due to program rounding errors that occur in the calculation of the simulated intervention indices. It should also be noted that, losses are not invariant with respect to the relative weights assigned to output and prices in the loss function. 61 disturbance when residents attempt to trade goods for money to restore portfolio balance. Since trade in goods, whenever it is not mutually beneficial at existing prices, will result in changing prices, the same policy that prevents individuals from trading goods to restore portfolio balance will prevent price variation. Consequently, the discussion of intervention policy associated with money demand disturbances is analogous to that provided for real disturbances with b=0 and need not be repeated. Tables 3.1(a), 3.1(b) and 3.2, indicate that the various games have very different implications for the equilibrium changes in endogenous variables. Unlike the Cournot game, both Stackelberg and CCV games result in partially accommodating monetary policies when disturbances originate in the monetary sector so that the equilibrium money stock is, to some degree, demand determined. Note that the clearly superior strategy of fully accommodating monetary policies is not available to the policy authorities since, by assumption, they cannot observe the disturbances directly and must choose their policies solely on the basis of their knowledge of the distribution of disturbances. 3.9 Cooperative Exchange Market Intervention In addition to the non-cooperative games that countries may choose to play, there are numerous alternative cooperative games by which exchange rate policies may be determined. In general, cooperative games are distinguished from non-cooperative games on the basis of the existence of binding pre-play agreements. The results of the foregoing section indicate that full intervention and zero intervention can, under special circumstances, represent equilibrium solutions to any one of the non-cooperative games considered. It is also possible to view these alternatives as cooperative regimes in that countries may enter into agreements either to refrain from intervening in the exchange market altogether or to allow the 62 nominal money supply to adjust through reserve flows in response to disturbances. Tables 3.3(a) and (b) summarize the losses and equilibrium outcomes associated with the rules: y=y*=0 and y=y*=l. Comparing these results with those of Tables 3.1(a) and (b), shows that the cooperative solutions are superior to the Cournot outcome in all cases but that the relative merits of these particular cooperative arrangements as compared to the Stackelberg and CCV outcomes depend on the correlation of disturbances and, in the case of real disturbances, also on the weight assigned price and consumption variations in the loss functions of the policy authorities. This indicates that neither perfectly fixed nor freely floating exchange rate regimes are likely to be optimal. An alternative, and more general, form of cooperation is one in which the policy authorities collude to minimize a weighted sum of their individual loss functions. When policy authorities agree to engage in joint loss minimization, the optimization problem becomes: Min L(X) = XL t(y,y*) + (l-X)L*t(y,y*) (3.29) The general optimality conditions for the joint loss minimization are given by: MLtfr.lT) (l-X)3L*t(y,y*) * + *Y = ° C3.30) X3Lt(y,Y*) (1-X)3L*t(Y,Y*) which, in the analytical framework of this chapter requires that \Q0 + (1-X)6* + [(l-b)/2][62iY+eiiY*] = 0 (3.31) 63 XQ + (1-X)8*0 + Kl-b^irenY+e^Y*] = 0 (3.31*). Under the assumption that [812®21 " 0 21 l l * 0» ^d conditional upon X, the unique joint loss minimizing equilibrium is then obtained as: [2/(i-b)]{xiee11 -e Qe 1 2] + a - w e ^ S n -e*e12]} = — ro A A 2 1 — ( 3 - 3 2 ) J [812821- 8 z n ] ^/(l-^nxieoe! 1 - e e 2 l ] + c i -x) [e*e„ - e*ne21]}  T j ~ [612621-02„] ( 3 - 3 2 ) > The determinant of the Hessian matrix, given by det [H] = [(l-b)/2]2[ 812621 -8^n] , is positive for all p £ 1 indicating that Yj and Y*J are loss minimizing solutions over the range of values relevant to this analysis. As with all of the non-cooperative games considered in this chapter, [ 612821 - 6^ ^ j ] = 0 whenever p = 1, causing the optimal intervention strategy to be undefined when disturbances are perfectly positively correlated. Joint loss minimization can be regarded as a bargaining solution in that the countries have to come to some agreement regarding the assigned value of X. The various loss distributions that are technically possible can be described by a loss possibilities frontier.15. The loss possibilities frontiers for the examples in which p(u)= -0.75, a u = 0.5 and CJ U*= 1, for the alternative cases in which b=0 and b=0.75 are illustrated in Figures 3.1 and 3.2, respectively. It is clear from these representative 1 5 Each point on the loss possibilities frontier is obtained as [Lt(YpiY*p)» L*t(Yp,Y*p)] where: {[8i i/(8-e*) + e 1 2 / ( e - e * 0 m * p + Le*/(6-e*) - e*0/(8-e*0)])  Y p [8ii/(6-e* 0)- e 2i/(6-e*)] 64 illustrations that each of the three non-cooperative solutions leads to higher losses than the cooperative alternative. In practice we observe that, with the exception of the EMS members, countries have over the last 15 years chosen to establish their exchange rate policies non-cooperatively. The question that arises is why this should be the case if a cooperative solution, such as joint loss minimization, must always be at least as good as any alternative non-cooperative solution. One reason for the absence of cooperative intervention rules is the inability of sovereign nations to make credible binding commitments to one another, the primary difficulty being that each participant has an incentive to break the agreement if he believes that his opponent will abide by it. The only situation in which a policy authority has no incentive to break the agreement is when the cooperative solution is also a non-cooperative solution. In the case of joint loss minimization, the domestic authority gains nothing by breaking the agreement only if X=l while the foreign authority has nothing to gain from abrogation only if X=0. It is relatively simple to show that neither player will, in general, have an incentive to sustain the agreement if he is convinced that his partner will abide by it. If the domestic policy authority believes that the foreign authority will honour the agreement, the domestic optimization problem becomes a special case of the Cournot optimization problem in which y* is set equal to Y*J- The domestic policy authority therefore solves the problem: aLt(Y,Y*:) — - - - = [2/(i-b>] e 0 + e 2iY + e l l Y * j = o 0.33). which implies that the domestic intervention index when the domestic authority breaks the agreement, Yb' i s 8 i v e n b v Y b = (~® 1 1 j - [2/(l-bVJ 801/621 • It can be shown that the domestic authority will have no incentive to break the agreement, 65 that is will choose Yb=Yj» ^ m^ onty if *- = 1 i Q 1 0 6 J o m t l ° s s function. For all other values of X, y^* Yj which implies that breaking the agreement must reduce domestic losses so that L(Yb,Y*j) < L(Yj.Y*p- Similarly, if the foreign policy authority believes that the domestic policy authority will abide by the agreement, the foreign policy authority's optimization problem is given by: [2/(l-b)] e* 0 + 012Y* + 9 nYj = 0 (3.33*) which implies that y*b = {" ® 11 Yj - [2/(1-b)] 9*o}/9!2. The foreign policy authority will have no incentive to break the agreement and will choose Y*b=Y*j if only if X=0 in the joint loss function. For all other values of X, Y*b* Y*j and foreign losses are reduced by breaking the agreement if the domestic policy authority does not. Consequently, rational policy authorities have no reason to expect that cooperative agreements will be sustained and will engage, in non-cooperative exchange market intervention. Figures 3.1 - 3.4 illustrate the simulated non-cooperative loss combinations reported in Tables 3.1(a), 3.1(b), and 3.2 as well as the losses associated with cooperative joint loss minimization.16 Although the diagrams indicate that the gains from cooperation may be substantial when the non-cooperative alternative is a Cournot game, they also show that there is at least one non-cooperative equilibrium loss combination that lies relatively close to the loss possibilities frontier regardless of the correlation of disturbances and the relative weights assigned by the policy authorities to price and consumption stability. 1 6 Since money demand disturbances result in intervention equilibria that are the same as those obtained for real disturbances with b = 0, Figures 3.1 and 3.3 also illustrate the loss combinations associated with non-cooperative games and joint loss minimization when disturbances originate in the monetary sector. aL*t(Yj.Y*) dy* 66 Figure 3.1 illustrates that when the policy authority is primarily concerned with price stability and disturbances are negatively correlated, the loss combination associated with the Stackelberg equilibrium lies further to the right of the loss possibilities frontier than the CCV equilibrium loss combination. However, when disturbances are negatively correlated and the policy authorities focus on stabilizing real consumption, Stackelberg and CCV games both result in loss combinations that lie just outside the loss possibilities frontier, as Figure 3.2 illustrates. Figures 3.3 and 3.4 show that a positive correlation between domestic and foreign disturbances tends to increase the gains from coordination, but that these gains remain modest as long as the Stackelberg game is a feasible non-cooperative alternative. The observation that all three non-cooperative equilibrium combinations lie furthest to the right of the loss possibilities frontier in Figure 3.3, suggests that countries may have the greatest incentive to cooperate when price stability is the primary policy objective. The analysis in this chapter has been conducted in the context of a static (one-shot) game of complete information.17 In reality, policy authorities interact repeatedly over successive time periods. It is worthwhile, therefore, to consider whether an analysis of strategic intervention modeled in the form of a repeated game would be likely to lead to different conclusions concerning the potential gains from cooperation. Repeated games, or supergames, are games in which the one-shot static game is replicated t+1 times, where t can be finite or infinite. In a static non-cooperative game, no player can make his choice of action conditional on the action chosen by his opponent while in repeated games players' actions in any peiod are conditional on their own past actions and all past actions taken by thie opponent. As in the 1 7 Complete information implies that the payoff functions as well as the strategies available to all players are common knowledge. 67 static game, a player's action in any given time period of the dynamic game, cannot be conditioned on the contemporatneous action of his oppenent. In a repeated game therefore, a strategy is a function which specifies, for each time t, an action as a function of all previous actions. Ideally, a repeated non-cooperative game should be modeled in a way that allows policy authorities to choose their actions over a finite time period with the knowledge that the world will continue to exist, and possibly be of importance to them, beyond this limit. 1 8 At present, no formulation of this sort exists and repeated games are either modeled with finite time horizons beyond which no event occurs which is of concern to policy makers or with infinite time horizons. It is well established that repeated games with finite time horizons simply result in the static solution being repeated each period and therefore lead to the same conclusions as those obtained on the basis of the constituent one-shot game. 1 9 The consequences of conducting the analysis in the context of an infinitely repeated game are somewhat different. Loosely speaking, the Folk Theorem says that any average per period payoffs which vector dominate the payoffs obtained in an equilibrium of the static game can be supported by a subgame perfect equilibrium in the dynamic game. This is possible because, in the dynamic game, tacit collusion can be maintained over time through the credible threat of future punishments for deviations from collusive behaviour. In other words, with a fixed finite time horizon we learn nothing new by using using a dynamic game analysis that we hadn't already learned using the simpler static formulation. On the other hand, with an infinite time horizon, the theory lacks predicitive power, allowing any outcome which both players like at 1 8 Note that this would be a game of incomplete information. 1 9 See Tirole (1988) for a concise exposition of this point. 68 least as much as the static outcome to be a possible equilibrium.20 In the present context, this means that the average per period gains from cooperation in the infinitely repeated game can be no larger than those obtained in the constituent static game. That is, the gains from cooperation calculated using the one-shot constituent game provide an upper bound for the average per period gains from cooperation in an infinitely repeated game.21 3.10 Conclusion This chapter has explored optimal intervention policy as a solution to games of strategy with the objective of providing some insight into the absence of an international agreement governing exchange rate policy. Exchange market intervention was chosen as the strategic variable in order to emphasize that monetary and foreign exchange intervention policies are close substitutes rather than independent policy instruments. A number of general conclusions can be drawn on the basis of the numerical simulations performed: (i) Money demand disturbances require less exchange market intervention and smaller money supply changes than real disturbances of equal magnitude. (ii) For both real and money demand disturbances, I y I increases as the correlation of disturbances becomes more positive. (iii) Intervention equilibria depend on the relative rather than absolute size of disturbances. 2 0 See Fudenberg and Tirole (1986) for an introductory survey of repeated games. See Fisher (1989) for a critique of the current use of repeated games in economic analysis. 2 1 It should be noted that binding agreements among sovereign nations have not in the past, nor are likely to be in the future, enforceable. The use of the cooperative alternative is therefore best viewed as an analytical construct that identifies the largest gains that would be possible under collusive behaviour. The complex question of the existence and nature of self-enforcing collusive solutions cannot be addressed in the context of the static analysis employed in this study. 6 9 The simulation results also show that when countries have similar policy objectives, at least one of the three non-cooperative games will lead to losses that are not substantially larger than those associated with joint loss minimization. In this study, the Cournot game always leads to extremely large welfare losses while the losses associated with the CCV game, though considerably smaller than Cournot losses, are close to the loss possibilities frontier only when disturbances are negatively correlated. The results of this static analysis suggest that the potential gains from policy coordination may be too small to induce policy authorities to engage in cooperative exchange market intervention whenever the alternative of playing a non-cooperative Stackelberg game exists.22 The analytical framework employed in this paper has a number of limitations of which the absence of an integrated world capital market, the exogeneity of output and the assumption that exchange rate policy is directed towards economic stabilization may be the most pervasive. In the absence of capital flows, policy authorities can prevent undesired one-way trade in goods by choosing a policy of zero intervention. The existence of a capital market enables private individuals to trade goods for securities which reduces the policy authorities' ability to control private behaviour through exchange market intervention. Consequently, by ignoring the existence of an integrated world capital market, the analysis in this paper overestimates the impact of exchange market intervention on economic stability. The analysis is also biased in favour of government intervention in that economic disturbances are assumed to originate in the private rather than the government sector. 2 2 As noted above, the analysis here assumes complete information. It is entirely possible that under conditions of incomplete information and imperfect information the gains from cooperation could be much larger if such cooperation improves the quality of information available to each player. 70 The assumption that output is exogenous has been maintained throughout for reasons of tractability. A price-responsive aggregate supply function, in the context of the analysis undertaken in this chapter, in addition to providing an additional avenue of interaction between the two countries, would ensure that a portion of the initial stochastic disturbance would be offset by an endogenous change in output. It is not clear Whether this would significantly affect the solutions associated with the various games and the joint loss minimization problem. 71 TABLE 3.1(a) Real Disturbances ou= 0.5, ou*= 1, p(u)= - 0.75; u= 0.5,u*= - 1 COURNOT STACKELBERG* CCV b = 0 0.75 0 0.75 0 0.75 1. y - 46.44 91.01 0.96 - 1.94 0.27 - 0.50 2. y* - 48.18 94.42 0.99 - 1.98 0.26 - 0.50 3. V T 41.18 20.47 0.13 0.05 0.65 0.32 4. V L * 41.73 19.79 1.57 0.63 0.80 0.39 5. Ap - 17.50 32.81 - 0.09 - 1.55 - 0.20 - 0.88 6. Ap* 18.00 - 32.31 0.59 2.05 0.70 1.38 7. Am - 17.00 33.31 0.41 - 1.05 0.30 - 0.38 8. Am* 17.00 - 33.31 - 0.41 1.05 - 0.30 0.38 9. Ae - 35.50 65.12 - 0.68 - 3.60 - 0.90 - 2.26 10. Ad - 17.00 33.31 0.41 - 1.05 0.30 - 0.38 11. Ad* 17.00 - 33.31 - 0.41 1.05 - 0.30 0.38 12. AeQ - 1.50 - 1.50 - 1.50 - 1.50 - 1.50 - 1.50 * Foreign country is the Stackelberg leader. 72 TABLE 3.1(b) Real Disturbances au= 0.5, au*= 1, p(u)= 0.75; u= 0.5,u*= 1 COURNOT STACKELBERG* CCV b = 0 0.75 0 0.75 0 0.75 1. y - 741.69 1460.92 0.96 - 2.54 - 4.99 9.62 2. Y* - 748.30 1473.96 0.99 -2.58 - 5.03 9.70 3. V T 457.47 225.27 0.12 0.12 3.55 1.72 4. V L * 457.93 225.49 0.83 0.24 4.03 1.96 5. Ap - 488.91 961.53 - 0.09 - 2.00 - 3.83 5.90 6. Ap* 489.41 - 961.03 0.59 2.50 4.33 - 5.40 7. Am - 488.41 962.03 0.41 - 1.50 - 3.33 6.40 8. Am* 488.41 - 962.03 - 0.41 1.50 3.33 - 6.40 9. Ae - 987.32 1922.56 - 0.68 - 4.50 - 8.16 1.13 10. Ad - 488.41 962.03 0.41 - 1.50 - 3.33 6.40 11. Ad* 488.41 - 962.03 - 0.41 1.50 3.33 - 6.40 12. AeQ - 0.75 - 0.75 - 0.75 - 0.75 - 0.75 - 0.75 * Foreign country is the Stackelberg leader. 73 T A B L E 3.2 Monetary Disturbances av= 0.5, ov*= 1, b=0; v= 0.5,v*= - 1 C O U R N O T S T A C K E L B E R G * CCV p = • 0.75 0.75 - 0.75 0.75 - 0.75 0.75 i . r - 46.44 - 741.68 0.96 0.96 0.27 - 4.99 2. y* - 48.18 - 748.30 0.99 0.99 0.26 - 5.03 3. V T 41.73 457.47 0.13 0.12 0.65 3.55 4. V L * 40.37 457.93 1.57 0.83 0.80 4.03 5. Ap - 17.50 - 488.91 - 0.09 - 0.09 - 0.20 - 3.83 6. Ap* 18.00 489.41 0.59 0.59 0.70 4.33 7. Am - 17.00 - 488.41 0.41 0.41 0.30 - 3.33 8. Am* 17.00 488.41 - 0.41 - 0.41 - 0.30 3.33 9. Ae - 35.50 - 978.32 - 0.68 - 0.68 - 0.90 8.16 10. Ad - 17.00 - 488.41 0.41 0.41 0.30 - 3.33 11. Ad* 1.7.00 488.41 - 0.41 - 0.41 - 0.30 3.33 12. AeD - 1.50 - 0.75 - 1.50 - 0.75 - 1.50 - 0.75 * Foreign country is the Stackelberg leader. 74 TABLE 3.3(a) Real Disturbances au= 0.5, ou*= 1, p(u) = - 0.75; u = 0.5, u*= -1 ZERO INTERVENTION FULL INTERVENTION Y = Y* = 0 Y = 7*=l b = 0 0.75 0 0.75 1. Y 0.00 0.00 1.00 1.00 2. Y * 0.00 0.00 1.00 1.00 3. V T 4.64 37.31 2.30 18.57 4. VT* 9.27 74.62 4.62 37.27 5. Ap - 0.50 - 0.50 0.25 0.25 6. Ap* 1.00 1.00 0.25 0.25 7. Am 0.00 0.00 0-75 0.75 8. Am* 0.00 0.00 - 0.75 - 0.75 9. Ae 0.50 0.50 0.00 0.00 10. Ad 0.00 0.00 0.75 0.75 11. Ad* 0.00 0.00 - 0.75 - 0.75 12. Ae r t - 1.50 - 1.50 - 1.50 - 1.50 TABLE 3.3(b) Real Disturbances o u = 0.5, o u *= 1, p(u) = 0.75; u = 0.5, u*= 1 ZERO INTERVENTION FULL INTERVENTION y = Y* = 0 Y = y* = 1 0 0.75 0 0.75 0.00 0.00 1.00 1.00 0.00 0.00 1.00 1.00 4.64 37.31 2.41 18.74 9.27 74.62 4.66 37.35 0^ 50 - 0.50 - 0.75 - 0.75 1.00 - 1.00 - 0.75 - 0.75 0.00 0.00 - 0.25 - 0.25 0.00 0.00 0.25 0.25 0.50 0.50 0.00 0.00 0.00 0.00 - 0.25 - 0.25 0.00 0.00 0.25 0.25 0.50 0.50 0.50 0.50 Figure 3.1 Losses Real Disturbances: p(u) = - 0.75; b = 0 Cournot• (u-l n.o.3~0 / Figure 3.2 Losses Real Disturbances: p(u) = - 0.75; b = 0.75 (Loo* <n O L / czo.«n, CO.O5,0.fe3) Figure 3.3 Losses Real Disturbances: p(u) = 0.75; b = 0 Figure 3.4 Losses Real Disturbances: p(u) = 0.75; b = 0.75 Ccof/iot . ( . o . i a , 0 . 2 4 ) Appendix 3.1 Simulation Results This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 b i l l i o n . Disturbances originate in the rea l sector and the partner countries play a Cournot-Nash game. DOMESTIC DISTURBANCE - .5 FOREIGN DISTURBANCE - 1 DOMESTIC FOREIGN b - CORR. GAMMA LOSS GAMMA LOSS 0. ,00 .1. 00- Division by Zero Divis ion by Zero 0. ,00 0. 75- 46. .4432- 1.7412 48. .1827- 1.6299 0. ,00 0. 50- 61. .9945- 1.0478 63.4941- 0.9843 0. 00 0. ,25- 87. .6080- 1.4656 89, .2014- 1.4314 0. 00 0. 00 130. .8504- 3.5275 132, .7249- 3.5280 0. 00 0. 25 198. .0742- 9.9883 200. .4459- 10.0379 0. ,00 0. 50 344. .2452- 37.4029 347, .7442- 37.5516 0. 00 0. 75 741. .6862- 209.2821 748, .3015- 209.7030 0. 00 1. 00 Divis ion by Zero Division by Zero 0. 25 1. 00- Division by Zero Division by Zero 0. 25 0. 75- 31, .5890- 0.4522 32, .7714- 0.4237 0. 25 0. 50- 43. .0102- 0.2830 44, .0497- 0.2664 0. 25 0. 25- 60. .1686- 0.3885 61. .2624- 0.3798 0. 25 0. 00 87. .9240- 0.8963 89, .1834- 0.8965 0. ,25 0. 25 132, .9246- 2.5299 134, .5160- 2.5428 0. ,25 0. ,50 233, .4515- 9.6757 235, .8242- 9.7142 0. 25 0. ,75 501, .9403- 53.9153 506, .4170- 54.0203 0. ,25 1. ,00 Division by Zero Division by Zero 0. .50 1. ,00- Division by Zero Division by Zero 0. .50 0. ,75- 0, .0000 0.0000 0, .0000 0.0000 0. ,50 0. ,50- 0 .0000 0.0000 0. .0000 0.0000 0. .50 0. ,25- 0 .0000 0.0000 0, .0000 0.0000 0. ,50 0. ,00 0, .0000 0.0000 0, .0000 0.0000 0, .50 0. .25 0 .0000 0.0000 0. .0000 0.0000 0, .50 0. .50 0 .0000 0.0000 0, .0000 0.0000 0 .50 0, .75 0 .0000 0.0000 0 .0000 0.0000 0 .50 1, .00 Divis ion by Zero Divis ion by Zero 0 .75 1 .00- Divis ion by Zero Divis ion by Zero 0 .75 0 .75- 91 .0096 0.4190 94, .4208 0.3916 0 .75 0 .50- 118 .9499 0.2418 121 .8298 0.2265 0 .75 0 .25- 169 .7612 0.3442 172 .8504 0.3358 0 .75 0 .00 259 .6333 0.8676 263 .3533 0.8676 0 .75 0 .25 393 .5231 2.4623 398 .2355 2.4742 0 .75 0 .50 676 .6263 9.0291 683 .5041 9.0655 0 .75 0 .75 1460 .9240 50.7452 1473 .9550 50.8475 0 .75 1 .00 Division by Zero Division by Zero Note: "Division by Zero" indicates that [ 6 1 2 8 2 i - 8 2 n ] = 0. This, program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 b i l l i o n . Disturbances originate in the real sector and the partner countries play a Stackelberg game. LEADER'S DISTURBANCE - 1 FOLLOWER'S DISTURBANCE - .5 LEADER FOLLOWER b - • CORR. GAMMA LOSS GAMMA LOSS 0. 00 1. 00- Divis ion by Zero Divis ion by Zero 0. 00 0. 75- 0. 9885 2.4816 0.9600 0.0169 0. 00 0. 50- 0. ,9883 2.1466 0.9600 0.0144 0. 00 0. 25- 0. ,9669 1.7854 0.9400 0.0121 0. 00 0. 00 0. 9881 1.5309 0.9600 0.0144 0. 00 0. 25 0. 9884 1.2516 0.9600 0.0069 0. 00 0. 50 0. 9880 0.9259 0.9600 0.0044 0. 00 0. 75 0. ,9908 0.6986 0.9600 0.0149 0. 00 1. 00 Divis ion by Zero Divis ion by Zero 0. 25 1. 00- Divis ion by Zero Divis ion by Zero 0. 25 0. 75- 0. ,6590 0.6229 0.6400 0.0049 0. 25 0. 50- 0. ,6317 1.0096 0.6000 0.1209 0. 25 0. ,25- 0. ,6337 0.9694 0.6000 0.1311 0. 25 0. ,00 0. .6587 0.3929 0.6400 0.0036 0. ,25 0. ,25 0. ,6589 0.3129 0.6400 0.0051-0. ,25 0. ,50 0. ,6139 0.5044 0.5800 0.0739 0. .25 0. .75 0, .5792 0.1825 0.5600 0.0000 0. .25 1. .00 Divis ion by Zero Divis ion by Zero 0, .50 1. ,00- Divis ion by Zero Divis ion by Zero 0. .50 0. ,75- 0 ,0000 0.0000 0.0000 0.0000 0. .50 0. .50- 0, .0000 0.0000 0.0000 0.0000 0, .50 0, .25- 0 .0000 0.0000 0.0000 0.0000 0. .50 0, .00 0 .0000 0.0000 0.0000 0.0000 0, .50 0 .25 0 .0000 0.0000 0.0000 0.0000 0 .50 0 .50 0 .0000 0.0000 0.0000 0.0000 0, .50 0, .75 0 .0000 0.0000 0.0000 0.0000 0 .50 1 .00 Divis ion by Zero Divis ion by Zero 0 .75 1 .00- Divis ion by Zero Divis ion by Zero 0 .75 0 .75- 1 .9772- 0.4029 1.9400- 0.0025 0 .75 0 .50- 2 .0582- 0.3429 2.0200- 0.0036 0 .75 0 .25- 2 .0528- 0.2484 2.0200- 0.0081 0 .75 0 .00 1 .9762- 0.2384 1.9400- 0.0036 0 .75 0 .25 1 .9767- 0.1884 1.9400- 0.0064-0 .75 0 .50 2 .1102- 0.1134 2.0800- 0.0021 0 .75 0 .75 2 .5788- 0.0579 2.5400- 0.0144 0 .75 1 .00 Divis ion by Zero Divis ion by Zero This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 b i l l i o n . Disturbances originate i n the re a l sector and the countries' reactions are characterized by symmetric consistent conjectural variations. 80 DOMESTIC DISTURBANCE - .5 FOREIGN DISTURBANCE - 1 DOMESTIC FOREIGN d - b - CORR. GAMMA LOSS GAMMA LOSS 0. ,93 0. .00 1. ,00- Division by Zero Division by Zero 0. ,95 0. .00 0. ,75- 0.2665 0.4200 0.2624 0.6401 0. .96 0. .00 0. ,50- 0.1059 0.4000 0.1001 0.6466 0. ,97 0. .00 0. 25- 0.0736 0.2700 0.0717 0.8551 0. .97 0. ,00 0. 00 0.5716- 0.5900 0.5832- 1.1729 0. 98 0. ,00 0. 25 0.2115- 0.3500 0.2131- 1.2214 0. 98 0. ,00 0. 50 1.6015- 1.9000 1.6170- 3.3549 0. 98 0. ,00 0. 75 4.9868- 12.6400 5.0310- 16.2379 0. 99 0. 00 1. 00 Division by Zero Division by Zero 0. ,93 0. ,25 1. 00- Division by Zero Division by Zero 0. 95 0. ,25 0. 75- 0.1838 0.1000 0.1813 0.1551 0. ,96 0. ,25 0. 50- 0.0555 0.1000 0.0514 0.1559 0. ,97 0. ,25 0. 25- 0.0447 0.0600 0.0434 0.2151 0. ,97 0. ,25 0. ,00 .. 0.3643- 0.1400 0.3722- 0.2896 0. ,98 0. ,25 0. 25 0.1410- 0.0900 0.1420- 0.3116 0. ,98 0. ,25 0. ,50 1.0831- 0.4800 1.0939- 0.8650 0. .98 0. ,25 0. ,75 3.3565- 3.2100 3.3876- 4.1121 0. ,99 0. .25 1. 00 Division by Zero Division by Zero 0. .93 0. .50 1. ,00- Division by Zero Division by Zero 0, .95 0. .50 0. ,75- - 0.0000 0.0000 0.0000 0.0000 0, .96 0. ,50 0. ,50- 0.0000 0.0000 0.0000 0.0000 0 .97 0. .50 0. ,25- 0.0000 0.0000 0.0000 0.0000 0. .97 0. .50 0. ,00 0.0000 0.0000 0.0000 0.0000 0. .98 0. .50 0. ,25 0.0000 0.0000 0.0000 0.0000 0. .98 0. .50 0. ,50 0.0000 0.0000 0.0000 0.0000 0. .98 0. .50 0. ,75 0.0000 0.0000 0.0000 0.0000 0 .99 0 .50 1. .00 Division by Zero Division by Zero 0, .93 0, .75 1. .00- Division by Zero Division by Zero 0. .95 0 .75 0. .75- 0.5041- 0.1000 0.4974- 0.1554 0, .96 0, .75 0, .50- 0.2563- 0.0900 0.2468- 0.1550 0, .97 0 .75 0. .25- 0.2096- 0.0500 0.2084- 0.2104 0, .97 0 .75 0, .00 1.1934 0.1400 1.2155 0.2969 0 .98 0 .75 0, .25 0.5076 0.0800 0.5092 0.3059 0 .98 0 .75 0, .50 3.2035 0.4700 3.2301 0.8479 0 .98 0 .75 0, .75 9.6176 2.9700 9.6961 3.8411 0 .99 0 .75 1, .00 Division by Zero Division by Zero This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 billion. Disturbances originate in the real sector and the countries participate ln joint loss minimization. DOMESTIC DISTURBANCE - .5 FOREIGN DISTURBANCE - 1 DOMESTIC FOREIGN LAMBDA b - CORR. GAMMA 0 .00 0 .00 1 .00- Division 0 .00 0 .00 0, .75- 1 .0120 0 .00 0 .00 0, .50- 1 .0118 0 .00 0 .00 0, .25- 0 .9908 0 .00 0 .00 0 .00 1 .0116 0 .00 0 .00 0, .25 1 .0119 0 .00 0 .00 0 .50 1 .0115 0 .00 0 .00 0, .75 1 .0144 0 .00 0 .00 1. .00 Division 0 .00 0 .25 1, .00- Division 0 .00 0 .25 0. .75- 0 .6747 0 .00 0 .25 0. .50- 0 .6484 0 .00 0 .25 0. .25- 0 .6502 0 .00 0 .25 0. .00 0 .6744 0 .00 0 .25 0. .25 0 .6746 0 .00 0 .25 0. .50 0 .6302 0 .00 0 .25 0. .75 0 .5957 0 .00 0 .25 1. ,00 Division 0, .00 0 .50 1. .00- Division 0. .00 0 .50 0. ,75- 0 .0000 0. .00 0 .50 0. ,50- 0 .0000 0 .00 0 .50 0. ,25- 0 .0000 0 .00 0 .50 0. .00 0 .0000 0 .00 0 .50 0. ,25 0 .0000 0 .00 0 .50 0. ,50 0 .0000 0 .00 0 .50 0. ,75 0 . 0000 0 .00 0 .50 1. ,00 Division 0 .00 0 .75 1. ,00- Division 0 .00 0 .75 0. .75- 2 .0241-0 .00 0 .75 0. .50- 2 .1021-0 .00 0 .75 0. ,25- 2 .0976-0 .00 0 .75 0. .00 2 .0233-0 .00 0 .75 0. ,25 2 .0238-0 .00 0 .75 0, .50 2 .1554-0 .00 0 .75 0, .75 2 .6202-0 .00 0 .75 1. ,00 Division 0 .25 0 .00 1. ,00- Division 0 .25 0 .00 0, .75- 1 .0062 0 .25 0 .00 0. ,50- 1 .0059 0 .25 0 .00 0. .25- 0 .9850 0 .25 0 .00 0, .00 1 .0057 0 .25 0 .00 0, ,25 1 .0060 0 .25 0 .00 0, ,50 1 .0056 0 .25 0 .00 0. .75 1 .0085 0 .25 0 .00 1. ,00 Division 0 .25 0 .25 1. ,00- Division LOSS by Zero 1.9926 1.7401 1.5026 1.2351 0.9927 0.7402 0.4877 by Zero by Zero 0.4938 0.4525 0.3790 0.3051 0.2439 0.1732 . 0.1099 by Zero by Zero 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 by Zero by Zero 0.5063 0.4225 0.3614 0.3201 0.2564 0.1929 0.1762 by Zero by Zero 1.1157 0.9713 0.8414 0.6901 0.5533 0.4089 0.2721 by Zero by Zero GAMMA Division by 0.9885 0.9883 0.9668 0.9881 0.9884 0.9880 0.9908 Division by Division by 0.6590 0.6316 0.6337 0.6587 0.6589 0.6139 0.5792 Division by Division by 0000 0000 0000 0000 0000 0000 0.0000 Division by Division by 1.9771-2.0582-2.0528-1.9762-1.9768-2.1102-2.5788-Division by Division by 0.9944 0.9942 0.9728 0.9940 0.9942 0.9939 0.9967 Division by Division by LOSS Zero 0.0001 0.0001 0.0004 0.0001 6.0002 0.0002 0.0002 Zero Zero 0.0001 0.0004 0.0004 0.0001 0.0002 0.0010 0.0021 Zero Zero 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Zero Zero 0.0001 0.0004 0.0004 0.0001 0.0002 0.0006 0.0090 Zero Zero 0.1212 0.1056 0.0877 0.0744 0.0588 0.0432 0.0276 Zero Zero DOMESTIC FOREIGN LAMBDA b - CORR. GAMMA LOSS GAMMA LOSS 0. 25 0. ,25 0. .75- 0. ,6803 0.2620 0.6730 0.0276 0. .25 0. !25 0. .50- 0. .6575 0.2504 0.6492 0.0190 0. 25 0. .25 0. .25- 0. .6576 0.2134 0.6494 0.0164 0. 25 0. ,25 0. .00 0. .6771 0.1719 0.6694 0.0136 0. .25 0. ,25 0. ,25 0. .6785 0.1377 0.6708 0.0097 0. ,25 0. .25 0. ,50 0. .6439 0.0951 0.6358 0.0055 0. .25 0. .25 0. .75 0. .6229 0.0562 0.6146 0.0032 0. .25 0, .25 1. .00 Division by Zero Division by Zero 0, .25 0, .50 1, .00- Division by Zero Division by Zero 0. .25 0. .50 0. .75- 0. .0000 0.0000 0.0000 0.0000 0. .25 0 .50 0. .50- 0. .0000 0.0000 0.0000 0.0000 0. .25 0, .50 0. .25- 0. .0000 0.0000 0.0000 0.0000 0. .25 0. .50 0, .00 0. .0000 0.0000 0.0000 0.0000 0. .25 0, .50 0, .25 0, .0000 0.0000 0.0000 0.0000 0. 25 0. 50 0, ,50 0. .0000 0.0000 0.0000 0.0000 0. 25 0. ,50 0. .75 0. .0000 0.0000 0.0000 0.0000 0. 25 0. ,50 1. .00 Division by Zero Division by Zero 0. 25 0. 75 1. ,00- Division by Zero Division by Zero 0. 25 0. .75 0. .75- 1. .9838- 0.2973 1.9588- 0.0235 0. 25 0. 75 0. ,50- 2. .0513- 0.2428 2.0290- 0.0233 0. 25 0. 75 0. 25- 2. .0517- 0.2068 2.0292- 0.0185 0. 25 0. ,75 0. ,00 1. ,9917- 0.1769 1.9678- 0.0149 0. 25 0. ,75 0. ,25 1. .9885- 0.1399 1.9645- 0.0101 0. 25 0. .75 0. ,50 2. .0908- 0.1121 2.0682- 0.0076 0. .25 0. ,75 0. ,75 2. .5158- 0.1043 2.4968- 0.0002 0. ,25 0, ,75 1. ,00 Division by Zero Division by Zero 0. .50 0. .00 1. ,00- Division by Zero Division by Zero 0. .50 0, ,00 0. .75- 1. .0003 0.4938 1.0003 0.5063 0, .50 0. .00 0, .50- 1, .0001 0.4326 1.0000 0.4451 0. .50 0. .00 0, .25- 0, .9792 0.3790 0.9788 0.3741 0. .50 0 .00 0. .00 0. .9999 0.3051 0.9999 0.3176 0. .50 0. .00 0, .25 1. .0001 0.2439 1.0001 0.2564 0, .50 0, .00 0, .50 0, .9998 0.1875 0.9998 0.1876 0. .50 0, .00 0. .75 1. .0026 0.1215 1.0026 0.1340 0, .50 0, .00 1. .00 Division by Zero Division by Zero 0. .50 0. .25 i . .00- Division by Zero Division by Zero 0. .50 0. .25 0, .75- 0, .6859 0.1068 0.6869 0.1436 0. .50 0. .25 0, .50- 0 .6666 0.1026 0.6668 0.1082 0, .50 0, .25 0 .25- 0, .6650 0.0882 0.6652 0.0900 0, .50 0 .25 0 .00 0 .6797 0.0726 0.6801 0.0744 0. .50 0 .25 0. .25 0 .6825 0.0576 0.6827 0.0588 0 .50 0 .25 0 .50 0 .6576 0.0414 0.6576 0.0432 0 .50 0 .25 0 .75 0 .6501 0.0258 0.6500 0.0276 0 .50 0 .25 1 .00 Division by Zero Division by Zero 0 .50 0 .50 1 .00- Division by Zero Division by Zero 0 .50 0 .50 0 .75- 0 .0000 0.0000 0.0000 0.0000 DOMESTIC FOREIGN LAMBDA b — ' CORR. GAMMA LOSS GAMMA LOSS 0. .50 0. 50 0. ,50- 0. ,0000 0.0000 0.0000 0.0000 0. .50 0. ,50 0. ,25- 0. ,0000 0.0000 0.0000 0.0000 0. 50 0. 50 0. 00 0. ,0000 0.0000 0.0000 0.0000 0. ,50 0. ,50 0. 25 0. 0000 0.0000 0.0000 0.0000 0. ,50 0. ,50 0. ,50 0. ,0000 0.0000 0.0000 0.0000 0. .50 0. .50 0. .75 0. ,0000 0.0000 0.0000 0.0000 0. ,50 0. 50 1. ,00 Division by Zero Division by Zero 0. ,50 0. ,75 1. ,00- Division by Zero Division by Zero 0. .50 0. .75 0. .75- 1. .9434- 0.1444 1.9404- 0.1035 0. ,50 0. ,75 0. ,50- 2. ,0004- 0.1151 1.9998- 0.0957 0. ,50 0. ,75 0. ,25- 2. ,0058- 0.0976 2.0055- 0.0813 0. .50 0. ,75 0. .00 1. .9602- 0.0826 1.9593- 0.0669 0. ,50 0. ,75 0. ,25 1. ,9531- 0.0593 1.9523- 0.0594 0. ,50 0. 75 0. .50 2. ,0262- 0.0489 2.0262- 0.0357 0. .50 0. ,75 0. ,75 2. ,4114- 0.0517 2.4148- 0.0189 0. 50 0. 75 1. 00 Division by Zero Division by Zero 0. 75 0. 00 1. ,00- Division by Zero Division by Zero 0. 75 0. 00 0. ,75- 0. ,9944 0.1194 1.0062 1.1325 0. 75 0. 00 0, ,50- 0. ,9942 0.1038 1.0059 0.9881 0. 75 0. 00 0. ,25- 0. ,9734 0.0872 0.9848 0.8582 0. 75 0. 00 0. ,00 0. .9940 . 0.0726 1.0057 0.7069 0. 75 0. ,00 0. ,25 0. .9942 0.0570 1.0060 0.5701 0. 75 0. ,00 0. .50 0. ,9939 0.0414 1.0056 0.4257 0. 75 0. 00 0. .75 0. ,9967 0.0258 1.0085 0.2889 0. 75 0. ,00 1, ,00 Division by Zero Division by Zero 0. ,75 0. ,25 1. ,00- Division by Zero Division by Zero 0. ,75 0. ,25 0. ,75- 0. ,6915 0.0180 0.7009 0.3140 0. .75 0. .25 0. ,50- 0. .6757 0.0218 0.6844 0.2641 0, .75 0, .25 0, .25- 0, ,6725 0.0182 0.6809 0.2251 0, .75 0. ,25 0, ,00 0, ,6824 0.0146 0.6907 0.1861 0. .75 0. ,25 0. .25 0. .6864 0.0133 0.6947 0.1419 0, ,75 0, .25 0, .50 0, ,6713 0.0081 0.6795 0.1122 0, ,75 0. ,25 0, ,75 0. ,6773 0.0061 0.6855 0.0697 0, .75 0, .25 1. .00 Division by Zero Division by Zero 0, .75 0 .50 1, .00- Division by Zero Division by Zero 0. .75 0, .50 0, .75- 0. ,0000 0.0000 0.0000 0.0000 0, .75 0, .50 0 .50- 0, .0000 0.0000 0.0000 0.0000 0. .75 0 .50 0 .25- 0, .0000 0.0000 0.0000 0.0000 0 .75 0 .50 0 .00 0, .0000 0.0000 0.0000 0.0000 0 .75 0 .50 0 .25 0, .0000 0.0000 0.0000 0.0000 0 .75 0 .50 0 .50 0 .0000 0.0000 0.0000 0.0000 0 .75 0 .50 0 .75 0 .0000 0.0000 0.0000 0.0000 0 .75 0 .50 1 .00 Division by Zero Division by Zero 0 .75 0 .75 1 .00- Division by Zero Division by Zero 0 .75 0 .75 0 .75- 1 .9031- 0.0386 1.9220- 0.2460 0 .75 0 .75 0 .50- 1 .9496- 0.0312 1.9706- 0.2172 84 DOMESTIC FOREIGN LAMBDA b — CORR. GAMMA 0. 75 0. 75 0. 25- 1. 9600-0. 75 0. 75 0. 00 1. 9287-0. 75 0. 75 0. ,25 1. 9178-0. 75 0. 75 0. ,50. 1. 9616-0. 75 0. 75 0. ,75 2. 3070-0. 75 0. 75 1. ,00 D i v i s i o n 1. 00 0. 00 1. 00- D i v i s i o n 1. 00 0. 00 0. .75- 0. ,9885 1. 00 0. 00 0. ,50- 0. 9883 1. 00 0. 00 0. .25- 0. ,9676 1. 00 0. 00 0. ,00 0. ,9881 1. 00 0. 00 0, .25 0. ,9884 1. 00 0. 00 0. ,50 0. ,9880 1. 00 0. 00 0. ,75 0. ,9908 1. 00 0. 00 . 1. ,00 D i v i s i o n 1. 00 0. 25 1. ,00- D i v i s i o n 1. 00 0. 25 0. ,75- 0. ,6971 1. 00 0. 25 0. ,50- 0, ,6848 1. 00 0. 25 0, ,25- 0. .6799 1. 00 0. 25 0. ,00 0. .6851 1. 00 0. 25 0. 25 0. ,6903 1. 00 0. 25 0. ,50 0. ,6850 1. 00 0. 25 0, ,75 0, ,7045 1. 00 0. 25 1. .00 D i v i s i o n 1. 00 0. 50 1. .00- D i v i s i o n 1. 00 0. 50 0. .75- 0. .0000 1. 00 0. 50 0. .50- 0, .0000 1. 00 0. 50 0. .25- 0, .0000 1. 00 0. 50 0. .00 0. .0000 1. 00 0. 50 0, .25 0. ,0000 1. 00 0. 50 0 .50 0, .0000 1. 00 0. 50 0 .75 0, ,0000 1. 00 0. 50 1, .00 D i v i s i o n 1. ,00 0. 75 1 .00- D i v i s i o n 1. ,00 0. ,75 0 .75- 1, .8627-1. ,00 0. .75 0 .50- 1 .8988-1. .00 0. ,75 0 .25- 1 .9141-1. .00 0. ,75 0 .00 1 .8972-1. .00 0. .75 0 .25 1 .8825-1. .00 0. .75 0 .50 1 .8970-1. .00 o. .75 0 .75 2 .2026-1, .00 0, .75 1 .00 D i v i s i o n LOSS GAMMA 0.0260 1.9818-0.0194 1.9508-0.0142 1.9400-0.0103 1.9842-0.0184 2.3328-Z e r o D i v i s i o n Z e r o D i v i s i o n 0.0001 1.0120 0.0001 1.0118 0.0004 0.9908 0.0001 1.0116 0.0002 1.0119 0.0002 1.0115 0.0001 1.0144 Z e r o D i v i s i o n Z e r o D i v i s i o n 0.0017 0.7149 0.0005 0.7020 0.0004 0.6966 0.0001 0.7014 0.0000 0.7066 0.0000 0.7013 0.0000 0.7209 Z e r o D i v i s i o n Z e r o D i v i s i o n 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Z e r o D i v i s i o n Z e r o D i v i s i o n 0.0008 1.9036-0.0006 1.9414-0.0001 1.9581-0.0001 1.9423-0.0000 1.9278-0.0001 1.9422-0.0024 2.2508-Z e r o D i v i s i o n LOSS 0.1885 0.1661 0.1291 0.0958 0.0462 Z e r o Z e r o 2.0176 1.7651 1.5254 1.2601 1.0177 0.7652 0.5125 Z e r o Z e r o 0.5702 0.4728 0.4052 0.3225 0.2525 0.1950 0.1226 Z e r o Z e r o 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Z e r o Z e r o 0.4461 0.3980 0.3564 0.3025 0.2475 0.1800 0.1002 Z e r o This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 billion. Disturbances originate in the monetary sector and the partner countries play a Cournot-Nash game. DOMESTIC DISTURBANCE - .5 FOREIGN DISTURBANCE - 1 DOMESTIC FOREIGN b - CORR. GAMMA LOSS GAMMA LOSS 0. 00 1. ,00- Division by Zero Division by Zero 0. 00 0. ,75- 46. 4432- 1.7415 48. 1827- 1.6299 0. 00 0. 50- 61. 9945- 1.0477 63. ,4941- 0.9843 0. 00 0. 25- 87. 6080- 1.4661 89. 2014- 1.4315 0. 00 0. 00 130. 8504- 3.5275 132. 7249- 3.5280 0. 00 0. 25 198. 0742- 9.9896 200. 4459- 10.0379 0. 00 0. 50 344. 2452- 37.4041 347. 7442- 37.5516 0. 00 0. 75 741. 6862- 209.2853 748. 3015- 209.7029 0. 00 1. 00 Division by Zero Division by Zero 0. 25 1. 00- Division by Zero Division by Zero 0. ,25 0. ,75- 46, .7133- 0.9355 48, .4271- 0.8939 0. .25 0. ,50- 61 .9885- 0.5832 63 .4879- 0.5590 0. ,25 0. 25- 88, .8757- 0.8338 90 .4757- 0.8210 0. ,25 0. ,00 130, .8623- 1.9746 132 .7369- 1.9744 0. ,25 0. .25 201 .8200- 5.8239 204 .2201- 5.8431 0. .25 0, .50 344 .4645- 21.0334 347 .9656- 21.0904 0. .25 0. ,75 774, .0688- 128.3090 780 .9378- 128.4750 0. ,25 1. .00 Division by Zero Division by Zero 0. .50 1. ,00- Division by Zero Division by Zero 0, .50 0. .75- 46 .7004- 0.4088 48 .4138- 0.4087 0, .50 0. ,50- 61 .9885- 0.2538 63 .4879- 0.2538 0, .50 0. ,25- 88 .8636- 0.3644 90 .4634- 0.3644 0, .50 0 ,00 130 .8623- 0.8687 132 .7369- 0.8688 0 .50 0 .25 201 .8017- . 2.5729 204 .2016- 2.5731 0 .50 0 .50 344 .4645- 9.3191 347 .9657- 9.3198 0 .50 0, .75 774 .0165- 56.9426 780 .8850- 56.9435 0 .50 1 .00 Division by Zero Division by Zero 0 .75 1 .00- Division by Zero Division by Zero 0 .75 0 .75- 46 .7391- 0.0975 48 .4538- 0.1114 0 .75 0 .50- 61 .9885- 0.0595 63 .4879- 0.0678 0 .75 0 .25- 88 .9017- 0.0867 90 .5021- 0.0912 0 .75 0 .00 130 .8623- 0.2107 132 .7369- 0.2110 0 .75 0 .25 201 .8565- 0.6326 204 .2570- 0.6268 0 .75 0 .50 344 .4645- 2.3083 347 .9657- 2.2901 0 .75 0 .75 774 .1733- 14.1857 781 .0433- 14.1317 0 .75 1 .00 Division by Zero Division by Zero This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 billion. Disturbances originate in the monetary sector and the partner countries play a Stackelberg game. LEADER'S DISTURBANCE FOLLOWER'S DISTURBANCE - .5 LEADER FOLLOWER b - CORR. GAMMA 0. .00 1. 00- Division 0. ,00 0. ,75- 0. ,9885 0. ,00 0. 50- 0. 9883 0. ,00 0. 25- 0. 9669 0. ,00 0. 00 0. 9881 0. 00 0. 25 0. 9884 0. 00 0. 50 0. 9880 0. 00 0. 75 0. 9908 0. 00 1. 00 Division 0. 25 1. 00- Division 0. ,25 0. .75- 0. .9879 0. ,25 0. .50- 0, .9882 0. ,25 0, .25- 0. .9880 0, ,25 0. .00 0, .9882 0. ,25 0. .25 0. .9880 0. ,25 0. ,50 0. .9886 0, ,25 0. ,75 0, .9891 0. .25 1. ,00 Division 0, .50 1. .00- Division 0. .50 0. ,75- 0, .9883 0. .50 0. .50- 0, .9882 0. .50 0, .25- 0, .9883 0, .50 0, ,00 0 .9882 0. .50 0. ,25 0 .9883 0. .50 0, ,50 0 .9886 0. .50 0, .75 0 .9899 0 .50 1, .00 Division 0 .75 1 .00- Division 0 .75 0 .75- 0 .9871 0 .75 0 .50- 0 .9882 0 .75 0 .25- 0 .9867 0 .75 0 .00 0 .9882 0 .75 0 .25 0 .9873 0 .75 0 .50 0 .9886 0 .75 0 .75 0 .9874 0 .75 1 .00 Division by by by by by by by by LOSS Zero 2.4882 2.1464 1.7890 1.5309 1.2565 0.9373 0.7124 Zero Zero 0.8526 0.7438 0.6220 0.5048 0.3845 0.2780 0.1640 Zero Zero 0.0977 0.0896 0.0815 0.0734 0.0653 0.0555 0.0448 Zero Zero 0.1458 0.1748 0.2160 0.2382 0.2688 0.2906 0.3310 Zero GAMMA Division 0.9600 0.9600 0.9400 0.9600 0.9600 0.9600 0.9600 Division Division 0.9600 9600 9600 9600 9600 9600 9600 Division Division 9600 9600 0.9600 0.9600 9600 9600 0.9600 Division Division 9600 9600 9600 9600 9600 0.9600 0.9600 Division 0. 0. 0. 0. 0. 0. 0. 0. 0. o: o. o. o. o. o. b y b y 0. 0. LOSS by Zero 0.0181 0.0148 0.0108 0.0100 0.0068 0.0058 0.0143 Zero Zero .0467 .0440 0.0357 0.0300 0.0229 0.0161 0.0102 Zero Zero ,1001 ,0920 .0839 .0758 ,0677 0.0589 0.0496 Zero Zero ,1572 ,1598 0.1467 0.1483 0.1382 0.1350 0.1287 by Zero by by 0. 0. 0. 0. 0. by by 0. 0. This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 b i l l i o n . Disturbances originate in the monetary sector and the countries' reactions are characterized by symmetric consistent conjectural variations. 87 DOMESTIC DISTURBANCE - .5 FOREIGN DISTURBANCE - 1 DOMESTIC FOREIGN d - b - CORR. GAMMA LOSS GAMMA 0. 93 0 .00 1. ,00- Division by Zero Division 0. 95 0 .00 0. .75- 0.2665 0.4241 0.2624 0. 96 0 .00 0. ,50- 0.1059 0.4089 0.1001 0. 97 0 .00 0. .25- 0.0736 0.2799 0.0717 0. 97 0 .00 0. ,00 0.5716- 0.5950 0.5832-0. 98 0 .00 0. 25 0.2115- 0.3681 0.2131-0. 98 0. .00 0. ,50 1.6015- 1.8954 1.6170-0. 98 0, .00 0. ,75 4.9868- 12.6649 5.0310-0. 99 0 .00 1. 00 Division by Zero Division 0. 93 0 .25 1. ,00- Division by Zero Division 0. 95 0 .25 0. ,75- 0.2422 0.1494 0.2373 0. 96 0 .25 0. .50- 0.1057 0.1249 0.1003 0. 97 0 .25 0. ,25- 0.0620 0.0756 0.0601 0. 97 0 .25 0. ,00 0.5734- 0.2068 0.5847-0. 98 0 .25 0. .25 0.2381- 0.1131 0.2396-0. 98 0 .25 0. .50 1.6093- 0.8487 1.6239-0. 98 0 .25 0. ,75 5.2854- 7.2872 5.3308-0. 99 0 .25 1. ,00 Division by Zero Division 0. 93 0 .50 1. ,00- Division by Zero Division 0. 95 0 .50 0. .75- 0.2425 0.0114 0.2376 0. 96 0 .50 0. ,50- 0.1057 0.0084 0.1003 0. 97 0 .50 0. ,25- 0.0623 0.0010 0.0604 0. 97 0 .50 0. .00 0.5734- 0.0183 0.5847-0. 98 0 .50 0. .25 0.2380- 0.0030 0.2396-0. 98 0 .50 0, .50 1.6094- 0.2179 1.6240-0. 98 0 .50 0. .75 5.2852- 2.7068 5.3307-0. 99 0 .50 1. ,00 Division by Zero Division 0. 93 0 .75 1. ,00- Division by Zero Division 0. 95 0 .75 0, .75- 0.2415 0.0448 0.2366 0. 96 0 .75 0. .50- 0.1057 0.0495 0.1003 0. 97 0 .75 0. .25- 0.0612 0.0584 0.0593 0. 97 0 .75 0. .00 0.5734- 0.0302 0.5847-0. 98 0 .75 0. .25 0.2381- 0.0501 0.2396-0. 98 0 .75 0. .50 1.6091- 0.0131 1.6238-0. 98 0 .75 0, .75 5.2858- 0.3505 5.3312-0. 99 0 .75 1. ,00 Division by Zero Division LOSS Zero 0.6401 0.6516 0.8601 1.1729 1.2264 3.3549 16.2429 Zero Zero 0.1117 0.1311 0.2100 0.3404 0.3436 1.3212 8.6408 Zero Zero 0.0005-0.0015 0.0000 0.0180 0.0031 0.2136 2.7010 Zero Zero 0.3000 0.2955 0.2600 0.2345 0.2157 0.0962 0.1641 Zero This program calculates intervention indices for symmetric Canadas using 1983 Ml - $43 b i l l i on . Disturbances originate in the monetary sector and the countries participate in joint loss minimization. DOMESTIC DISTURBANCE - .5 FOREIGN DISTURBANCE - 1 DOMESTIC FOREIGN LAMBDA b - . CORR. GAMMA 0 .00 0. ,00 1 .00- Division 0 .00 0. 00 0 .75- 1 .0120 0 .00 0. ,00 0 .50- 1 .0118 0 .00 0. ,00 0 .25- 0 .9908 0 .00 0. 00 0 .00 1 .0116 0, .00 0. 00 0 .25 1 .0119 0, .00 0, ,00 0 .50 1 .0115 0 .00 0. ,00 0 .75 1 .0144 0 .00 0. 00 1 .00 Division 0, .00 0. 25 1. .00- Division 0. ,00 0. 25 0. .75- 1, .0114 0. ,00 0. 25 0. ,50- 1, .0117 0. 00 0. 25 0. .25- 1, .0116 0. ,00 0. 25 0. ,00 1, .0117 0. 00 0. 25 0. ,25 1. .0115 0. 00 0. 25 0. ,50 1, .0122 0. 00 0. 25 0, ,75 1, .0127 0. ,00 0. 25 1. ,00 Division 0. 00 0. 50 1. .00- Division 0. ,00 0. 50 0, ,75- 1, .0118 0. ,00 0. 50 0, .50- 1 .0117 0. ,00 0. 50 0. ,25- 1, .0118 0. .00 0. 50 0. .00 1 .0117 0. ,00 0. 50 0 .25 1 .0118 0. ,00 0. 50 0, .50 1 .0122 0. ,00 0. 50 0. .75 1 .0135 0. .00 0. 50 1 .00 Division 0, .00 0. 75 1 .00- Division 0. .00 0. 75 0 .75- 1 .0107 0. .00 0. 75 0 .50- 1 .0117 0 .00 0. 75 0 .25- 1 .0102 0 .00 0. 75 0 .00 1 .0117 0 .00 0. 75 0 .25 1 .0109 0 .00 0. 75 0 .50 1 .0122 0 .00 0. 75 0 .75 1 .0110 • 0 .00 0. 75 1 .00 Division 0 .25 0. ,00 1 .00- Division 0 .25 0. ,00 0 .75- 1 .0059 0 .25 0. ,00 0 .50- 1 .0058 0 .25 0, .00 0 .25- 1 .0059 0 .25 0. .00 0 .00 1 .0058 0 .25 0. .00 0 .25 1 .0059 0 .25 0, .00 0 .50 1 .0063 0 .25 0 .00 0 .75 1 .0076 0 .25 0 .00 1 .00 Division 0 .25 0 .25 1 .00- Division LOSS Zero 1.9926 1.7401 1.5026 1.2351 0.9927 0.7402 0.4877 Zero Zero' 0.9144 0.8115 0.7165 0.6215 0.5266 0.4315 0.3366 Zero Zero 0.2507 0.2495 0.2482 0.2470 0.2458 0.2445 0.2463 Zero Zero 0.0314 0.0615 0.0915 0.1215 0.1515 0.1815 0.2144 Zero Zero 1.1222 0.9806 0.8391 0.6975 0.5560 0.4200 0.2773 Zero Zero GAMMA Divis 0.9885 0.9883 0.9668 0.9881 0.9884 0.9880 0.9908 Divis Divis 0.9879 0.9882 0.9880 0.9882 0.9880 0.9886 0.9891 Divis Divis 0.9883 0.9882 0.9883 0.9882 0.9883 0.9886 0.9899 Divis Divis 0.9871 0.9882 0.9867 0.9882 0.9873 0.9886 0.9874 Divis Divis 0.9941 0.9941 0.9942 0.9941 0.9942 0.9945 0.9958 Divis Divis ion by ion by ion by ion by ion by ion by ion by ion by ion by ion by ion by LOSS Zero 0.0001. 0.0001 0.0004 0.0001 0.0002 0.0002 0.0002 Zero Zero 0.0609 0.0506 0.0503 0.0500 0.0497 0.0494 0.0491 Zero Zero 0.2418 0.2412 0.2406 0.2400 0.2394 0.2388 0.2481 Zero Zero 0.5427 0.5419 0.5409 0.5400 0.5390 0.5382 0.5572 Zero Zero 0.1227 0.1067 0.0908 0.0749 0.0590 0.0449 0.0269 Zero Zero 8 9 DOMESTIC FOREIGN LAMBDA b - CORR. GAMMA LOSS GAMMA LOSS 0. .25 0. .25 0. .75- 1.0056 0.4696 0.9939 0.0029 0. .25 0. .25 0. ,50- 1.0058 0.4252 0.9941 0.0047 0. .25 0, .25 0. .25- 1.0057 0.3808 0.9940 0.0065 0. .25 0. .25 0. .00 1.0058 0.3364 0.9941 0.0083 0. .25 0. .25 0. ,25 1.0057 0.2920 0.9939 0.0101 0. .25 0. .25 0. ,50 1.0063 0.2512 0.9945 0.0137 0. .25 0. .25 0, .75 1.0069 0.1990 0.9951 0.0132 0. .25 0. .25 1. ,00 Division by Zero Division by Zero 0. ,25 0. .50 1. ,00- Division by Zero Division by Zero 0. ,25 0. .50 0. .75- 1.0059 0.1076 0.9941 0.1004 0. ,25 0. .50 0. ,50- 1.0058 0.1187 0.9941 0.1115 0. ,25 0. .50 0. .25- 1.0059 0.1298 0.9942 0.1226 0. ,25 0. .50 0. ,00 1.0058 0.1409 0.9941 0.1337 0. 25 0. ,50 0. .25 1.0059 0.1520 0.9942 0.1448 0. 25 0. ,50 0. ,50 1.0063 0.1656 0.9945 0.1559 0. 25 0. ,50 0. ,75 1.0076 0.1742 0.9958 0.1685 0. 25 0. ,50 1. ,00 Division by Zero Division by Zero 0. 25 0. ,75 1. ,00- Division by Zero Division by Zero 0. 25 0. ,75 0. ,75- 1.0051 0.0347 0.9933 0.4303 0. 25 0. 75 0. ,50- 1.0058 0.0603 0.9941 0.4405 0. 25 0. ,75 0. ,25- 1.0045 0.0862 0.9927 0.4507 0. 25 0. ,75 0. ,00 1.0058 0.1121 0.9941 0.4609 0. 25 0, ,75 0. ,25 1.0051 0.1380 0.9934 0.4711 0. 25 0. ,75 0. ,50 1.0063 0.1643 0.9945 0.4813 0. 25 0. ,75 0. ,75 1.0054 0.1898 0.9936 0.4915 0. 25 0. ,75 1. ,00 Division by Zero Division by Zero 0. ,50 0. ,00 1. .00- Division by Zero Division by Zero 0. .50 0. ,00 0. ,75- 1.0000 0.4994 1.0000 0.5104 0. .50 0. ,00 0. .50- 1.0000 0.4363 1.0000 0.4472 0. .50 0. ,00 0. .25- 1.0000 0.3732 1.0000 0.3841 0. .50 0. .00 0. .00 1.0000 0.3100 1.0000 0.3210 0. .50 0, .00 0, .25 1.0000 0.2469 1.0000 0.2579 0. .50 0. .00 0. .50 1.0004 0.1841 1.0004 0.1961 0. .50 0. .00 0. .75 1.0017 0.1216 1.0017 0.1336 0, .50 0. .00 1. .00 Division by Zero Division by Zero 0. .50 0, .25 1, .00- Division by Zero Division by Zero 0. .50 0, .25 0, .75- 0.9999 0.1762 0.9999 0.0803 0, .50 0 .25 0 .50- 1.0000 0.1642 1.0000 0.0683 0. .50 0 .25 0 .25- 0.9999 0.1522 0.9999 0.0563 0 .50 0 .25 0 .00 1.0000 0.1401 1.0000 0.0442 0, .50 0 .25 0 .25 0:9998 0.1281 0.9998 0.0322 0 .50 0 .25 0 .50 1.0004 0.1161 1.0004 0.0202 0 .50 0 .25 0 .75 1.0011 0.1041 1.0011 0.0082 0 .50 0 .25 1 .00 Division by Zero Division by Zero 0 .50 b .50 1 .00- Division by Zero Division by Zero 0 .50 0 .50 0 .75- 1.0000 0.0294 1.0000 0.0210 DOMESTIC FOREIGN LAMBDA b - CORR. GAMMA LOSS GAMMA LOSS 0.50 0. ,50 0. .50- 1. ,0000 0.0441 1.0000 0.0357 0.50 0. .50 0. .25- 1, ,0000 0.0588 1.0000 0.0504 0.50 0. .50 0. ,00 1. .0000 0.0735 1.0000 0.0651 0.50 0. .50 0. .25 1. .0000 0.0882 1.0000 0.0798 0.50 0. .50 0. .50 1. .0004 0.1029 1.0004 0.0945 0.50 0. .50 0. ,75 1, ,0017 0.1176 1.0017 0.1092 0.50 0, .50 1. .00 Division by Zero Division by Zero 0.50 0, .75 1. ,00- Division by Zero Division by Zero 0.50 0. .75 0. .75- 0, ,9996 0.0543 0.9996 0.3279 0.50 0. .75 0. .50- 1, ,0000 0.0729 1.0000 0.3465 0.50 0, .75 0. ,25- 0, .9988 0.0915 0.9988 0.3651 0.50 0, .75 0. ,00 1, .0000 0.1101 1.0000 0.3837 0.50 0. .75 0. ,25 0. ,9994 0.1287 0.9994 0.4023 0.50 0. .75 0. ,50 1. ,0004 0.1473 1.0004 0.4209 0.50 0. .75 0. ,75 0, .9999 0.1659 0.9998 0.4395 0.50 0. .75 1. ,00 Division by Zero Division by Zero 0.75 0. ,00 1. ,00- Division by Zero Division by Zero 0.75 0. ,00 0. ,75- 0, .9941 0.1228 1.0059 1.1331 0.75 0. 00 0. ,50- 0. ,9941 0.1069 1.0058 0.9915 0.75 0. 00 0. 25- 0. ,9942 0.0910 1.0059 0.8500 0.75 0. ,00 0. ,00 0. .9941 0.0750 1.0058 0.7084 0.75 0. 00 0. ,25 0. ,9942 0.0591 1.0059 0.5669 0.75 0. ,00 0. ,50 0, .9945 0.0445 1.0063 0.4256 0.75 0. ,00 0. ,75 0, .9958 0.0288 1.0076 0.2821 0.75 0. 00 1. ,00 Division by Zero Division by Zero 0.75 0. ,25 1. ,00- . Division by Zero Division by Zero 0.75 0. ,25 0. ,75- 0, .9941 0.0281 1.0059 0.3111 0.75 0. ,25 0. .50- 0. ,9941 0.0299 1.0058 0.2666 0.75 0. .25 0. ,25- 0. .9941 0.0317 1.0058 0.2223 0.75 0. .25 0. ,00 0, .9941 0.0335 1.0058 0.1778 0.75 0. .25 0, ;25 0, .9940 0.0353 1.0058 0.1335 0.75 0. ,25 0. ,50 0, .9945 0.0389 1.0063 0.0894 0.75 0. .25 0. ,75 0, .9953 0.0389 1.0071 0.0447 0.75 0. .25 1. ,00 Division by Zero Division by Zero 0.75 0. .50 1, .00- Division by Zero Division by Zero 0.75 0, .50 0. .75- 0, .9941 0.0141 1.0059 0.0113 0.75 0, .50 0. .50- 0, .9941 0.0252 1.0058 0.0224 0.75 0. .50 0. ,25- 0. .9942 0.0363 1.0059 0.0335 0.75 0. .50 0, .00 0, .9941 0.0474 1.0058 0.0446 0.75 0 .50 0, ,25 0. .9942 0.0585 1.0059 0.0557 0.75 0, .50 0 .50 0, .9945 0.0696 1.0063 0.0675 0.75 0 .50 0, .75 0, .9958 0.0828 1.0076 0.0779 0.75 0 .50 1 .00 Division by Zero Division by Zero 0.75 0 .75 1 .00- Division by Zero Division by Zero 0.75 0 .75 0 .75- 0 .9940 0.0881 1.0058 0.2409 0.75 0 .75 0 .50- 0, .9941 0.0983 1.0058 0.2668 9 1 DOMESTIC FOREICN LAMBDA b - CORR. GAMMA 0 .75 0 .75 0 .25- 0. 9931 0 .75 0 .75 0 .00 0. 9941 0 .75 0 .75 0 .25 • 0. 9937 0 .75 0 .75 0 .50 0. 9945 0 .75 0 .75 0 .75 0. 9943 0 .75 0 .75 1 .00 Division 1 .00 0 .00 1 .00- Division 1 .00 0 .00 0 .75- 0. 9883 1 .00 0 .00 0 .50- 0. 9882 1 .00 0 .00 0 .25- 0. 9883 1 .00 0 .00 0 .00 0. 9882 1 .00 0 .00 0 .25 0. 9883 1 .00 0 .00 0 .50 0. 9886 1 .00 0 .00 0 .75 0. 9899 1 .00 0 .00 1 .00 Division 1 .00 0 .25 1 .00- Division 1 .00 0 .25 0 .75- 0. 9883 1. .00 0 .25 0 .50- 0. 9882 1 .00 0 .25 0 .25- 0. 9882 1 .00 0 .25 0 .00 0. 9882 1 .00 0 .25 0 .25 0. 9882 i . .00 0 .25 0 .50 0. 9886 I .00 0 .25 0 .75 0. 9895 I , .00 0 .25 1 .00 Division l . .00 0 .50 1 .00- Division I .00 0 .50 0 .75- 0. 9883 l .00 - 0 .50 0 .50- 0. 9882 l .00 0 .50 0 .25- 0. 9883 l . .00 0 .50 0 .00 0. 9882 l . .00 0 .50 0 .25 0. 9883 l . .00 0 .50 0 .50 0. 9886 l .00 0 .50 0 .75 0. 9899 I .00 0 .50 1 .00 Division I .00 0 .75 1 .00- Division l . .00 0 .75 0 .75- 0. 9885 I .00 0 .75 0 .50- 0. 9882 I .00 0 .75 0 .25- 0. 9873 I .00 0 .75 0 .00 0. 9882 l .00 0 .75 0 .25 0. 9880 l .00 0 .75 0 .50 0. 9886 . l .00 0 .75 0 .75 0. 9888 l .00 0 .75 1 .00 Division LOSS 0.1085 0.1187 0.1289 0.1391 0.1493 Zero Zero 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 Zero Zero 0.0159 0.0131 0.0128 0.0125 0.0122 0.0119 0.0116 Zero Zero 0.0618 0.0612 0.0606 0.0600 0.0594 0.0588 0.0606 Zero Zero 0.1377 0.1369 0.1359 0.1350 0.1340 0.1332 0.1322 Zero GAMMA 1.0048 1.0058 1.0054 1.0063 .1.0061 Divis Divis 1.0118 1.0117 1.0118 1.0117 1.0118 1.0122 1.0135 Divis Divis 1.0119 1.0117 1.0118 1.0117 1.0117 1.0122 1.0131 Divis Divis 1.0118 1.0117 1.0118 1.0117 1.0118 1.0122 1.0135 Divis Divis 1.0120 1.0117 1.0109 1.0117 1.0115 1.0122 1.0123 Divis ion by ion by ion by ion by ion by ion by ion by ion by ion by LOSS 0.2927 0.3186 0.3445 0.3704 0.3963 Zero Zero 2.0208 1.7695 1.5183 1.2670 1.0158 0.7645 0.5125 Zero Zero 0.6875 0.5891 0.4941 0.3991 0.3042 0.2092 0.1142 Zero Zero 0.0652 0.0640 0.0627 0.0615 0.0603 0.0590 0.0588 Zero Zero 0.1653 0.1954 0.2253 0.2554 0.2854 0.3154 0.3454 Zero PART II QUANTITATIVE MEASURES O F EXCHANGE RATE POLICY 92 CHAPTER 4 THE EMPIRICAL ANALSIS OF EXCHANGE RATE POLICY 4.1 Introduction The foregoing chapters, which collectively constitute Part I of this project, have dealt with theoretical aspects of the choice of exchange rate policy. In Part II, attention is focused on an issue of importance in the empirical analysis of exchange rate policy; namely, the formulation of quantitative measures of exchange rate policy and exchange market pressure. This chapter begins with a general discussion of the need for quantitative measures of exchange rate policy. Following this, the quantitative measures proposed by Girton and Roper (1977) and Holden, Holden and Suss (1978) are discussed in some detail in order to illustrate some of the problems associated with measuring exchange market policy and also to provide a point of departure for the new measures that are presented in Chapter 5. 4.2 A Brief Overview The International Monetary Fund regularly publishes international financial statistics in which three broad categories of exchange rate policy are recognized. On the basis of reports made by the member countries to the IMF, countries are classified as having a pegged currency, limited flexibility in terms of a single currency or group of currencies, or a more flexible system than either of these two. As of December 31, 1987, 93 countries are classified as having a fixed exchange rate regime: 39 are pegged to the U.S. dollar, 14 to the French Franc, 8 to the SDR and 33 to 93 94 other currencies or currency composites.1 Of the 12 countries falling into the category of limited flexibility, 8 are members of the European Monetary System while the remaining 4 currencies have shown limited flexibility in terms of the U.S. dollar.2 The balance of the membership, 46 countries in all, reportedly operates a more flexible exchange rate policy: 5 report that the external value of domestic currency is adjusted in response to a set of indicators, 23 claim to practice a system of managed floating and the remaining 18 declare themselves to be independently floating. Although, in all but the most extreme cases, it may be difficult to distinguish empirically between exchange rate arrangements on the basis of the IMF classification, it is fairly clear that countries diverge - widely in their choices of exchange rate policy. Consequently, theoretical literature concerned with the determinants of exchange rate policy since the breakdown of the Bretton Woods system has focused on providing a theoretical framework within which the observed diversity of exchange rate arrangements can be explained. Following the example set by Poole (1970), Fischer (1977) restricted the choice to fixed and flexible exchange rates and based his analysis on the assumption that exchange rate policy is the appropriate instrument for achieving economic stability, which he defined in terms of the variance of real consumption.3 While in subsequent work (see for example Boyer (1978), Buiter (1979), Frenkel and Aizenman (1982), Buiter and Eaton (1984), Turnovsky (1984) and Turnovsky and d'Orey (1987)) economic stability, variously defined in terms of the stability of real consumption, output, and the price level, is retained as the objective of exchange rate policy, the need to explain observed 1 International Financial Statistics, March 1988: p.16. 2 Ibid. 3 Poole (1970) analyses the appropriate choice of monetary policy instrument in the context of a closed economy. His contribution to the methodology employed in the analysis of optimal exchange rate policy is discussed in greater detail in Chapter 1. 95 preferences for exchange rate regimes in which currencies are neither completely fixed nor allowed to float freely, has resulted in the development of a general optimizing approach to the problem of exchange rate policy determination. The various studies differ in methodology and emphasis but have in common the conclusions that (i) the optimal degree of exchange rate flexibility depends on the nature of disturbances to the economy and (ii) neither perfectly fixed nor freely floating exchange rates will, in general, be optimal.4 Although the first theoretical result (i) provides a general hypothesis that clearly lends itself to empirical testing, the only example of such quantitative work to date is that of Melvin (1985). One possible explanation for the surprising lack of empirical work is that it is difficult to formulate a suitable quantitative measure of exchange rate policy to serve as the dependent variable. Such difficulties are not encountered in studies concerned with the determinants of the balance of payments under a system of fixed exchange rates and of the exchange rate when policy authorities refrain from intervening in the exchange market altogether. In each case, the relevant dependent variable can be easily identified and observed in the form of reserve changes when exchange rates are fixed, and as exchange rate changes under a policy of freely floating exchange rates. However, since theory suggests that the optimal exchange rate policy will most often be an intermediate or "mixed" regime in which the exchange rate is neither held completely fixed over the observation period nor allowed to float freely in response to market forces, empirical studies cannot reasonably be restricted to one of the two extreme exchange rate systems. The inclusion of intermediate regimes as a possible policy alternative makes it difficult to identify the dependent variable because under an intermediate system 4 A more extensive survey of the theoretical literature is provided in the introduction to Part 1. 96 both exchange rate and reserve changes are observed to occur simultaneously and jointly reflect the type of exchange rate regime. While it must be the case that any intermediate exchange rate system can be characterized in terms of the relative magnitudes of exchange rate and reserve changes, it is not immediately clear precisely how the relationship between exchange rate and reserve changes should be formulated in order to obtain a composite measure of exchange rate policy. Melvin, following the example of Heller (1978), solves the dependent variable problem by using the IMF exchange rate classification as an indicator of exchange rate policy. He assigns, in order of increasing flexibility, a value of 1, 2, or 3 to the policy variable of each country depending on whether its exchange rate is recorded by the IMF as being, respectively, (i) fixed to a single currency, (ii) fixed to a basket of currencies or (iii) allowed to float freely or follow a crawling peg. Using a trichotomous LOGIT estimation procedure, Melvin finds that the greater are foreign price shocks, the more likely is the policy variable to have an assigned value of 3, and the more prevalent are monetary shocks, the greater the likelihood that the policy variable has an assigned value of 1. Melvin interprets these results as supporting the theoretical propositions that countries subject primarily to domestic monetary shocks choose to hold their exchange rates fixed while countries for whom foreign price shocks are the main form of disturbance allow their exchange rates to float freely in response to market forces. Although likelihood ratio statistics and t-statistics indicate that Melvin's estimation equation contains significant explanatory power and that the model successfully discriminates between the three policy types, there is some question as to the interpretation of policy values of 1, 2 and 3 as representing exchange rate policies of increasing flexibility. The classification scheme employed by Melvin is based on the premise that the exchange rates of countries pegging to a single 97 currency are less flexible than those fixed to a basket of currencies or those described as crawling pegs. This need not necessarily be true and in fact, under some circumstances, the reverse may be the case. Although it is true that, in a nominal sense, a country that fixes its exchange rate to the U.S. dollar (for example) operates a fixed exchange rate system, it does so only in terms of the U.S. dollar, so that if the U.S. dollar floats against all other currencies in the world, then the currency that is fixed to the U.S. dollar must do the same. If we now wish to categorize that currency as fixed or floating, we are faced with a question - is the fact that the currency floats against all other currencies the characteristic of primary importance, or is the only relevant factor the relationship of the currency in question to the U.S. dollar? One might reasonably take the latter position if the United. States is clearly the single dominant trading partner, since the majority of external influences would then be directed to the domestic economy through the U.S. dollar. The difficulty here is one of confusion between concepts of bilateral and multilateral exchange rate regimes. In general, it is unlikely that exchange rate systems defined on a bilateral basis, as they are in the IMF classification scheme, will be reliable indicators of relative exchange rate flexibility overall; one would expect the fixity of a given currency with respect to some effective exchange rate (for example, a trade weighted average of major trading partners' exchange rates) to provide a more accurate reflection of the flexibility of an exchange rate policy. A further problem emanates from the fact that the IMF classification, and therefore Melvin's grouping scheme, is based on the exchange rate policies that countries declare themselves to be employing. As it is fairly well known that a number of the countries claiming to float independently actually do intervene in the exchange market quite regularly, it is difficult to equate independent floating with freely floating exchange rates; it would perhaps be more accurate to interpret the 98 policy choices of countries in the independently floating category as engaged in non-cooperative exchange rate management.5 As Melvin has grouped crawling pegs in the same category as independently floating currencies, however, the failure to report exchange rate policy truthfully may, in this instance, not have any significant impact on the results of the analysis. The results obtained by Melvin support the contention that countries choose their exchange rate system in response to the nature of economic disturbances. However, to the extent that the classification scheme employed misrepresents the relative flexibility of exchange rate systems, it is not possible to discern under which circumstances these systems exhibit a greater or lesser degree of flexibility. It is also worth noting that countries have not shown much movement between categories over time so that finer distinctions regarding changes in the exchange rate policies of individual countries over time cannot be made on the basis of the IMF classification. This imposes fairly stringent limitations on the type of empirical work that can be undertaken. While cross sectional tests of the determinants of exchange rate policy, like the one conducted by Melvin, can be undertaken using the IMF classifications (though not without ambiguity), time series studies of the policies employed by individual countries are unlikely to be illuminating. 5 From late 1978 until early 1984, the Canadian central bank's policy was one of resisting depreciation of the Canadian dollar against the U.S. dollar. Howitt claims that this policy had the effect of holding the value of the Canadian dollar fixed against a trade-weighted average of the G-10 countries. Yet during this period Canada appeared in the IMF classification under the heading of "independently floating" - see Howitt (1986), p.4. 99 4.3 Quantitative Measures of Exchange Rate Policy The alternative to using qualitative indicators such as the IMF exchange rate classification is to formulate a quantitative measure of exchange rate policy. One way of doing this is to define an index of exchange market intervention which allows the flexibility of an exchange rate policy to be expressed in terms of variables that are both observable and measurable. Since the degree of exchange market intervention practised has a direct impact on the level of the exchange rate and/or official foreign exchange reserves, it is natural to use these variables as indicators of exchange rate policy. The problem then is one of interpreting observed, changes in reserves and/or exchange rates in terms of the flexibility of exchange rate policy. Ideally, a quantitative measure of exchange rate policy should reflect the effort made by the policy authority to maintain equilibrium at a given exchange rate level. Exchange market disequilibrium exists when, at the prevailing exchange rate level, the quantity of foreign exchange supplied is not equal to the quantity demanded. Among the many causes of exchange market disequilibrium are changes in the supply of domestic credit by national policy authorities, structural changes in the economy, and changes in the preferences and expectations of economic agents. Exchange rate policy can be characterized by the extent to which such disequilibria are alleviated through the purchase or sale of official foreign exchange reserves by the the policy authority, that is, through official exchange market intervention. Accordingly, exchange rate policy can be measured quantitatively as the proportion of exchange market disequilibrium removed by official exchange market intervention. Defined in this way, an intervention index reflects the efforts of the policy authority to maintain the initial exchange rate level by measuring the actual amount of intervention relative to prevailing conditions in the foreign exchange market. 100 In practice, exchange market disequilibria cannot be observed directly. Instead we observe the changes in exchange rates and reserves that jointly restore equilibrium. The size of the underlying exchange market disequilibrium is reflected in the relative magnitudes of the equilibrating changes in reserves and exchange rate that it initiates. This composite measure of exchange market disequilibrium is referred to in the literature as exchange market pressure. The intervention index can therefore be defined as the proportion of exchange market pressure relieved by intervention in the exchange market. A quantitative measure that conforms to this definition is the ratio of the observed change in reserves to exchange market pressure. Alternatively, an index of exchange rate flexibility could be computed as the ratio of the observed change in the exchange rate to exchange market pressure. In this case there would be an inverse relationship between the value of the index and the degree of exchange market intervention undertaken by the policy authority. As measures of reserve and exchange rate change are easily obtained from a variety of published sources, the difficulty in calculating indices of intervention and flexibility lies in aggregating the two observable but incommensurate variables into a single composite measure of exchange market pressure. Given that, indices of intervention and flexibility calculated, respectively, as ratios of reserve and exchange rate changes to exchange market pressure should be ordinally reciprocal. A reasonable requirement for the aggregate variable is that the ranking assigned in terms of exchange market pressure to given time periods be unaffected by whether the measure is expressed in terms of exchange rate or reserve units. One aggregate measure of exchange market pressure is proposed by Girton and Roper. The authors set out to test the explanatory power of the monetary approach to external balance allowing for the possibility of managed floating. The monetary approach can be interpreted as a theory of the determinants of exchange market 101 pressure. Under fixed exchange rates, exchange market pressure is fully reflected in the reserve changes required to maintain the fixed exchange rate target; hence the original exposition of this theory as the monetary approach to the balance of payments. Under an intermediate exchange rate system, exchange market pressure is jointly relieved by changes in the level of the exchange rate and foreign exchange reserves. Consequently, the dependent variable appropriate for testing the monetary approach under managed floating is one that aggregates observed changes in exchange rates and reserves. Girton and Roper propose the difference between percentage changes in official reserves and exchange rate, r - e (where e = percentage change in the domestic currency price of foreign currency and r = change in reserves expressed as a percentage of the money supply), as a measure of exchange market pressure; Since its introduction, the Girton-Roper measure of exchange market pressure has been employed in numerous empirical studies. Among those who have used the Girton-Roper measure as the dependent variable are Connolly and Da Silviera (1981), Hodgson and Schneck (1981), Laidler, Bentley, Johnson and Johnson (1983), and Kenneally and Van Nhan (1986). The main problem with the Girton-Roper measure of exchange market pressure is that in simply taking the difference between observed reserve and exchange rate changes it implicitly assumes a one-to-one (inverse) relationship between the percentage change in the exchange rate and foreign exchange reserves, that is de/dr = 1. Unless the true elasticity of the change in reserves with respect to the change in the exchange rate is incorporated into the calculation, the proposed measure will not accurately reflect the degree of exchange market pressure. It is relatively easy to see that whenever de/dr f= 1, the Girton-Roper measure in its unmodified form overestimates or underestimates the true exchange market pressure depending on the relative signs and magnitudes of e and 102 f. 6 Furthermore, the assumption that de/dr > 0 implies that exchange rate devaluations improve the balance of payments within one period, which makes no allowance for the possibility of a J-curve effect. From an empirical point of view, the validity of this assumption depends crucially on the length of the observation period. The assumption of unitary elasticity of the change in reserves with respect to the change in the exchange rate is a direct result of the specification of the model from which the Girton-Roper measure of exchange market pressure is derived. For example, Girton and Roper assume that the change in the uncovered interest rate differential is independent of expected exchange rate changes. If it is assumed instead that changes in interest rate differentials reflect changes in the expected rate of exchange rate depreciation, the elasticity of reserve changes with respect to exchange rate changes is unitary elastic only if the demand for money is perfectly interest inelastic.7 What is required in order to obtain a more accurate measure of exchange market pressure is that the Girton-Roper measure be amended to become either t(de/9r)r - e] or [r - (dr/de )e] . The first measure expresses the observed changes in the exchange rate and foreign exchange reserves in terms of the exchange rate change that would have been required to restore exchange market equilibrium had the policy authority undertaken no intervention. The second measure expresses 6 Assume, for example that the true elasticity of the change in reserves with respect to the change in the exchange rate is de/dr = 05 and that the observed percentage changes in the exchange rate and foreign exchange reserves are e = -2 and r = 4, respectively. Then the Girton-Roper measure of exchange market pressure is given by r - e = 6. while the true measure of exchange market pressure is given by [(3e/dr)f - e] = 4. In this case the Girton-Roper measure overestimates the true exchange market pressure. 7 Details are provided in Appendix 4.1. 103 exchange market pressure in terms of the reserve change that would have been required in order to maintain the exchange rate at its initial (beginning of period) level. These two measures, except in the case where 3e/3r = dr/de = 1, result in different absolute estimates of exchange market pressure, but preserve ordinal relationships since the two measures are linear transformations of one another - i.e., [(3e/3r)f - e] = (3e/3r)[f - (3r/3e)e]. In the context of a two-country model, the modified Girton-Roper measures define ordinally consistent indicators of exchange market pressure. However, a practical problem arises in the application of these measures to a world composed of more that two countries. The reason for this is that the Girton-Roper measure, even in its modified form, makes no distinction between bilateral and multilateral concepts of external balance. While the percentage change in the exchange rate, e, is defined in terms of a bilateral exchange rate, the observed change in reserves, r, must be the net result of multilateral transactions so that the two components are not strictly conformable. This problem is minimized if exchange market pressure is calculated with respect to a dominant trading partner with whom the largest portion of trade in goods and financial assets is conducted. Since, in the case of Canada, the U.S. represents such a dominant trading partner, a modified Girton-Roper measure should provide a reasonable accurate indication of Canada/U.S. exchange market pressure.8 One possible solution to this problem is to define two distinct measures, one bilateral and the other multilateral. A bilateral measure could be obtained by disaggregating the observed percentage change in foreign exchange reserves into bilateral components. Then the bilateral measure of exchange market pressure, EMPJ(b), is given by: 8 This is of course due to the fact that when,as in the case of Canada/U.S., exchange market pressure is calculated with respect to the dominant trading partner, there is very little difference between the bilateral and multilateral measures. 104 3e J . i EMP-(b) = • 1 (4.1) 3r where ej is the percentage change in the value of country j currency with respect to the currency of country i, and rj measures the percentage change in total reserves of country j associated with international transactions between countries i and j. A multilateral measure of exchange market pressure for country j , EMPj(m), could be obtained analogously as: where e: is now a trade weighted (or effective) exchange rate such that e: = ZejWj reflect the degree of exchange market pressure if and only if: (1) The true elasticity of the change in reserves with respect to the exchange rate is equal to 1. . (2) Exchange market pressure is calculated with respect to a dominant trading partner such that w: is very close to 1, in which case there will be very EMP:(m) = (4.2) To summarize, the unmodified Girton-Roper measure will accurately little difference between EMPj(b) and EMP:(m). Bilateral and multilateral indicators of exchange rate policy can be calculated on the basis of the measures of exchange market pressure given by equations (4.1) and (4.2), respectively. The ratios g(m) = e/[(9e/3r)r - e] or g'(m) = r/[ r - (3r/3e)e] 105 are equally suitable as multilateral indices of exchange rate policy. The index g(m), which measures the flexibility of exchange rate policy, takes on a value of 0 when exchange rates are perfectly fixed and a value of 1 under perfectly flexible exchange rates. The index g'(m) measures the degree of exchange market intervention and, as the complement of g(m), takes on a value of 0 under freely floating exchange rates and a value of 1 when exchange rates are perfectly fixed. Intermediate exchange rate systems are reflected by index values between 0 and 1 for g(m) and g'(m)-9 Even if the exchange market pressure component of the index is appropriately modified (i.e., reflects the true elasticity of the change in reserves with respect to the exchange rate and properly distinguishes between bilateral and multilateral concepts of external balance), there remains a fundamental objection to the use of indices such as g(m) or g'(m) as quantitative measures of exchange rate policy. Although these indices systematically assign to the observed conditions in the exchange market a numerical value, their formulation is essentially arbitrary so that it is not always clear how such values, which in theory can range from minus to plus infinity, are to be interpreted in terms of exchange rate policy. While it is not difficult to interpret index values falling in the range 0 to 1, there is no theoretical framework within which to interpret index values less than 0 or greater than 1. As there are no grounds for excluding values outside the [0,1] interval a priori, the 9 Analogous bilateral exchange market intervention indices can be defined as: • i «i Although these bilateral intervention indices are presented in the interests of completeness, the usefulness of a such measures is open to question since intervention with respect to any currency that is freely traded, must lead to changes in the value of the domestic currency relative to all other freely traded currencies as well. 106 inability to provide a credible interpretation for such values is a serious shortcoming which cannot be overcome unless the index is formulated in the context of an acceptable theoretical model. An alternative to a measure of exchange market intervention based on the Girton-Roper measure of exchange market pressure is provided by Holden, Holden and Suss (1978), who undertake an empirical test of the optimum currency area propositions. These propositions state that the flexibility of exchange rate policy is determined by the openness of the economy, capital mobility, diversification of the external sector, geographic concentration of trade, and the divergence between rates of inflation among trading partners. Rather than use the IMF taxonomy as an indicator of the flexibility of exchange rate policy, Holden, Holden and Suss (henceforth referred to as HHS) construct a quantitative index of exchange rate flexibility, Fj, for each country in their sample. The HHS index of exchange rate flexibility is measured as the 24 month sum of absolute monthly percentage change in exchange rates expressed as a proportion of the absolute monthly change in official foreign exchange reserves measured as a percentage of imports plus exports. HHS calculate the flexibility index, Fj, according to the formula: f1 E(t-k)-E(t-k)-l h I E(t-k)-l J 23 Fj = I ! (4.3) k=0 f\ R( t-k)-R(t-k)-l 1 > 11 S(X(t-k)-j+I(t-k)-j> Vj=0 ) 107 where: E t = an index of the trade-weighted exchange rate of country i at time t, = U.S. dollar value of country i's holdings of foreign exchange at time t, X t = U.S. dollar value of exports of country i in month t, and It = U.S. dollar value of imports of country i in month t. The HHS flexibility index measures the flexibility of exchange rate policy on the basis of the relative magnitudes of observed changes in the exchange rate and the level of foreign exchange reserves. An exchange rate regime is interpreted as being relatively fixed when exchange rate changes are small relative to reserve changes and Fj takes on a value close to 0. Relatively flexible exchange rate systems are those for which the numerator of Fj is large relative to the denominator and the index takes on large positive values. A technical problem with the HHS index is that while perfectly fixed exchange rate are characterized by ah index value of 0, perfectly flexible exchange rate regimes, in which one would observe no change in official foreign exchange reserves over the relevant period, are undefined since in this case the denominator of Fj takes on a value of zero. Clearly this will only present a practical problem if the observation period includes periods in which no reserve changes are recorded. It is possible to express the HHS flexibility index given by equation (4.3) in a form more consistent with the quantitative measures discussed previously. With some minor simplification and rearrangement, the HHS index can be written as: 108 where: e = the percentage change in an index of the trade-weighted exchange rate, fh= the percentage change in the U.S. dollar value of foreign exchange holdings, X= U.S. dollar value of exports, I = U.S. dollar value of imports, ^ . 1 = U.S. dollar value of initial (beginning of period) foreign exchange holdings. It is evident that the HHS index measures exchange rate flexibility simply as the ratio of the observed percentage change in the exchange rate relative to the observed percentage change in reserves weighted by the ratio of total trade to initial reserves. If the flexibility index were not weighted in this way and was calculated simply on the the basis of le/ "rh 1, the index would underestimate the degree of exchange market intervention practised by countries with large initial reserve balances relative to countries with smaller initial holdings of official foreign exchange reserves.10 Flexibility scores were calculated by HHS for 76 countries for the 24 months ending December 1975. The regression results indicate that 42% of the variability of the flexibility measure is explained by the independent variables enumerated above. The flexibility scores were reported by HHS as ranging from 0.01, for Italy and a number of small developing economies, to a value slightly in excess of unity for the United States. As defined, the HHS flexibility index has a range from 0 to infinity, 1 0 Consider the situation of two countries, identical in all but their beginning of period foreign exchange reserve balances. Assume that country A has a reserve balance of $2,000 while that of country B is $20,000. Assume also that le/*rhl for each country is equal to 0.5. Under these conditions, in order to obtain a 5% change in the exchange rate, country A need only alter its official reserve holdings by $200 while country B would have to accept a $2,000 change in official foreign exchange reserves. A flexibility index based on the observed responsiveness of the exchange rate to changes in official foreign exchange reserves would reflect both countries as having intervened in the exchange market to the same degree although, in absolute terms, the effort made by country B to prevent the exchange rate from changing more than 5% is clearly greater than that of country A. The inclusion of the weight (R t_j)_1 alleviates this difficulty. The component (X + I) serves a similar purpose. 109 with 0 representing a perfectly fixed exchange rate and values close to infinity representing fully floating exchange rates. The relatively narrow range of the flexibility scores obtained by HHS indicates that all countries included in the sample practiced a high degree of exchange market intervention over the observation period. This result is at variance with Emminger's suggestion that countries such as Germany and Switzerland abandoned the fixed exchange rate system in early 1973 for the express purpose of allowing their exchange rates to float against the U.S. dollar.11 The most likely explanation for the surprisingly low index values obtained by HHS is that the numerator of the index weight, (X+I)/Rt_j, excludes capital flows. The exclusion of a measure of international financial transactions is of particular importance to the observation period relevant to the HHS analysis. The reason for this is that countries such as Germany and Switzerland had, prior to abandoning the Bretton Woods system, been forced to absorb large balance of payments surpluses due to short term capital inflows. Consequently, the initial official reserve balances applicable to the observation period would be quite large relative to total trade, causing the flexibility scores to be very restricted in terms of their range. The exclusion of capital flows from the numerator of the index weight causes the flexibility index to overestimate the absolute degree of exchange market intervention practised by the various countries and, in all likelihood, results in countries being incorrectly ranked in terms of relative degree of exchange market intervention as well. Unfortunately, the HHS flexibility index is unlikely to produce a correct ranking even if the index weight reflects the size of the external sector as a whole (i.e., includes the capital account) rather than the foreign trade sector alone. From iiEmminger (1980). 110 equation (4.4), it is clear that the HHS flexibility index suffers from the same shortcoming as the Girton-Roper measure of exchange market pressure - namely, that its components wil l not, in general, be commensurate. In particular, the exchange rate and reserve components of the HHS flexibility index wi l l be commensurate only i f [R t . j / ( X + I ) ] = de/3r h . This means that the HHS index is not suitable for cross sectional comparisons of the flexibility of exchange rate policy unless [R^j /CX+I) ] = 3e/3rh for all countries in the sample or [R|.i/(X+I)] *3e /ar h is the same for all countries in the sample. When [RJ.J /CX+I)] = 9e/8rh for all countries and the index weight accurately reflects the relative size of the external sector, the HHS index produces a cardinally correct measure of exchange rate flexibility whereas Fj = (e/ r N ) [ (X+I) /Rt- l ] is only ordinally correct when [RJ.J /GX+I) ] £ 3 e / 3 r h . The fundamental source of difficulty with the HHS index is that while the authors recognize that "the amount of intervention is only relevant when it is examined relative to the pressure on the exchange rate", they do not explicitly formulate a measure of exchange market pressure. As the foregoing discussion indicates, the inclusion of the weight, ( X + I ) / R t _ i , in the flexibility index does not provide a satisfactory alternative measure of the relative effort made by policy authorities to maintain the observed exchange rate level. In general, the HHS flexibility index will generate a reliable (inverse) ranking of the degree of exchange market intervention if and only if (1) [R T . ! / (X+I) ] = 3e/3rh or [R^j /CX+I)] *3e/3r h is the same for all countries throughout the sample period. (2) The degree of exchange market pressure is the same for all countries throughout the sample period. I l l As these conditions are fairly restrictive, the HHS flexibility index is of limited practical use as a quantitative measure of the relative degree of exchange market intervention. 4.4 Conclusion The absence of an international monetary agreement since the breakdown of the Bretton Woods system has allowed domestic policy authorities unrestricted choice of exchange rate policy. The resulting diversity of exchange rate practices has generated a large body of theoretical work concerned with explaining the determinants of exchange rate policy. Although these studies differ in many respects, there is widespread agreement that stability maximizing policy authorities will, in general, choose to operate intermediate rather than perfectly fixed or flexible exchange rate regimes. Consequently, empirical studies of exchange rate policy must allow for the possibility of systems of managed floating in which exchange market disequilibria are removed by a combination of reserve and exchange rate changes. One way to ensure that all existing exchange rate practices are represented is to use the IMF classification as an indicator of exchange rate policy. Unfortunately, this classification does not distinguish between bilateral and multilateral concepts of exchange rate policy, so that it is unlikely to be a reliable indicator of the degree of exchange rate flexibility even if member countries are truthful in their reports to the IMF. The alternative, quantitative approach, poses an aggregation problem: namely, that of finding a sensible way of aggregating observed exchange rate and reserve changes into a single, composite measure of exchange rate policy. Significant progress towards solving this problem has been achieved in the 112 quantitative measures proposed by Girton and Roper and Holden, Holden and Suss but, as neither measure provides a reliable classification of exchange rate policy, these can only be regarded as partial solutions. The minimum requirement for such an index to be useful as a measure of exchange rate policy is that it be ordinally correct. The task of the following chapters is to formulate a cardinally correct measure of exchange market intervention that can be used to conduct both time series and cross-sectional analysis of exchange rate policy. 113 Appendix 4.1 Girton and Roper asume that international capital flows respond to interest rate differentials unadjusted for exchange rate expectations so that 0 = i - i* where i and i* are, respectively, domestic and foreign interest rates and 6, the interest rate differential, does not depend on expected changes in the exchange rate. If, instead, it is assumed that capital flows respond to interest rate changes adjusted for expected exchange rate changes, the deviation from interest rate parity is given by: 6 = tE(et+l) (AAA) where t E(e l + 1 ) is the expected percentage change in the price of domestic currency per unit of foreign currency. Subsituting (4.1.1) into the Kenneally and Finn (1985) version of the Girton-Roper reserve flow equation yields: r t = aipt + a2yt + a3*t + *4mt + a5dt (4.1.2) where: p.y.r, and d denote the percentage changes in prices, real income, reserves and domestic credit. Kenneally and Finn assume that the demand for money is determined by m t = ao + aip t + a 2 i t + a3yt so that the coefficients ai, a2, and a3 denote the price, interest and income elasticities of the demand for money, respectively. Imposing PPP, setting ai = 1, and rearranging (4.1.2) results in rt = (^""t + Cj) + a2yt + a3(i* + tE(et+1)} + a4mt + asdt (4.1.3). 114 But ^ ( ^ + 1 ) can be written in logs as tE(e t +j) - ^ and since e^  is defined as the percentage change in the exchange rate, ^ = ^ - e|_j. The expected percentage change in the exchange rate is then given by t E ( C j + j ) = t^^ e t + l^ " et-1 " *t" Substituting this expression into (4.1.3) yields: r t = p*t + et.+ a2yt + a3(i* + tE(e t + 1) - ^ .j - e^  + a4mt + asdt (4.1.4). Consequently, the expression for exchange market pressure is given by: r t + fo-l)^ = p*t + a2yt + a3{i* + tE(e t + 1) - e^ }+ a4iht + asdt (4.1.5). It is clear that a one-to-one trade-off between reserve and exchange rate changes requires that aj = 0. With the money demand function given in logarithms as: d m t = pt + a2yt + a3it the assumption that a3 = 0 implies that the demand for money is perfectly interest inelastic. CHAPTER 5 MEASURING EXCHANGE MARKET INTERVENTION AND EXCHANGE MARKET PRESSURE 5_J introduction In the preceding chapter it was pointed out that the possibility of systems of managed floating makes the empirical study of exchange rate practices difficult in that it requires the aggregation of observed changes in the exchange rate and foreign exchange reserves into a composite measure of exchange rate policy. The main purpose of this chapter is to propose a solution to this aggregation problem in the form of an index of exchange market intervention and a related measure of exchange market pressure. The general methodology is as follows: Beginning with exchange market intervention, the index is defined and interpreted in terms of observed changes in exchange rates and the balance of payments. Then, on the basis of a simple monetary model, the relationship between exchange rate changes and the balance of payments is derived and used to aggregate the two variables in accordance with the definition of the intervention index. The measure of exchange market pressure is obtained in a similar manner. 115 116 5.2 Exchange Market Intervention The principle underlying the definition of the degree of exchange market intervention, introduced in Chapter 2 and employed throughout Part 1, is that it is possible to distinguish between exchange rate systems on the basis of their observed consequences for the balance of payments. By definition, the balance of payments measures the amount by which the value of goods and financial assets exported exceeds the value of those imported over a given time period. Assuming, for simplicity, that all international transactions are settled in the currency of the seller, it follows that the balance of payments for any country must be reflected in the excess demand for the domestic currency of that country in the market for foreign exchange. Under a system of freely floating exchange rates, the rapid response of the exchange rate to market forces prevents the development of an excess demand for any currency so that the balance of payments is always zero. Under a system of fixed exchange rates, on the other hand, the policy authority intervenes in the exchange market in order to prevent the exchange rate from deviating from its target level in response to market forces. The size of the resulting payments imbalance is equal to the amount of intervention required to maintain the exchange rate target. Intermediate exchange rate systems are characterized by exchange rate targets that lie between the exchange rate required to bring about market equilibrium and the exchange rate of the previous period so that exchange market disequilibrium is removed by a combination of exchange rate adjustment and intervention. In perfectly fixed exchange rate systems, the target in each period is the exchange rate of the preceding period. Since, under perfectly fixed exchange rates, no portion of the initial exchange market disequilibrium is removed by exchange rate adjustment, the amount of intervention required is, ceteris paribus, greater than under an intermediate exchange rate system so that there is an inverse relationship between the size of the payments imbalance and the flexibility of the 117 exchange rate system. It is therefore possible to obtain information about the type of exchange rate system from observations on the balance of payments. In the preceding chapter, the degree of exchange market intervention was proposed as a quantitative measure of exchange rate policy. Although, in theoretical models, the intervention practices of policy authorities are usually given a simple form, such as the purchase or sale of foreign exchange reserves, there are in practice many different ways in which intervention can be effected and not all of these activities are easily identified on the basis of published data. One way to solve this problem is to define the index of intervention on the basis of the balance of payments. Using the balance of payments associated with a fixed exchange rate regime as the point of reference, the degree of exchange market intervention, y, is defined as:1 BOP t( actual) BOPt(actual) EMP t = BOPt(fixed) ( 5 1 ) * where: BOPt(actual) measures the observed payments imbalance EMP t measures exchange market pressure BOPt(fixed) measures the balance of payments that would have been recorded had exchange rates remained fixed. 1 This measure of exchange market intervention assumes that the policy authority does not employ domestic credit changes as an instrument of exchange rate policy. When this assumption is not fulfilled, the degree of exchange market intervention is more appropriately measured as 7t(d): Adt(actual) + BOP t(actual) where Ad. is the change in domestic credit and EMP t = Ad .(actual) + BOP.(fixed). 118 Since, under fixed exchange rates, the payments imbalance is a measure of exchange market pressure, the index defined in (S.l) measures the actual intervention undertaken by the policy authority relative to exchange market pressure over the relevant period. With EMPt = BOPt(fixed), EMPt < 0 indicates that there is an excess supply of domestic currency while EMPt > 0 reflects the existence of excess demand in the domestic money market. Theoretically, the intervention index can vary from minus to plus infinity with the values of 0 and 1 representing perfectly floating and fixed exchange rates, respectively. In practice, one would not expect the degree of intervention to approach either positive or negative infinity. Positive intervention indices that exceed 1 indicates that a country is attempting to maintain an exchange rate in opposition to market forces.2 Given this interpretation of y > 1, one would expect such values to pertain primarily to shorter periods as they are severely limited, in the case of upward pressure on the exchange rate, by the stock of reserves and, in the case of downward pressure on the exchange rate, by the country's willingness to accept increased inflationary pressure over the longer term. At the other end of the spectrum, negative values of the intervention index indicate that the country has either engaged in sterilized exchange market intervention or used an active monetary policy to reinforce exchange rate changes initiated by market forces. Given that feasible increases or decreases in the money supply are constrained by the size of the existing monetary base as well as other conditions in the economic environment, one would not expect such changes in the money supply to result in extremely large intervention index values on an annual basis. Values of the intervention index falling between 0 and 1 reflect intermediate exchange rate regimes in which money market disequilibrium is alleviated through a combination of exchange rate and reserve changes. Whether multilateral intervention indices 2 See Chapter 2 for the appropriate theoretical derivation. 119 register intermediate values or negative values when a country fixes its exchange rate in terms of the currency of one partner country while that partner allows its exchange rate to float against all other currencies, depends on the correlations between currency movements. Both bilateral and multilateral indices will take on values between 0 and 1 if a country switches between pegged and floating exchange rates within one observation period. 5.3 Measuring Exchange Market Intervention The measurement of the degree of exchange market intervention as defined in (5.1) is made difficult by the fact that BOP(fixed) not directly observable. In order to impute BOP(fixed) it is necessary to establish some relationship between the unobservable quantity BOP(fixed), and the two observed variables, BOP(actual) and the change in the exchange rate (AE). In general terms, this relationship can be expressed as:3 BOP t(fixed) = BOPt(actual) (d[ BOP.(actual)] > A E . (5.2). dEt where: E denotes the number of home country currency units per unit of foreign currency. In its general form, equation (5.2) suffers from the same shortcoming as the Girton-Roper formulation in that it does not clearly distinguish between bilateral and multilateral concepts of external balance. Ideally, the bilateral balance of payments under a system of fixed exchange rates should be imputed as: 3 Equation (5.2) is a first order approximation whenever the relationship between changes in the balance of payments and the exchange rate is not a linear one. [BOPJ(t)Kfixed) = [BOPJ(t)Kactual) 120 ^ [ B O p i ( t ) ] ( a c t u a l ) V I ( T ) ( 5 3 ) v J where: BOPJ is the portion of country i's payments balance resulting from trade with country j and E | is the bilateral exchange rate (number of country i currency units per unit of country j currency). In order to impute [BOP(t)](fixed) on a multilateral basis equation (2) must be interpreted as: [BOPHOKfixed) = [BOP^OKactual) -(atBOP^OKactual) "\ dE^t) AE'(t) (5.4). such that: BOP^t) = £ BOPJ(t) and E'(t) = E Wj EJ(t) where wj measures the proportion of country i's trade that is conducted with country j. Bilateral, Yj(t), and multilateral, y(t), intervention indices can be defined on the basis of the relationships described in equations (5.3) and (5.4), respectively. The bilateral intervention index of country i with respect to country j is defined as: [BOPJ(t)](actual) Y i ( t ) = " i <5'5>-J [BOPj(t)](fixed) Similarly, the multilateral exchange market intervention index of country i is defined as : y i • = IBOPfoKactual) [BOP 1(t)](fixed) 121 It is clear from equations (5.3) - (5.6) that knowledge of the relationship between the balance of payments and exchange rate changes, 3 B O P t / 3 E t , is necessary in order to measure exchange market pressure and the degree of exchange market intervention. 5.4 Measuring Exchange Market Pressure Since the relationship between reserve and exchange rate changes cannot be observed directly, it must be obtained on the basis of economic theory. This requires the development of a theoretical model of external adjustment in which the relationship between the balance of payments and the exchange rate is explicitly formulated. In this chapter, a short run monetary adjustment model is developed for the small open economy and also for interdependent economies. The models are initially formulated for the case in which the domestic economy has a single trading partner - in the small open economy model this trading partner is assumed to be very large while in the model incorporating interdependence, the two countries are assumed to be of similar size. These models are subsequently extended to encompass the more general n-trading partner case. The models developed in this chapter have several distinguishing features. To begin with, the exchange rate regime is not assumed to be either perfectly fixed or flexible so that the theoretical relationship established between reserve and exchange rate changes pertains to all possible degrees of exchange market intervention. Secondly, prices are neither assumed to be completely unresponsive in the Keynesian manner, nor to exhibit neoclassical perfect price flexibility. Instead, domestic prices are represented as a linear combination of the two extremes reflecting the notion that price responsiveness is governed by structural and institutional factors which may vary among countries. An important consequence of the assumption that price flexibility may, in the short run, be determined largely by 122 domestic institutions, is that it raises the possibility of the existence of short run deviations from purchasing power parity, not only for interdependent economies, but also for the small open economy. Finally, in contrast to the monetary adjustment models of Fischer (1977) and Frenkel and Aizenman (1982), in which money market disequilibria are removed through a partial stock adjustment process, the analysis in this paper assumes that the money market clears continuously so that the economy is always on its long run demand for money function. The short run nature of the model is reflected in the assumption that real output is fixed and that deviations from purchasing power parity can persist over the period of analysis. For the purposes of this paper therefore, the short run is defined as the period of time over which output is fixed and deviations from purchasing power parity can be maintained. 5.5 The Small Open Economy In this section, the simplest small open economy model is presented. The model is of a small country which engages in trade in both goods and financial assets with the rest of the world which, for the present, is represented as a single large trading partner. There is only one traded good and the world price of this good is given in terms of foreign currency. Domestic and foreign bonds are assumed to be perfect substitutes, with the nominal return on foreign bonds (i.e., the world interest rate) given exogenously. It is assumed that money is held for transactions purposes and that all purchases must be paid for in the currency of the seller. Economic agents hold money balances only in their domestic currencies so that all foreign exchange is held by the policy authority. It is also assumed that individual agents maintain portfolios composed of goods, money and bonds. Equations (5.9) - (5.16) describe this economy. 123 m t = mj for all t (5.9) s _ m j = rrij + Ar^  (5.10) m | = nij_ j + Adj (5.11) m d = a 0 + a i y t + a 2 i t + pt (5.12) p t = ap t + (l-a)p t.i (5.13) Pt = P*t + h ' d e v t (5.14) i t = i* t + [^(e^j) - ej] (5.15) Et<et+P " et = " P d e v t (5.16) where: m s is the observed nominal supply of money m d is the demand for nominal money balances m is the amount of nominal money supplied by the policy authority which is composed of the inherited money stock plus any change in domestic credit Ar is the change in reserves expressed as a percentage of the initial money stock and represents the endogenous change in the nominal money supply (i.e., Art = [Rt - R ^ j / M ^ = B O P t / M M ) Ad is the change in domestic credit expressed as a percentage of the initial money stock and represents the exogenous change in the nominal money supply (i.e., Ad t = [D t - D ^ l / M ^ ) y is the current level of real aggregate output i is the nominal domestic interest rate p is the domestic price level p is the perfectly flexible, market clearing price level p * denotes the world price level 124 e is the exchange rate (defined as the number of domestic currency units per unit of foreign currency) dev is the short run deviation from purchasing power parity is the foreign (world) nominal interest rate is the exchange rate that is expected to prevail in period t+l based on the information available in the current period t. All variables are expressed in logarithms. Equation (5.9) reflects the assumption that the money market clears continuously. The money supply equations, (5.10) and (5.11), indicate that the observed nominal money supply, m t , is determined by the size of the inherited money stock, m t_i, and the net effect of endogenous reserve changes, Ar t , and exogenous changes in domestic credit, Ad t. Equation (5.12) describes the demand for nominal money balances, m^, as a function of the level of real output, domestic interest rates, and domestic prices. The domestic price level is described in equation (5.13) as a linear combination of the perfectly flexible market clearing price, pt, and last period's price level, pt_ j . Note that pt is defined as the price level that would be required to entirely remove any existing money market disequilibrium instantaneously, regardless of the source of the disturbance. In this model there are three possible sources of exogenous disturbance: Ad t , Ap* t , and A i * t . Since, when domestic prices change instantaneously to remove money market disequilibria Ar t = Ae t = 0, the market clearing price change Ap t can be expressed in terms of the three possible sources of exogenous disturbance as:4 A s d 4 Continuous clearing in the money market implies that for all t, Am { =Am t so that Ad t + Ar t = a 2 Ai t + a3Apt. Since Ap t = Ap* t + Ae t - Adevt, A i t is given by Ai t = A i * t -f>Adevt = Ai* t + P(Apt - Ap* t - Aet) and Ad t + Ar t = a2{Ai* t + P(Ap t - Ap* t - Aet} + a3Apt. When prices are perfectly flexible, all money market disequilibrium is removed by a 125 AP t = 1 [ A d t (5.17). (a2p + a3) - a 2 A i * t + Equation (5.14) provides a link between domestic and foreign prices that allows for short run deviations from purchasing power parity. The assumption that domestic and foreign bonds are perfect substitutes leads to the interest parity condition (5.15). The expectations formation equation, (5.16), forms a link between prices and interest rates in that whenever p ^ 0, short run deviations from purchasing power parity observed in the current period lead investors to expect offsetting exchange rate changes in the future which affect the expected returns on investment. When p = 1, agents expect the deviation from PPP to be fully removed through exchange rate changes next period, while P = 0 indicates that agents expect the exchange rate to remain fixed so that Ae t +j= 0 and Ar t + j = - devt. The model represented by equations (5.9) - (5.16) is clearly not the only one that could have been employed. In choosing this particular representation of monetary adjustment, two main factors were taken into consideration. The first of these was that the model remain simple enough to allow for tractable multiple country extensions. It is primarily for this reason that the goods market is not modelled explicitly. The second major consideration was that the adjustment processes described by the model should, wherever possible, be supported by exisiting empirical evidence. As the proportion of money market adjustment attributed to exchange market intervention depends crucially on the nature of alternative channels available for removing monetary disequilibrium, the change in the domestic price level and the induced interest rate change caused by the deviation from PPP accompanying the change in domestic prices. Consequently, when prices are perfectly flexible, Art = Aet = 0 and A p t = A ?t = u^+aa) [ A d t" a 2 A i * + t a 2 P A P * t ] (5.17). 126 specification of the process by which monetary equilibrium is restored is of particular importance to the measurement of exchange market pressure and exchange market intervention. Equations (5.9) and (5.13), respectively, reflect the observation that while money markets tend to clear very rapidly, prices may, for a variety of institutional reasons, be less than perfectly flexible. The empirical finding that the purchasing power parity relationship does not hold in the short run is captured by equation (5.14), which allows for short run deviations from purchasing power parity. Empirical studies have also shown that the PPP relationship does appear to hold in the long run with the result that exchange rate changes, over the longer term, are dominated by relative price movements.5 When P > 0, equation (5.16) ensures that short run deviations from PPP will be eliminated in the long run. However, equation (5.16) also makes a strong statement about the manner in which private agents form expectations about future exchange rates. It is well known that the results obtained on the basis of models incorporating forward looking expectations are very sensitive to the assumptions made about the way in which private agents form their expectations about the future. It is therefore necessary to justify equation (5.16), quite independently of its role in ensuring that PPP holds in the long run, as a reasonable representation of the expectations formation process. The main problem with specifying expectation formation equations is that relatively little is known about how individuals form their expectations about the future. In recent years, the representation of expectation formation in terms of an adaptive, backward-looking, process has been replaced by the notion of model-5 The proposition that PPP holds in the long run but that deviations from PPP persist in the short run is supported by Hakkio's (1984) multi-country study. The results obtained in this study also suggest that previous results (see, for example, Frenkel (1981) and Dornbusch (1980)) which have cast doubt on the long run purchasing power parity relationship may have been due to a lack of precision in the estimation procedure. 127 consistent expectations, first introduced by Muth (1961). This concept of expectation formation asserts that agents are rational in the sense that they form their expectations about the future paths of economic variables on the basis of all available information and their knowledge of the structure of the economy, thereby eliminating the systematic forecast errors that result from an adaptive expectations process. In the absence of a greater understanding of the related processes of learning and expectation formation, the practice of using of model-consistent expectations to represent forward looking behaviour has become so widely accepted that it is necessary to justify not only the expectation formation process described by equation (5.16), but also the decision not to employ an alternative, model-consistent, representation. There are two main reasons for not using a model-consistent expectations formation equation in place of equation (5.16). The first of these has to do with the nature of government policy objectives. In the context of the present study, it is assumed that policy authorities intervene in the exchange market for the purpose of achieving a particular set of unspecified economic objectives. In order to achieve its objectives, the policy authority must therefore respond to the prevailing economic conditions in some systematic way. Over time, the government's exchange rate policy will therefore cause exchange rate and reserve changes to be related to a linear combination of all endogenous economic variables. Since the resulting relationship, or government reaction function, can be observed and estimated by economic agents, an equation that describes expected exchange rate changes in terms of a forecast based on the estimated policy rule is a natural model-consistent alternative to equation (5.16). However, while such a process of expectation formation is rational in the sense that it uses all available information, it will only provide good forecasts of future exchange rate changes if the policy authority's objectives remain fairly constant over time. If this is not the case, then rational 128 agents, observing that forecasts based on current and past policy responses are poor predictors of future exchange rate movements will likely form their expectations on some other basis. In practice, the objectives of policy authorities can be strongly influenced by political concerns of domestic and foreign origin that, by their nature, are subject to change over relatively short periods of time. Under such circumstances, equation (S.16) may very well represent a more appropriate expectations formation process than one based on a forecast of an unstable government reaction function. The second reason for using equation (5.16) has to do with the integrity of the model itself given that international trade in financial assets is described using the uncovered interest parity condition, equation (5.15). In order to hold, the uncovered interest parity condition requires that forward exchange rates are unbiased predictors of future spot rates and that the spread between forward and spot exchange rates eliminates arbitrage profits. There is now an extensive empirical literature documenting the violation of the first these requirements, which suggests that international trade in financial assets among rational agents is not captured by the uncovered interest parity condition.6 In recent empirical work, however, van Norden (1989) has employed a model with multiple short run equilibria to reconcile the assumptions of rational expectations and uncovered interest parity. It can be shown that, in the context of a multiple-equilibrium model, equation (5.16) represents a process of rational expectations formation that is consistent with uncovered interest parity. The supporting argument is provided in Appendix 5.1. 6 Cumby and Obstfeld (1984), Diebold (1988), Frankel and Froot (1987), Froot and Frankel (1989), Giovanni and Jorion (1987), and Obstfeld (1987) are all cited by van Norden (1989). 129 5.6 Money Market Adjustment According to equation (5.13), any price level observed in a given period can be described as some linear combination of the past price level and the market clearing price that would obtain under perfect (and instantaneous) price flexibility. That is, the prevailing price level, p t, can be written as: Pt = a Pt + 0 - a ) P t - l (5.13). When a=1, prices are perfectly flexible and the actual price level equals the market clearing price level p t, where p t = m t - ao - aiy t - a 2 i t . When a=0, prices are fixed so that the last period's price level is maintained regardless of changes in n^ or the demand for real money balances. Values of a between 0 and 1, reflect intermediate degrees of price stickiness. In this model, short run deviations from purchasing power parity can occur either directly, as a result of an initial exogenous disturbance to the economy, or indirectly, as a result of the adjustment process to such a disturbance. It should be noted that the existence of a net deviation from purchasing power parity, regardless of source, must lead to a change in domestic interest rates whenever (5*0. This implies that when prices are perfectly flexible the market clearing price level, p t, is that price which together with the induced interest rate change restores money market equilibrium. Given the assumption that the money market always clears quickly, and that prices are sticky, so that p t is not equal to ~p\, there must exist additional avenues of adjustment through which the remaining money market disequilibrium is removed. The mechanism by which the money market achieves equilibrium when prices fail to be fully flexible depends on the chosen exchange rate regime. Under fixed exchange rates, the residual adjustment is accomplished through an endogenous s change in the money supply, so that the observed quantity of money, m t , is actually 130 equal to m t + 4 r ( . When exchange rates are fully flexible, any money market disequilibrium remaining after domestic prices have adjusted is removed through a change in the exchange rate and an accompanying change in the domestic interest rate. Under intermediate exchange rate systems, money market equilibrium is restored by a combination of price, interest rate, reserve and exchange rate changes. The way in which price, interest rate, reserve, and exchange rate channels operate to restore money market equilibrium, can be illustrated by considering the case in which a money market disturbance originates with a change in the quantity of domestic credit such that Ad t > 0. For the purposes of this illustration it is assumed that there are no other disturbances, so that A p * t = A i * t = 0. Continuous money market clearing requires that: (5.9). Under the assumption that real income is slow to change so that y t = y t . i , the current period demand for money can be characterized as: m d = ao + aiy t_i + a2(it_i + Ai t) + a 3 ( p M + Ap t) smj 1 j + a 2 A i t + a3 Ap t (5.18). Substitution of (5.10) and (5.18) into (5.9) yields: [ m t - md_j] + [ A r t - a 2 A i t - a3 Ap t] = 0 (5.19) where [ m ( - md_j] = Ad t identifies the size of the initial money market disequilibrium caused by the change in the quantity of domestic credit, Ad t , and [Ar t - a 2 A i t - a3 Ap t ] 131 represents the adjustment to nominal money balances, domestic prices, and interest rates required to restore money market equilibrium.7 The extent to which monetary equilibrium is restored through each of these channels of adjustment depends on the exchange rate system chosen as well as the degree of price flexibility. With the domestic price determined according to equation (5.13), the excess supply of money remaining after the initial price change, A p t , is given by [ ihj - m _^j - a3 Ap t]. If exchange rates are completely fixed (Aet =0) and prices are perfectly inflexible (so that a =0) , then under the current assumptions Apt = Ap*t + Aet = 0 so that Adevt = 0 also. With Adevt = 0, A .= A i * t - Adevt = 0 so that the entire adjustment to restore money market equilibrium is achieved through an endogenous change in the nominal money supply such that Art = - [ h\ - m^j] = - Adt (5.20). Under a system of fixed exchange rates, the policy authority accommodates the initial increase in the demand for foreign goods and assets by providing the required foreign currency at the prevailing exchange rate. The resulting outflow of foreign 7 The general form of equation (5.19), which includes all possible disturbance sources, is given by: [ mt - md_j - a 2 Ai* t - a3 Ap*t] + [ Ar t - a 2 A i t - a3 Apt] = 0 (5.19'). since m t = m t.j + Ad t equation (5.19') can be expressed as [Ad t-a2Ai* t-a3Ap* t] + [Ar t -a2Ait-a3Ap t ] = 0 (5.19') where [ A d t - a2Ai* t - a3 Ap* t] identifies the size of the initial money market disequilibrium by source and [ Ar t - a 2 A i t - a3 Ap t] represents the adjustment to nominal money balances, domestic prices and interest rates required to re-establish money market equilibrium. 132 exchange reserves contracts the monetary base thereby restoring money market equilibrium. If, on the other hand, exchange rates are perfectly flexible and a = 0, the entire adjustment occurs through a change in the domestic interest rate that is initiated by the response of the exchange rate to a change in the demand for foreign goods and assets. In the case of an increase in the quantity of domestic credit, the following occurs when exchange rates are perfectly flexible. The increase in domestic credit leads to an excess supply of money in private portfolios, causing domestic residents to demand greater quantities of all goods and assets, domestic as well as foreign. The increased demand for foreign goods and assets leads to an exchange rate depreciation. With domestic and foreign prices unresponsive so that Ap t = Ap* t = 0, the exchange rate depreciation causes a short run deviation from purchasing power parity such that Adev t = Ae t = - Ad t/a2P- According to equation (5.16), the observed deviation from PPP leads investors to expect an exchange rate appreciation, causing domestic bonds to become relatively more attractive. As a result of this increase in demand, the price of domestic bonds rises and the domestic interest rate falls by A i t = Ad t/a2- The reduction in the domestic interest rate reduces the opportunity cost of holding money so that the demand for domestic currency increases, restoring money market equilibrium. When a=l, prices are perfectly flexible and the monetary imbalance initiated by the increase in domestic credit is removed by a combination of price and interest rate change such that Ap t = Adt/(a2P + a3) and Ai t = pAdt/(a2P + a3), regardless of the degree of exchange rate flexibility since no residual disequilibrium remains after the initial price adjustment has taken place. A schematic representation of the adjustment process following a change in domestic credit is provided in Figure 5.1. Figure 5.1 Money Market Adjustment Initial Disequilibrium —> [ m^  - md_j] £ 0 Initial Adjustment (i) Ap t = A devt 1 (ii) A i t = p Adevt Disequilibrium j - a3 Apt - a2 Aij] A m pure float A ej <— managed float EXCHANGE MARKET PRESSURE Ai t <-Policy Authority chooses degree of EXCHANGE MARKET INTERVENTION pure fix 134 5.7 Solving the Small Open Economy Model The system of equations (5.9) - (5.16) can be solved more easily if it is reduced to the following system of differenced equations: " A r t + a 3Ap t + a2Ait - Ad t = 0 Apt - Ap*t - Aet + Adevt =0 Ai t - Ai* t + 0 A d e v t = 0 Apt - aApt + (1- a)Apt_i = 0 money market equilibrium (5.21) PPP with short run deviation (5.22) interest rate parity condition (5.23) price adjustment equation (5.24) In matrix form, this system can be represented as: / -1 a3 a2 0 fAIt) 0 1 0 1 Apt 0 0 1 P A i t V 0 1 0 0 J ^Adevt^ Ad, t Ap* t + Ae t Ai* t \oAp t + (1- a)Apt.jy (5.25). The matrix arrangement reveals that the endogenous variables are Ar t, Ap t, Ai t , and Adevt, while Ad t, Ap* t, Ai* t , Ap t, and Apt_j are assumed to be exogenous. Since, according to equation (5.17), APt = ( & 2 p 1 + a3) ( A d t " a 2 P A i * t + a2PAP*t> w h i c h i s clearly endogenous, the only right hand side variable requiring justification is A e^ 135 The degree of exchange market intervention can be expressed, in terms of equations (5.21) - (5.24), as Ar t Art(actual) Ar t Yt = EMP t = Art(fixed) = /3r t\ ( 5 1 ) [Ar t 1 1 [aetJ Aet] BOP t 9r t where: Ar t s ——- , and is the semi-elasticity of the balance of payments with respect to the exchange rate.8 In the analytical framework employed here, the degree of exchange market intervention is a policy instrument and as such is chosen by the policy authority. In this model exchange market pressure, measured as /3r t\ Art(fixed) = Ar { - Ae t , is fully determined by exogenous money market V v disturbances and the initial price change Ap t = aAp t + (1- a)Apt_ j , causing changes in reserves and the exchange rate to be linearly dependent. Consequently, choosing Ar t as the policy objective causes Ae t to be determined as a residual while Ar t is endogenous when Ae t is the target of government policy. For the purposes of this analysis, it is assumed that the policy authority focuses on Ae t as the object of policy choice so that, in solving the model, Ar t is treated as endogenous while Ae t appears on the right hand side as an exogenous variable. Solving the system (5.25) for Ar t using Cramer's rule yields: Ar t = -Adt + a2Ai*t + (a2? + a3)(aApt.i) + a2P(-Aet - Ap*t) = -(1 - a)Adt + (1 - ab)a2Ai* t - a2P(l - a)Ap* t + (a2P + a3)(l - a)Ap t.j - a2PAe t (5.26). 8 Substitution of Art(actual) = [BOP^actuaOl/Mj.! and Art(fixed) = [BOP^fixed)]/!^.! into equation (5.T) yields equation (5.1) in its original form. Note that EMP t is now measured as [BOPt(fixed)]/Mt.j. 136 The elasticity of the balance of payments with respect to the exchange rate is therefore given by •H = ^ = - P a2 (5-27). Since a 2 is the interest elasticity of the demand for money and therefore expected to be negative in sign, the elasticity of the balance of payments with respect to the exchange rate will be positive whenever the expectations parameter, p, is positive in sign. When this is the case, an exchange rate depreciation can be expected to improve the balance of payments. In terms of the channels of adjustment shown in Figure 5.1, a 2 and p jointly determine the degree to which the demand side of the 3i t money market responds to changes in the exchange rate. With = - p and a 2 < 0, the larger are these two parameters, the smaller is the exchange rate change required to remove a given residual money market disequilibrium and the greater is T) , the elasticity of the balance of payments with respect to the exchange rate.9 9 The elasticity of the domestic interest rate with respect to the exchange rate, 8i,/3e, = - p, is obtained by solving (5.25) for Ai,. 137 It is possible to represent the relationship between changes in reserves, exchange rates, and exchange market pressure by means of a simple diagram. Figure 5.2 Exchange Market Pressure v. The amount of exchange market pressure which corresponds to the residual disequilibrium [ m t - md_j - a 2 A i t - a 3 A p t ] shown in Figure 5.2, is measured under fully floating exchange rates by the distance OE and under perfectly fixed exchange rates by the distance OR. Equation (5.27) indicates that for the small open economy, the slope of the line RE is - pa2. Consequently, Art(fixed), - Pa2Aet(float), and [ A r a +• f$a2 A e a ] are all equivalent measures of exchange market pressure.10 1 0 This is demonstrated in Appendix 5.2. Note that all three measure exchange market pressure in terms of reserve units. That is, in terms of the percentage change in reserves, defined in this analysis as A R t / M t _ j , that would have been 138 Once the elasticity of the balance of payments with respect to the exchange rate is estimated, any observed combination of exchange rate and reserve change can be used to measure exchange market pressure over a given time period. The general definition of exchange market pressure, measured in reserve units, is therefore given by: EMPt = Art - T] Aet (5.28) 3rt where T| = measures the elasticity of the balance of payments (or reserve changes) with respect to the exchange rate.1 1 5.8 Small Open Economy with Multiple Trading Partners Up to this point the trading partners of the small open economy have been represented as a single composite designated as "the rest of the world". This commonly employed analytical convenience, however, gives rise to empirical difficulties with respect to the appropriate measurement of the world price level, p* t , and the world level of interest rates, i* t . In this section, the composite small open economy trading partner is disaggregated into individual country components. required to restore money market equilibrium under a system of perfectly fixed exchange rates. 1 1 It was pointed out in Chapter 4 that an equally valid measure is one based on exchange rate units. That is, EMP't = Tl'Art - Aet where H"13 3et/3rt. According to this definition, exchange market pressure is measured in terms of the percentage change in the exchange rate that would have occurred under a pure float. The measure of exchange market intervention corresponding to EMP't is given by: Ae, y = = l -v 1 Tl'Art - Aet 'f With reference to foonote 1, when the policy authority uses changes in domestic credit to implement exchange rate policy, the appropriate measure of exchange market pressure is given by EMPt(d) = Ad t + A r t - T | A e t and the corresponding measure of exchange market intervention by Yt(d) = [Adt + Art]/EMPt(d). 139 Extending the model in this way allows p*t and i* t to be interpreted, respectively, as measurable weighted averages of price and interest rate levels in the relevant partner countries. In the multiple trading partner model it is assumed that the small open economy trades a different good with each of the partners (i.e., there are n goods) and that in each case the world price of the good is given in terms of the trading partner's currency. It is assumed also that the relationships among the n trading partners are unaffected by the activities of the small open economy so that only the relationship between the small open economy and each of its trading partners is explicitly formulated. It is possible to incorporate these assumptions into the small open economy model by appropriately modifying equations (5.14) and (5.15). If the small open economy has n trading partners with whom different goods are traded, then for each of the n goods: P t = P*t + et - devt 2 * 2 2 A 2 P t = P*t + e t * d e v t n n n n „_x Pt = p t + \ ' d e vt (5.29). Since trade in each good constitutes some proportion, wl, of total trade, the average domestic price level is given by: n n + Pt w (5.30) 1 1 2 2 ^ pt= ptw + pt w + n z 140 where w-J is the proportion of total trade conducted with country j . Substituting (5.29) into (5.30) yields the n-country equivalent to equation (5.14): p t = Z (p*j + ej - devj) w1 (5.31). It is assumed that all bonds are perfect substitutes so that the interest parity condition becomes i t = i*J + [ E ^ p - e J ] = i*2;+ [ E ^ ) - e2] = = i*° + [ E ^ j ) - ef] = i*j + [E t(ej+ 1) -ej] for all j = 1, n. (5.32). Then it is possible to express the interest parity condition as i t = Z J i*{ + [E t (e J t + 1 ) - e{] I w>" . (5.33). When a country has a single trading partner, expectations regarding future exchange rate changes are formulated according to the rule Et( et+l)" et = "P dev t (5.16). A multiple country analog of equation (5.16) that is consistent with equations (5.31) and (5.33) is given by: n , . . n . . E J E t ( e J t + 1 ) - e J t w1 =-p_Ldev J t w J (5.34). Substituting equation (5.34) into equation (5.33) yields the expression i t = £ i*J w 1 '- p 2 devi j=l 1 j=l 1 (5.35). The multiple partner small open economy model can be represented by the following system of simultaneous equations: Art + a 3 Apt + a 2Ai t - Ad t = 0 (5.36) " " " . Ap. - £ Ap*J w3 - £ AeJ w1 + £ AdevJ w* = 0 (5.37) j=l 1 j= l 1 j= l 1 n . n . Ai, - £ i*J w1 - p £ devi w3 = 0 j=l 1 j=l 1 (5.38) Apt - aApt + (1- a)Apt_i = 0 (5.39) where Ap t is now given by Apt = 1 (a 2 p + a 3) ' A d . - a 2 p £ Ai* J, w j + a , p £ Ap*Jt j= l 1 j= l 1 (5.40). Solving the system for Ar t yields Ar, = -(1 - a)Ad, + (1 - aP)a2 £ Ai*] w3 - a2p(l - a) £ Ap*} w* j=l 1 j=l 1 + (a2p + a3)(l - a)Ap t.j - a2p £ Ae| w* (5.41). 142 The elasticity of the balance of payments with respect to the multilateral exchange rate, 2 ej w', is therefore given by j=l 1 TJ = drt f n i Z eJt w» j=l 1 (5.42). 5.9 Two Interdependent Economies The two country model differs from the small open economy model in that world prices and interest rates are no longer taken as given but are jointly determined by the exchange rate and domestic credit policies undertaken by the policy authorities in each of the two countries. From a technical point of view, the extension of the small open economy model to one that incorporates international interdependence has three main implications: 1. The payments balances of the two countries must sum to zero. This condition is imposed by means of the consistency constraint derived for the two country model in Part I. (5.43). 2. There are only three contemporaneous exogenous variables. These are domestic credit changes in each of the two countries, Ad t and Ad t, and the percentage change in the exchange rate, Aet. As in the case of the small open economy model, it is assumed that the policy authority focuses on the exchange rate 143 rather than reserve changes, so that the change in the exchange rate is the policy instrument. 3. The definition of the market clearing price change Apt (for the domestic economy) and Ap*t (for the foreign economy) is amended to give explicit recognition to the possibility of spillover effects in the two country model. Definition : The market clearing domestic price change, Apt, is defined as the change in domestic prices needed to restore equilibrium in the domestic money market after a change in the supply of domestic credit without giving rise to spillover effects in the foreign money market. Similarly, the market clearing foreign price change, Ap*t, is the change in foreign prices needed to restore foreign money market equilibrium without causing spillover effects in the domestic money market. A change in domestic prices causes spillover effects in the foreign money. market whenever the deviation from PPP caused by the domestic price change is not fully offset by the accompanying interest rate change. That is, spillover effects occur whenever Ai* t = Ai t + pAdevt £ 0. Consequently, the domestic market clearing price, Apt, must fulfill the conditions: A. a<j Ap^  + &2 A*t ~ B. AL + p Adev. = 0. 144 Since, in the absence of an exchange rate change, Adev t = Ap* t - Ap t , condition B implies that A i t = P {Ap * t - Ap t ) . Substituting this expression into A yields the algebraic definition of the domestic market clearing price change, Ap t: A p t = -^p-) < A d t + *2 P a P M < 5 4 4>-Similarly, the market clearing price change for the foreign country, A p * t , is obtained as: APV= («*3A*2P) { Ad*t + a*2P APt) (5-44*). The system of equations for the two county model is composed of equations (5.9) - (5.16), (5.43), (5.44), (5.44*), and the foreign country equivalents of equations (5.9) -(5.13). The two country model, expressed in terms of differenced equations, is given by: M M A r t + E l . 1 M * t . 1 A r * t =0 (5.43) - Art + a3Ap t + a 2Ai t - Ad t =0 (5.21) - Ar* t + a 3*Ap* t + a 2*Ai* t - Ad* t =0 (5.21*) Ap t - Ap* t - Aet + Adevt =0 (5.22) Ai t - Ai* t + pAdevt =0 (5.23) Apt - aApt + (1- a)Apt_! (5.24) Ap* t - a *Ap* t + (1- a*)Ap* t _! A p t - ^-fi {Ad t + a 2 | 3 A p M = 0 = 0 Ap { Ad* t + a*2 P Ap t) = 0 ;t (a*3+a*2P) Substitution of (5.44) into (5.24) and (5.44*) into (5.24*) yields: A p t = (a3+a2W { A d t + & 2 P A p * t } + ( 1 - a ) A P t - l = 0  A p*t = ( a * 3 + ! a * 2 P) { A d *t + a*2P A P t ) + ( 1 - a^ApVj = 0 In matrix form, this system can be represented as: 145 (5.24*) (5.44) (5.44*). (5.45) (5.45*). where: A = 1 0 0 0 ^ 0 0 0 a 3* a 2* 0 -1 0 1 0 - 1 p A 0 0 1 0  0 j (.3 +2a2P) ' A * " (as* lK£» ' U ^ P ) { ^ } + f M t-1 0 0 E t - l M * t 1 a 3 a 2 o 0 0 0 -1 0 1 0 0 0 0 1 0 0 1 0 0 I 0 A* 0 0 Ap t Aij A r * t Ap* t A i * t ^Adev ty a Ad, •t Ad* Ae. t V D * J (5.46). a ™ d D V l s ( a 3 * + a 2 * P ) { A d *t > + a-«*)AP*t-l-Solving the system for Ar, yields: 146 Ar, E M M V i a2(l -AA*)Ad* t + a2(a3* + a2*p)(A*D t - D*t) +a2*(a3 + a2P)(Dt - AD* t) + a2*(l - AA*)Ad t + »232*P(1 - AA*)Aet. - (1 - AA*)(a 2 M t . 1 + a 2 * E t _ 1 M * M ) (5.47). The elasticity of the balance of payments with respect to the exchange rate for the two country model is then obtained as Tl = drt - E t_ 1M* t . 1Pa2a2* det ~ a 2 M t . ! + a2*E t_jM* t_ 1 (5.48). 5.10 Interdependence with Multiple Trading Partners The two country model can be extended to encompass the case in which the domestic economy has many trading partners. As in the extension of the small open economy model, it is assumed that the domestic economy trades a different good with each of the n trading partners and that all bonds are perfect substitutes. These assumptions lead to a purchasing power parity equation of the form Ap, - £ Ap*} - £ Ae} v? + Z Adev} w1 = 0 j=l 1 j=l 1 j=l 1 (5.37) 147 and an interest rate parity equation given by n . . n . . Ai. - £ i*] w1 - p £ dev] w1 = 0 (5.38). j=l 1 j=l 1 In order to keep the system of equations down to a manageable size, only the direct interrelationship between the domestic economy and its trading partners is modeled explicitly. That is, second order effects are ignored under the assumption that they are relatively small. The system of equations that describes a world composed of a domestic economy and its n trading partners is then given by: M M A r t + £ EJ.jMJ.jAr*! = 0 (5.49) -Ar t + a 3 Apt + a 2Ai t - Adt = 0 (5.36) n . • n . . . n . . . n • . . £ Ar*] + £ a*Ap*] w1 - £ aiAi*] w1 - £ Ad] w3 = 0 (5.50) j = l 1 j = l j 1 j = l ^ 1 j - i ~ • • n . . •, n n . Ap. - £ Ap*] w3 - £ Ae] w* + £ Adev] w3 = 0 (5.37) j=l 1 j=l 1 j=l 1 Ai. - £ i*] w1 - p £ dev] w> = 0 (5.38) j=l 1 j - i 1 Apt - aAp t - (1- a)Ap t.j = 0 (5.39) Z Ap*] J - Z r^Ap, w1 - Z (1- o,)Ap*J , w3 = 0 j=l 1 j = l j = l W 148 (551) Ap. -1 (a3+a2p) { Ad. + a? p Z Ap*} w1} = 0 j = l 1 (5.52) Z Ap*. w1 j = l 1 Z a*iwJ+p Z a*J~wJ j=l 3 j=l • V { Z Ad*JwJ + p Apt Z a*iwJ)} j = l 1 lj = l 2 = 0 (5.53). This system can be solved for Ar t to yield the elasticity of the balance of payments with respect to the trade weighted exchange rate: T) = lt Z eJt wJ j = l l - a 2 P( E ^ . j M j . j a ^ w J ) a 2 M t - i + J (5.54). 5.11 Conclusion This chapter has focused on establishing a systematic relationship between exchange rate and reserve changes so that changes observed concurrently in these variables can be jointly interpreted in terms of a composite measure of money market disequilibrium. The ultimate aim is to provide a quantitative measure of exchange rate policy that can be used to classify exchange rate policies and test empirically the recent theoretical propositions concerning the determinants of exchange rate policy in the absence of a formal international monetary agreement. 149 To this end, exchange rate policy is measured in terms of an intervention index which is defined as the proportion of money market disequilibrium removed by the intervention activities of the policy authority. Money market disequilibrium itself, is measured on the basis of observed exchange rate and reserve changes. The relationship between observed changes in these two channels of money market adjustment is derived for both the small open economy as well as interdependent economies and is used to obtain quantitative indicators of money market disequilibrium and exchange rate policy. Measures of exchange market pressure and the degree of exchange market intervention over the period 1973(1) - 1984(IV) are calculated for Canada, Germany, Japan, U.K., and U.S.A. in the following chapter. Appendix 5.1 150 The objective of this appendix is to show that equation (5.16) represents an expectation formation process that is consistent with the assumption that uncovered interest parity holds and the empirical evidence that the forward rate is not an unbiased predictor of future spot rates. The rationale presented here is based on the regime switching model with stochastic bubbles developed by van Norden ( 1 9 8 9 ) . The argument, in brief, runs as follows: Under rational expectations, the uncovered interest parity condition can lead to multiple short-run equilibria. If the economy moves stochastically between these solutions, rational agents will assign probabilities to the various expected outcomes so that the expected future exchange rate is a probability-weighted average of expected outcomes. When the information available to agents is incomplete, uncovered interest parity may hold even though the forward exchange rate, established by the arbitrage acitivities of risk neutral agents, is not an unbiased predictor of the future spot rate. For simplicity it is assumed that there are only two possible equilibria, one of which is characterized by fixed exchange rates. Investors know that at each time t, there is a probalility of ftt+i that the exchange rate will remain fixed so that e t +j = e^ . However, if the exchange rate does not remain fixed, then the expected value of next period's spot rate is et - | l t + j . The true expected value of next period's exchange rate, A e l + j is therefore A et+l The analysis of Chapter 5 assumes that agents do not know the form of the policy authority's objective function but are aware of the possibility of multiple equilibria. Faced with an incomplete information set, rational agents assign the subjective probabilities p t + i and (1 - p t + j ) to the alternative outcomes et and (e^  - | i . t + j ) , respectively. The conditional expectation of next period's exchange rate is therefore given by: = JCt+1(et) + (l-rc t +i)(e t-H t + 1) (5.1.1). 151 E(et+1IIt) = p t+1(e t) + (l-p t + 1)(e t-p: t + 1) (5.1.2) where E(e t+1II t) indicates that expectations of future spot rates are conditional on all currently available information contained in the information set It. As agents act on their expectations, competitive speculative activity will ensure that the forward rate, ft, reflects expectations regarding the future exchange rate so that E(e t + j IIt) =-fj. In the context of this analysis, the forward rate, ft, is an unbiased predictor of A the true spot rate. e t +j when (e^j - ft) = 0. Subtracting equation (5.1.2) from (5.1.1) above yields e t + 1 - ft = (7C t + 1-p t + 1)p: t + 1 (5.1.3). Since P-t+i 1 S non-zero by assumption, the forward rate will not be an unbiased predictor of the spot rate unless = Pt+1-If it is now assumed that P t + 1 is a linear function of the observed deviation from PPP such that p- t +j = a(pt - p*t - e^ , then equation (5.1.1) yields E(et+1IIt) - et = - (1-p t + 1) a(pt - p*t - et) (5.1.4) from which equation (5.16) can be obtained directly as E(e t +j) - e^  = - P(devt) with E(e t + 1) - E(et+1IIt), p s (1- p t +i)a and devt - pt - p*t - ^. Appendix 5.2 152 It is relatively easy to verify that Art(fixed) = - Pa2 e^float). Under fully floating exchange rates, Ar t = 0 so that the system (5.21) becomes: - 1 1 0 1 o o 1 p V 0 1 0 0 ( A e t > Apt Ai t ^ Adevt Adt Ap* t Ai*, \ y aAp t + ( 1 - a ) A p t . j J (5.25'). Solving the system for Ae t yields: Aet = - Pa2 '{- Ad t +. (a3 + a2p)[ aApt + (1 - a)Ap t.j ] - a2pAp* t + a2i* t) Under fully fixed exchange rates, Aet = 0 so that the system becomes: f Adt \ 0 1 0 1 0 0 i p V o i o o f Ar t Apt Ai t Adevt J t Ap*, Ai*, ^ aAp t + ( 1 - a ) A p t . ! J Solving this system for Ar t results in: Art = - Ad t + (a3 + a2p)[ <xApt + (1 - a)Ap t.j ] - a2pAp* t + a 2i* t. It is immediately clear that Art(fixed) = - Pa2 Aet(float). (5.25"). CHAPTER 6 ESTIMATION AND TESTING: A PRELIMINARY EXPLORATION 6.1 Introduction The degree of exchange market intervention can be defined as the proportion of exchange market pressure that is alleviated by a change in the domestic money supply, either through reserve flows or an equivalent change in domestic credit. Under systems of managed floating, changes in reserves and exchange rates jointly reflect the magnitude of exchange market pressure, creating an aggregation problem. One solution to this problem lies in the estimation of the elasticity of the balance of payments with respect to the exchange rate. Unfortunately, the measurement of the required elasticity is not a matter of simple calculation. The main difficulty, from the point of view of obtaining a quantitative measure of exchange rate policy, is that any measure of this sort is likely to be model-specific. Since the true relationship between reserve and exchange rate changes is not known, it must be derived and estimated on the basis of a theoretical model of economic adjustment. The characteristics of the resulting elasticity measure may vary considerably, depending on the assumptions made about the nature of the adjustment process. Just how sensitive the elasticity is to alternative specifications is something that can only be discovered by employing a variety of alternative models to measure it. 153 154 In this chapter, the multiple partner elasticities derived in Chapter 5 are estimated as a first step in the process of obtaining an elasticity measure that is robust across a variety of model specifications. The primary objective is to provide a set of elasticity estimates that can be used as a basis of comparison in future empirical work. With this in mind, the results of a limited number of preliminary estimations, in which a variety of estimation techniques and parameter restrictions were employed, are reported and briefly discussed. The elasticities of the balance of payments with respect to the exchange rate for Canada, Germany, Japan, the United Kingdom and the United States are then estimated over the period 1973(I)-1984(IV) using two stage least squares. Based on these estimates, exchange market pressure and the degree of exchange market intervention are calculated for each country, and presented graphically. For purposes of comparison, intervention indices consistent with the Girton-Roper measure of exchange market pressure and the Holden, Holden, and Suss flexibility index are also calculated. 6.2 Preliminary Estimation In this section, the multiple-partner small open economy model is used to develop a system of equations suitable for estimating the parameters needed to measure Tl , the elasticity of the balance of payments with respect to the exchange rate. In order to provide some insight into the potential sensitivity of these estimates to changes in the structure of the underlying model and the method of estimation, preliminary estimations were undertaken using a variety of methods of estimation and parameter restrictions. A representative sample of the results obtained are summarized in Tables 6.1 and 6.2. 155 The small open economy model introduced in Chapter 5 (section 5.2) can be represented by the the following four equation system:1 m t = ao + a l v t + a2*t + a3Pt p t = p*t + ej - devt i t =i* t -pdev t p t = apt + (l-a)pt_1 where: I n n ^ t = (a2p + a3) ( A d t " a2PA i*t + a2PAP*t>. - P * f 2 p*{ w>, i*t = .Z •!*{ w1, and n e t = Z e] w3 with p*t, i* t , e. and Ad. exogenous. j = l 1 In Chapter 5, the coefficients a 2 and P were found to determine the elasticity of the balance of payments with respect to the exchange rate in the small open economy. In order to estimate these coefficients on the basis of equations (6.1) - (6.4) above, the variables in the system are measured, wherever possible, as:2 m = Ml money supply y = real GNP i = domestic nominal interest rate on 3-month treasury bills, expressed annually p = domestic consumer price index 1 Equation (6.1) is obtained by by substituting (5.12) into (5.9) and setting yt = y t.j. Substitution of (5.16) into (5.15) results in equation (6.3). Equations (6.2) and (6.4) are obtained directly from equations (5.14) and (5.13), respectively. 2 The trade weights, w3, calculated for each country are given in Appendix 6.1. Variables are identified by IFS source code in Appendix 6.2. Owing to the absence of quarterly interest rate data for Saudi Arabia, i * t for Japan is measured as the weighted average of interest rates prevailing in the economies of the remaining two largest trading partners, U.S.A. and Australia. (61) (6.2) (6.3) (6.4) 156 p* = £ p*3 v? = weighted average of the CPIs of three largest trading j = l partners n i* = £ i*3 W* = weighted average of 3-month treasury bill rates of j = l three largest trading partners = total trade (imports + exports) conducted with country j expressed as a proportion of total trade with the three largest trading partners over the period 1973 - 1984 d = domestic credit n . . e = E w* = MERM effective exchange rate index. j = l Data source: IMF International Financial Statistics. Estimation procedures are essentially processes of inference in which specified systematic relationships between variables are quantified on the basis of their observed values. A common problem in empirical work of this sort arises when the variables in a model cannot be measured in a way that strictly satisfies their conceptual definitions causing the relationships that are actually being estimated to differ from the ones specified by the model. In the presence of this type of measurement error, some of the parameter restrictions implied by the conceptual model, may not be appropriate for estimation purposes. In the theoretical analysis developed in Chapter 5, the systematic relationship between domestic and foreign prices and the exchange rate, which in this chapter is described by equation (6.2), depends on the assumption that all goods are freely traded. The theoretical analysis also assumes that multilateral foreign price and exchange rate levels can be measured accurately. In practice, neither of these conditions is likely to be fulfilled. In the first place, many goods are not freely traded so that the consumer price indices used to measure domestic and foreign price , 157 levels may have a significant non-traded component. Secondly, practical considerations make it necessary to limit the number of trading partners included in the calculation of composite foreign price and exchange rate levels. In this analysis, the number of trading partners is limited to three. The extent to which the three country composite is representative of the average foreign price that is of importance to the domestic economy depends on the proportion of total trade conducted with the three largest partners as well as the extent to which movements in their consumer price indices reflect changes in the average price of traded goods. The final point is concerned with the measurement of a multilateral exchange rate. The main problem with obtaining such a measure is that bilateral exchange rates are non-commensurate. This means that multilateral exchange rates cannot be measured simply as a weighted average of bilateral exchange rates. The MERM effective exchange rate index, employed in this analysis, provides a solution to this problem but also introduces an additional source of measurement error because it differs from n . the conceptual multilateral exchange rate variable, £ w*.3 j = l In the theoretical model, the absence of measurement error and the assumption that all goods are freely traded allows the relationship between domestic and foreign price levels to be described in equation (6.2) as p t = p*t + et - devt. Given the various sources of measurement error and the fact that non-traded goods may exist in significant proportions, the relationship between domestic and foreign prices is more appropriately estimated as: p t= do + dip* t + d2et - devt (6.2*). For similar reasons, the interest parity equation, (6.3), is better described for estimation purposes as: 3 The precise definition of this exchange rate index is given in Appendix 6.2. 158 i t = Po + Pl i* t + P2dcvt (6.3'). Substitution of (6.3') into (6.2') yields the system of estimation equations' A m t = a 0 + a 1y t + a 2 i t + a 3p t (6.5) Pt= bo + blP*t + b2 et + b3H + b4!*t Pt = co + c l A d t + °2 A i *t + c3AP*t + c4Pt-l (6.6) (6.7) where: b o s do-(Po/P2)> b l s d 1- b2 s d2> b3 s -0#2>' b4 E <P l/?2> = co B "o-ci = a i / (a 3 - p 2 a 2 ) , c 2 = - a i a 2 P i / ( a 3 - p 2 a 2 X c 3 - a i a 2 P 2 d i ( a 3 - p 2 a 2 ) , and C4 H ( a 2 - ap. The parameter values required to calculate the small open economy elasticity separately, and equation (6.6), in which b 3 = -(1/P2) = -(1/P)- One of the objectives of this study is to offer some insight into the sensitivity of the elasticity measure to the specification of the underlying model. One way to do this, without having to formulate a complete set of alternative estimation equations, is to apply a variety of estimation techniques and parameter restrictions to equations (6.6) and (6.5). The estimates of a 2 and p obtained using unrestricted 2SLS and 3SLS, restricted 2SLS and 3SLS, and non-linear maximum likelihood estimation (NL) are reported in Tables 6.1 and 6.2 along with selected summary statistics. Ordinary least squares estimation could not be employed because equations (6.6) and (6.7) each have at least one 4 Equation (6.7) is obtained by deriving the analog of equation (5.17) using (6.2') and (6.3') and substituting the resulting expression into the modified version of (6.4), given by: pt = a 0 + a i p t + a2Pt-i- Note that when, as in equation (6.4), ct0= 0 and t*2= (1 - oq) = (1 - a), c0= 0 and C4= 1. 159 endogenous explanatory variable. What follows is a brief description of the restrictions imposed to obtain the reported results. Estimates of &2 m& P under the column heading 2SLS were obtained using unrestricted 2SLS estimation of equations (6.5) and (6.6), respectively. The estimates of P found in column 2 of Table 6.2 under the heading 2SLS-R were obtained by setting p0= 0 and P i = 1 which imposes the restriction b 3 = - b4 = - (1/p) and the cross equation restriction b0= do on equation (6.6). The 3SLS estimates of a 2 m& P reported in columns 2 and 3 of Tables 6.1 and 6.2, respectively, were obtained on the basis of 3SLS estimation of equations (6.5) - (6.7) in which the only parameter restriction was c 4 = l . 5 As with the 2SLS-R estimate of p, the restricted 3SLS estimates (3SLS-Ri), reported in columns 3 and 4 in Tables 6.1 and 6.2 respectively, were obtained by setting p0= 0 and Pi= 1. 3SLS estimation incorporating, in addition to the restrictions Po= 0 and Pi= 1 and cA = 1, the requirement that c 2 = - c3 in equation (6.7) yields the 3SLS-R2 estimates of &2 P- The maximum likelihood estimates (NL) were obtained on the basis of equations (6.2'), (6.3), (6.4) and (6.6) and therefore incorporate all of the primary assumptions of the theoretical model in the form of the parameter restrictions: b3 = - b 4 = -(1/p), cQ = 0, cj = aj/(a2 - P2a3)» 2^ = * «i>2Pl^ a2 " P2a3^« c3 = " a l a 2 P 2 d l ^ a 2 " P2a3^' c4 = 1, where p 2 = p and a 2=l-oij. The estimation procedures described above were undertaken for Canada, Germany, Japan, U.K., and U.S.A. over the period 1973 - 1984 using quarterly data. The estimated values of the interest elasticity of the demand for money, s^ , obtained for each country are reported in Table 6.1. The summary statistics provided are the t-statistic (t) associated with the parameter estimate, a Durbin-Watson statistic (DW), and a measure of the degree to which the variables shown on the right hand side of 5 This restriction was imposed in order to avoid problems associated with undertaking 3SLS estimation in the presence of a lagged dependent variable. Equation (6.7) was therefore actually estimated as: Apt = cD + CjAdt + C2Ai*t + C3Ap*t (6.7'). 160 equation (6.5) explain movements in the dependent variable, Ml. In the case of the 2SLS and 3SLS, the reported measure of goodness of fit is R 2. For the non-linear estimations a likelihood ratio test of the hypothesis that all coefficients are equal to 0 was undertaken to provide a measure of overall explanatory power. Since the likelihood ratio statistic reported in Table 6.1 follows a Chi-square distribution with 6 degrees of freedom, the degrees of freedom being determined by the number of coefficients estimated, a measure of the goodness of fit can be obtained for the NL system by comparing the reported LR value to a chi-square statistic having 6 degrees of freedom. The chi-square statistic that is relevant at the 1% level of significance is X2= 16.8119. The results reported in Table 6.1 show that, with the exception of Canada, the estimated equations appear to fit the data extremely well. Germany, Japan, U.K., and U.S.A. all have R 2 values between 0.9729 and 0.9797 as well as significant LR statistics. All of the coefficient estimates obtained for these four countries have the expected negative sign. The t-statistics indicate that for Germany and the U.K., all of the estimated coefficients are statistically significant while only the non-linear estimate is not significant for the United States. Although the coefficient estimates obtained on the basis of single equation methods do not vary much for Japan, only the 2SLS coefficient is statistically significant. For all four countries, the magnitudes of significant coefficient estimates fall within a reasonable range of the values obtained in other studies.6 6 See, for example, Fair (1987) and Hoffman and Schlagenhauf (1982). Some preliminary estimation of equation (6.5) was undertaken using a Goldfeld-Chow specification as well as a rational lag structure. In common with other studies that have employed these specifications, the initial estimates showed, in the case of the Goldfeld-Chow specification, a coefficient of money market adjustment that was too small to be plausible and, in the case of the rational lag specification, coefficient signs that alternated over time in a manner that could not be explained on theoretical grounds. 161 By contrast, the estimation results obtained for Canada are quite poor. Although the R 2 values lie within an acceptable range, the lowest being 0.6680 and the highest 0.7261, none of the coefficient estimates are statistically significant and the 2SLS estimate is not of the correct sign. In addition to this, the fact that the highest Durbin-Watson statistic is 0.40S1 suggests that the estimated model is not very well suited to the Canadian data. It should be pointed out, however, that the Durbin-Watson statistics for the U.K. and U.S.A. are also low, indicating that there may be some model misspecification for these countries also. The likelihood ratio tests of the restrictions, reported in the row labled LRT, confirm that the results obtained are relatively insensitive to the structural assumptions imposed by the various estimation procedures. Table 6.2 indicates that the estimation results associated with equation (6.6) are less promising than those obtained for Germany, Japan, U.K. on the basis of equation (6.S). Although all countries have significant LR statistics and R 2 values within the range 0.9110 - 0.9973, only nine of the twenty-five coefficients estimated are significantly different from zero.7 Significant coefficient estimates are obtained for Germany, using 2SLS, and for the U.K., using 3SLS. For the remaining countries, both 2SLS and 3SLS yield significant estimates of p\ The U.S.A. is the only country for which the NL estimate is significant. Estimation of equation (6.6) using 2SLS-R, 3SLSRi, and 3SLS-R2 was unproductive of significant estimates of |3 for all countries in the sample. Evidence of model misspecification is provided by the Durbin-Watson statistic which, for all countries except Germany, falls within the range 0.7044 - 0.0770. The low Durbin-Watson statistics also suggest the R 2 values and t-statistics are likely to be 7 It should be noted that the estimates of P do not fall in the interval [0,1] which the analysis of Chapter 5 suggests is the appropriate range for this coefficient. The justification for magnitudes of f? outside the [0,1] range is provided in the following section. 162 overestimated. Unlike the estimates of a2 presented in Table 6.1, the estimates of P obtained for all countries except Japan appear to be sensitive to the restrictions imposed under 2SLS-R, 3SLS-Ri, 3SLS-R2 and NL estimation. The restrictions imposed by these procedures produce sign changes in the estimates obtained for Germany, U.K., and U.S.A. as well as a significant change in magnitude for Canada. The results of the likelihood ratio tests of these restrictions indicate that they are not valid for Canada, Germany, Japan, and the United States. It is interesting that 3SLS estimation is also rejected for Germany although this is the only estimation procedure that yields a statistically significant p estimate for that country. Table 6.1 Small Open Economy A a2 2SLS 3SLS 3SLS-Ri 3SLS-R2 NL Canada A DW R 2 /LR LRT 0.00693 (0.0437) 0.3903 0.7261 -0.03534 (-0.22442) 0.4051 0.7208 0.8367 -0.20090 (-1.3316) 0.3475 0.6680 8.9582 -0.18301 (-1.2113) 0.3409 0.6695 8.7452 -0.00053 (-0.38512) 0.3996 504.84 0.0000 Germany a 2 t DW R 2 /LR LRT -0.14578 (-7.9370) 1.8194 0.9742 -0.14761 (-8.1024) 1.7840 0.9739 4.9354 -0.14859 (-8.1568) 1.7722 0.9737 5.3058 -0.15429 (-8.6199) 1.7069 0.9730 7.7498 -0.08422 (-5.1045) 1.3221 542.50 9.0210 Japan A a2 t DW R 2 /LR LRT -0.04908 (-2.0430) 1.6310 0.9754 -0.04407 (-1.8546) 1.6189 0.9751 0.5830 -0.03142 (-1.3451) 1.5156 0.9729 4.5395 -0.03688 (-1.5634) 1.5171 0.9733 4.2725 -0.00675 (-0.6452) 1.2142 622.33 10.9766 U.K. A a2 t DW R 2 /LR LRT -0.17100 (-3.0041) 0.5510 0.9792 -0.17176 (-3.0215) 0.5189 0.9791 0.3822 -0.11433 (-2.4721) 0.4732 0.9799 0.0000 -0.09821 (-2.1376) 0.4528 0.9797 0.0000 -0.08001 (-3.1766) 0.3695 603.54 5.0470 U.S.A. A a2 t DW R 2 /LR LRT -0.11294 (-4.6080) 0.7786 0.9784 -0.11140 (-4.5518) 0.7863 0.9779 1.0662 -0.15269 (-6.6006) 0.7271 0.9732 10.2174 -0.13989 (-6.1852) 0.7457 0.9752 6.5336 -0.00762 (-1.1189) 0.5885 621.73 15.4778 2 * 01 6.6349 7.3776 15.0863 18.4753 Canada p t DW R 2 / L R LRT A Germany p t DW R 2 / L R LRT A Japan P t DW R 2 / L R LRT U.K. P t DW R 2 / L R LRT U.S.A. p t DW R 2 / L R LRT 2 5C.01 164 Table 6.2 Small Open Economy A 3SLS 3SLS-Ri 3SLS-R2 NL 2SLS 9.5657 (2.8901) 0.6748 0.9973 60.4961 (1.3018) 1.6009 0.9895 4.8400 (2.0903) 0.5187 0.9764 -3.5898 (-2.3078) 0.5004 0.9758 -13.9540 (-4.1518) 0.7044 0.9971 2SLS-R 28.6599 (1.1337) 0.1616 0.9944 35.5059 -126.8681 (-0.56728) 1.1245 0.9871 9.6926 4.6026 (1.8533) 0.3122 0.8958 70.4951 7.0492 (1.8502) 0.2439 0.9830 6.1349 28.8717 (1.0875) 0.0876 0.9898 59.3637 6.6349 8.4090 (3.3950) 0.6931 0.9970 4.4796 15.8909 (2.3808) I. 4032 0.9866 I I . 3346 4.7865 (2.1142) 0.5252 0.9760 0.7144 -7.9611 (-1.2486) 0.3074 0.9841 0.8063 -14.7223 (-3.9961) 0.6031 0.9970 1.5081 6.6349 29.7300 (1.1488) 0.9941 37.4828 1.0193 0.9854 15.2685 5.7097 (1.5752) 0.2473 0.9116 62.1842 24.3605 (0.7328) 0.1374 0.9846 1.6040 35.8140 (0.9021) 0.0787 0.9893 61.7120 9.2103 26.8075 (1.2677) 0.9940 38.7362 0.9978 0.9849 17.9358 5.9952 (1.5244) 0.2266 0.9110 62.3755 25.9848 (0.6857) 0.1414 0.9846 1.8467 41.9674 (0.7636) 0.0770 0.9896 60.4586 15.0863 -81.600 (-0.7301) 0.1435 504.84 20.6907 2703.8 (0.0444) 0.7525 542.50 91.2127 -31.4580 (-0.9594) 0.1236 622.33 0.8661 9.87xl0 1 5 (0.0000) 0.3695 603.54 22.5076 18.103 (2.4678) 0.1152 621.73 86.8018 16.8119 0.1300 0.1309 -58.4727 -50.5000 (-1.2615) (-1.4832) 165 6.3 Small Open Economy Estimation It was pointed out in Chapter 4 that the Girton-Roper measure of exchange market pressure is model-specific. In this study, the Girton-Roper measure is generalized. In the generalized measure of exchange market pressure, the elasticity of the balance of payments with respect to the exchange rate is used to make observed exchange rate changes commensurate with observed changes in reserves thereby allowing exchange market pressure to be measured in a manner consistent with any chosen model of external adjustment. On the basis of the model presented in Chapter 5, the components of the required elasticity were found to be the interest elasticity of the demand for money, &2> and the expectations parameter, p. The primary objective of this section is to obtain reliable estimates of the elasticity, T|, m order to gain some insight into the sensitivity of the exchange market pressure measure to changes in the weights assigned to its components. The Durbin-Watson statistics reported in Tables 6.1 and 6.2, indicate that there is a significant degree of model misspecification associated with both equations (6.5) and (6.6). Although the Durbin-Watson test is designed to test for first order serial correlation, it can also pick up the effects of other forms of model misspecification such as, for example, the failure to allow for the possibility of structural shifts in the data. If the only problem is the presence of serial correlation then the coefficient estimates will be unbiased but inefficient causing the t-statistics in Tables 6.1 and 6.2 to be overstated. This, of course, makes it difficult to evaluate the results obtained. If the source of misspecification captured by the Durbin-Watson statistic is structural instability of the underlying equation, the problem is more serious because the parameter estimates will not be unbiased estimates of the true coefficient values. Under these circumstances, one reasonable way to proceed is to begin by assuming that the problem is first order serial correlation and correct for the serial correlation using an approved method. Since, in the absence of structural 166 misspecification, the serial correlation correction should leave the parameter estimates unaffected, changes in the values of the estimated coefficients provide evidence of the possibility of structural instability. In those cases where structural instability is suspected, dummy variables can then be used to improve estimation results. This is, in fact the procedure that is adopted in this section. The decision to estimate equations (6.5) and (6.6) using 2SLS rather than one of the alternative procedures was based on a number of considerations. The first of these was that the procedure employed should be appropriate for as many countries as possible. The results of the likelihood ratio tests of the restrictions, reported in Table 6.2 indicate that the restriction imposed by 3SLS, 3SLS-Ri and NL are rejected by at least one country, leaving 2SLS and 3SLS-R2 as procedures that could be applied to all countries to estimate equation (6.5). The results reported in Table 6.2 show that all of the alternatives to 2SLS estimation are rejected on the basis of the LRT statistic, making 2SLS the method of choice for equation (6.6). Given the possibility of significant serial correlation for four of the five countries, 2SLS estimation also the preferred method of estimating equation (6.5) since it is not possible to correct for autocorrelation in 3SLS estimation. The initial estimates of a2 and P for the period 1973(1) - 1984(IV), reported in Table 6.3, were obtained by 2SLS using the exogenous variables y t.i. P*f P*t-1' e f 'i*t» '*t-l> m ^ A d t ^ instruments for i t and pt in the first stage regressions, and the standard second stage transformation to correct for first order autocorrelation.8 Hereafter, estimations in which a correction for first order autocorrelation has been undertaken are referred to as 2SLS-A. 8 The Cochrane-Orcutt procedure was employed to estimate the first order serial correlation coefficient. All estimations were accomplished using Shazam version 6.1. 167 Table 6.3 Estimates of a2 and P using 2SLS-A Canada Germany Japan U . K . U . S . A . A a2 A Pa R2 -0.12019 -0.14497 -0.02391 -0.25662 -0.17285 (-0.5246) (-7.8378) (-0.49178) (-3.8528) (-4.8612) 0.87333 (12.2011) 0.6142 0.06201 (0.4260) 0.9742 0.51023 (4.0673) 0.9711 0.60404 (5.1962) 0.9717 0.75185 (7.8176) 0.9682 Pp t R2 28.5185 (2.3083) 0.98080 (34.4808) 0.9922 54.6807 (1.5941) -0.97523 (-0.5172) 0.9891 13.9723 (2.0641) 0.94178 (19.2020) 0.9628 1043.7324 (0.0366) 0.98637 (41.0903) 0.9628 115.3908 (0.61916) 0.99400 (62.3088) 0.9666 The t-statistics indicate that the the estimated auto-correlation coefficients, p a and p p .are significant for all countries except Germany. It is also apparent from the relatively minor reductions in the R 2 values obtained, that the correction for first order serial correlation does not significantly reduce the explanatory power of equations (6.5) and (6.6). A comparison of the results reported in Table 6.3 with those for 2SLS estimation in Tables 6.1 and 6.2, shows that the correction for first order serial correlation has caused substantial changes in the estimates of a 2 and p obtained for all countries except Germany. In addition to the significant changes in 168 magnitude common to all four countries, the P estimates for U.K. and U.S.A. exhibit a change in sign. The t-statistics indicate that although the magnitudes of the P coefficients estimated for U.K. and U.S.A. using 2SLS-A are very large as compared to the 2SLS estimates, they are not significantly different from zero. It is interesting A that the 2SLS-A estimate of p Canada is very close to the value obtained for 2SLS-R estimation which, according to the likelihood ratio test, was found to impose an invalid restriction on the estimation of equation (6.6). With respect to a 2, Table 6.3 shows that the 5% increase in the magnitudes of the parameter estimates obtained for U.K. and U.S.A. are supported by improved t-statistics. Canada's a 2 estimate is also improved by the correction for autocorrelation in the sense that the coefficient, although still not statistically significant, now has the expected sign. Table 6.3 shows that Germany is the only country for which the estimated magnitudes of a 2 and p are not significantly affected by the correction for serial correlation. All other countries show substantial changes in their parameter estimates. In addition, the estimates of a 2 obtained for Canada and Japan and the estimates of P obtained for Germany, U.K., and U.S.A. using 2SLS-A are not significantly different from zero. One possible explanation for this is that there were structural shifts over the estimation period which are not reflected in equations (6.5) and (6.6), causing one or both of these equations to be misspecified. In the context of this study, there are two reasons to be concerned with the possibility of structural instability. The first of these arises as a result of the characteristics of the model being estimated. Specifically, since the structural parameters a 2 and p are not derived within an optimizing framework, they cannot be assumed to be policy invariant.9 The second source of concern has to do with the fact that in the estimates of a 2 required to calculate the elasticity Tj must be obtained on 9 The reasons for choosing this type of model were discussed in the previous chapter (see section 5.5). Lucas (1976) discusses the problem of structural instability in models of this sort. 169 the basis of equation (6.5), which is a money demand equation. The instability of demand for money functions arising from financial innovations is by now well documented.10 Although the model employed in this study cannot be estimated to recover policy invariant parameters, it is possible to use dummy variables in the estimation equations in order to reflect structural shifts in the parameter estimates over time. The t-statistics associated with the dummy coefficients reflect the significance of any observed shifts and provide and indirect test parameter stability. The Chow test, which is a direct test of parameter stability, is not valid when 2SLS estimation is employed.11 While the inclusion of dummy variables in the estimation equation does not identify the source of the shift, this method does provide more stable parameter estimates. Since the number of observations (48) on each variable is relatively small in this study, it is reasonable split the sample period into two equal sub-periods in order to test for parameter instability. With the number of sub-samples limited to two, the introduction of slope and intercept dummies into equations (6.5) and (6.6) results in the estimation equations : mt = (a0+Da0) + (a1+Da1)yt + (a2+Da2)it + (a3+Da3)pt (6.5*) pt = (b0+Db0) + (b1+Db1)p*t + (b2+Db2)et + (b3+Db3)it + (b4+Db4)i*t (6.6') where D = 0 over the period 1973(1) - 1978(TV) and D = 1 from 1979(1) - 19840V). 1 0 Judd and Scadding (1982) and Laidler (1985), among others, have surveyed the empirical research on the demand for money. See also Cockerline, Helliwell and Lafrance (1988). 1 1 It is possible to get negative F statistics when applying the Chow test to 2SLS parameter estimates. 170 Initial 2SLS estimation of equations (6.5') and (6.6') included all dummy variables. Based on the results obtained, dummy variables with coefficients not significantly different from zero were eliminated one at a time, beginning with the lowest t-statistic. Dummy variables were included as instruments in the first stage regression when their inclusion improved the Durbin-Watson statistic. Any serial correlation remaining after the final iteration was removed using 2SLS-A. The estimates of a2 and p obtained by this method and the associated elasticity, T|, are reported in Table 6.4. Estimates of a2 for Germany, and P for Japan and U.S.A. were obtained by 2SLS as the estimated correlation coefficient associated with 2SLS-A was not significantly different from zero.12 The remaining estimates are the result of 2SLS-A estimation of equations (6.5') and (6.6'). Dummy variables were included as instruments in estimating a2 for Japan and p for all countries except Canada. Results of the final iteration are reported fully in Appendix 6.3. The results reported in Table 6.4 indicate that the interest rate coefficient, a2, has the expected sign for all countries but is not found to be significantly different from zero for Canada, over the period 1979(1) -1984(IV), and for the United States, over the period 1973(1) - 1978(IV).13 The results also show that for these two countries there were significant changes in the elasticity of the demand for money over the sample period. The value of the expectations parameter, p, is stable and statistically significant for Canada, Germany and U.S.A. over the entire sample period. For the U.K. the coefficient estimate is stable but not statistically significant over the sample period. For Japan, only the p estimate pertaining to the first sub-1 2 Although for Japan, the estimated correlation coefficient was not found to differ significantly from zero, 2SLS-A estimates of a 2 were used to obtain T| because the t-statistic was improved by the correction for first order serial correlation. 1 3 It should also be noted that over the period 1979(1) - 1984(IV) the estimated price elasticity of demand for money is found to be negative, a counter intuitive result which suggests that the model employed does not fit the Canadian data very well over this period. 171 sample is significantly different from zero. The observation that Japan is the only A country that exhibits a significant shift in f> presents a misleading picture Table 6.4 of the stability of equation (6.6). The estimation results in Appendix 6.3 show that while the estimated value of p remains stable for all countries except Japan, Canada is the only country for which equation (6.6) as a whole is stable over the sample period. Table 6.4 Small Open Economy Final Estimates of a2, p, and T) 1973(1) - 1978(IV) 1979(1) - 1984(IV) A A . A A ^ A a2 P T| a 2 p t| Canada Germany Japan U.K. U.S.A. - 0.1881 (-3.5670) - 0.1459 (-7.9370) - 0.0630 (-2.1419) - 0.2566 (-3.8528) - 0.02508 (-0.4803) 28.5144 (2.3086) 10.9876 (4.7724) 7.5523 (13.4270) 53.5332 (0.8677) - 49.5786 (-3.3654) 5.3641 1.6031 13.7366 - 1.2434 - 0.0087 (-0.03438) - 0.1459 (-7.9370) - 0.2566 (-3.8528) - 0.15808 (-2.5918) 28.5144 (2.3086) 10.9876 (4.7724) 37.0370 (-1.4200) 53.5332 (0.8677) - 49.5786 (-3.3654) 0.2484 1.6031 2.3322 13.7366 - 7.8374 0.4756 - 0.0630 (-2.1494) It is interesting to note that the results reported in Table 6.4 indicate that the United States is the only country in the sample for which an exchange rate devaluation will 172 not result in an improvement in the balance of payments within one quarter.14 Although equation (6.5) does not appear to fit the Canadian data very well over the period 1979(1) - 1984(IV), all of the a 2 estimates reported in Table 6.4 have the expected negative sign and lie within the range of values obtained in other related studies. Unfortunately, the same cannot be said of the estimates of P obtained from equation (6.6) since none of the coefficients estimated fall within the [0, 1] interval established on the basis of the theoretical model presented in Chapter 5. One possible explanation for the poor estimates is that the small open economy model is not an appropriate framework within which to study countries such as Canada, Germany, Japan, U.K. and U.S.A., all of which have well-developed industrial economies that are capable of influencing world prices and interest rates (though perhaps in varying degrees) and are therefore more appropriately studied in the context of a model that explicitly incorporates economic interdependence.15 As the parameters a 2 and p are estimated on the basis of a multiple-partner interdependent economy model in A Section 6.5, futher discussion of p is deferred to Section 6.6. 6.4 Exchange Market Pressure and Intervention Exchange market pressure and the degree of exchange market intervention can be calculated using the estimated elasticity measure, i\ , given in Table 6.4. Measures of exchange market pressure, calculated as EMPt = Ar t - T| Ae t, are represented graphically for each country in Figures 6.1(a) - 6.5(a). For purposes of comparison, the Girton-Roper measure of exchange market pressure, given by 1 4 It was noted in Chapter 5 that Tj > 0 implies that an exchange rate devaluation leads to an improvement in the balance of payments. 1 5 In fact, the estimation results obtained in Section 6.5 show that this is not the case and that a more fundamental form of model misspecification is more likely to be the source of the problem. Further discussion is provided in Section 6.6. 173 GRP t = Art - Aet, is also included. Small open economy measures of the degree of exchange market intervention as defined in equation (6.1) as well as two others based on the HHS flexibility index and the Girton-Roper measure of exchange market pressure are presented in Figures 6.1(b) - 6.5(b). These indices are calculated according to the following definitions:16 GAMMA: Yt = (6-9) Ar t - Tj Ae t Ar t GAM-GR: y(GR)t = — (6.10) 1 Ar^ - Ae^ Ar(h)t GAM-HHS: y(HHS)t = — " (6.11) 1 Ae, where: Ar t= BOP t/M t_j, Aet = percentage change in the MERM effective exchange rate index, Ar(h)t E BOPt/(Xt + It), X t = total value of exports, and It = total value of imports. The quarterly estimates of exchange market pressure and exchange market intervention represented by these graphs are given in Appendix 6.5. The graphical representations of exchange market pressure and exchange market intervention clearly indicate that both measures are very sensitive to the assumptions made about the relationship between reserve and exchange rate changes. The consequence of this is that the measure of exchange market pressure 1 6 The HHS intervention index, y(HHS) = BOPt/Aet(Xt+It), is the inverse of the flexibility index originally formulated by Holden, Holden and Suss. Since the inverse of the flexibility index, like the intervention index developed in this paper, takes on a value of 0 under a pure float, the inverse is more useful than the original flexibility index for the purpose of comparing the measures of exchange market intervention obtained under the alternative definitions given by equations (6.9) -(6.11). 174 developed in this paper and the Girton-Roper measure of exchange market pressure will coincide only over periods in which the exchange rate is held relatively fixed, as it was in Canada over the period 1979(1) - 1984(IV), or when, as in the case of the Germany over the period 1973(1) - 1984(IV), the estimated elasticity of the balance of payments with respect to the exchange rate is very close to 1, the value Girton and Roper implicitly attribute to the elasticity measure T]. 1 7 The graphs show that, of the two measures of exchange market pressure, the Girton-Roper measure has the narrower range for all countries in the sample. As a result, the Girton-Roper measure of exchange market intervention varies over a wider range than y t. For all countries except the United States, the Holden-Holden and Suss index varies over a significantly wider range than either of the alternative intervention measures. For the United States by contrast, the HHS intervention index consistently reports a perfect float over the entire sample period while the other two indices show varying degrees of exchange market intervention. The most likely explanation for this is that the trade weight, (Xt + It), employed in calculating the HHS index is so large in the case of the United States, that it completely dominates any movements in reserves and exchange rates that may have occurred over the period. 1 7 With exchange rate stability the target of monetary policy in Canada over the period 1978(1) - 1984(IV), changes in domestic credit represent and additional means of relieving exchange market disequilibrium. Under these circumstances, the degree of exchange market intervention is more accurately measured as ?t(d) = [Adt + Art]/EMPt(d) where EMPt(d) = Adt + Art - t\Aet. As a result, the measures represented in Figures 6.1(a) and 6.1(b) will underestimate the magnitude of exchange market pressure and the degree of exchange market intervention pertaining to this period whenever Adt ± 0. Figure 6.1(a) CANADA Exchange Market Pressure 175 YEAR 20-Figure 6.1(b) CANADA Exchange Market Intervention 10-A 10 + 20-30-G-R HHS GAMMA l l l l l l l l I l l l 74 75 76 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 7B 79 YEAR 81 B2 83 B4 cc cn w PS (X E -iC CC < C w o z <c IE O X Figure 6.2(a) GERMANY Exchange Market Pressure 176 - 1 2 61 82 83 84 YEAR 150 2 100 > W E - 50 E-w o z <c nc X w Figure 6.2(b) GERMANY Exchange Market Intervention G-R HHS GAMMA 100 I I l i l l l I I l I l I I l l l l l I l l l l l l l I I l l l I l I l I I i I I i i l i I 75 76 80 YEAR Figure 6.3(a) JAPAN Exchange Market Pressure 177 YEAR E— Z 6 3 > K 6 3 E—' E— 6 3 6 3 O z •< ac u> X 6 3 20--10+ Figure 6.3(b) JAPAN Exchange Market Intervention G-R HHS GAMMA - 2 0 - I I I 1 I 1 I I I 11 1 1 1 I I II I I I I I I I I I I I I I I I M M II I I I I I 1 75 76 76 79 80 81 YEAR 150-Figure 6.4(a) UNITED KINGDOM Exchange Market Pressure 100 + 50+ o+--50--100- i i i i i i i i i I i i i i i i i i i i i I i I I I I I I I i i I I I I i i i i . I i I i I 80 83 YEAR 80-60 40 20+ Figure 6.4(b) UNITED KINGDOM Exchange Market Intervention -20 V -- G-R - HHS - GAMMA -40 I l I I l I l l l l I J l I I I I I I I I I I I I I I I I I I I I I I I l I I I I I I I I I YEAR Figure 6.5(a) UNITED STATES Exchange Market Pressure 179 YEAR 20-Figure 6.5(b) UNITED STATES . Exchange Market Intervention 10+ G-R HHS GAMMA i i i i i -10 1 I l l l l l l l l l I l I I l l l I i i l l l i l l l l I 1 74 76 77 76 78 80 81 82 63 YEAR 180 6.5 Interdependent Economies The distinguishing characteristic of interdependent economies is that the price and interest rate levels in all trading partners are jointly determined. As a consequence, the elasticity measure T | , in interdependent economies, depends on money demand and expectations parameters in both principal and partner countries. When countries are interdependent so that all price and interest rate levels are jointly determined, the elasticity of the balance of payments with respect to the exchange rate (derived in section 5.6) is given by; ' - a 2 P( 2 E|.1M{.1aJ2*wJ) dv j = 1 1 1 = Be! = n • . . , <6'12>-« 2 M t . 1 + In the small open economy model, the assumption that foreign prices and interest rates are exogenous leads to an elasticity measure, T) = - a2p, which depends only on the magnitude of the interest elasticity of the demand for money, a 2, and the expectations parameter, p, in the domestic economy. This suggests that estimating T|, as defined in equation (6.12), on the basis of the interdependent economy model would provide additional insight into the sensitivity of the estimated elasticity t o changes in model specification. It also provides an opportunity to test the hypothesis that the small open economy assumptions were responsible for the poor p estimates obtained in Section 6.3.18 1 8 It should be noted however, that favourable estimation results obtained on the basis of the two country model cannot rule out the possibility of other specification errors. For example, if the expectation formation or dynamic adjustment processes are misspecified, then changing the instruments employed in the estimation procedure may simply change the way in which parameters are biased, without either instrument set being right, or even preferable, to the other. 181 It is clear from equation (6.12) that in interdependent economies, in addition to the domestic parameters a 2 and p\ the elasticity measure, T ) , depends on a weighted average of the interest elasticities of the demand for money in partner countries as well as relative money supply size. The fact that foreign interest elasticities are weighted by the size of the foreign money stock (expressed in domestic currency units) reflects that the economic impact that trading partners exert on one another is directly related to their relative economic size. In order to calculate Tj, as given by equation (6.12), for each principal country, it is necessary to estimate equation (6.5') for each principal country and its three major trading partners.19 Since only the domestic expectations parameter, |3, enters into the calculation of T), equation (6.6') need only be estimated for Canada, Germany, Japan, U.K., and U.S.A. The estimation procedures employed in this section are identical to those used to obtain the final small open economy estimates of T), the only difference being a change in the instrument list employed in the first stage of 2SLS and 2SLS-A estimation. In the case of interdependent economies, in which all price and interest rate levels are jointly determined, foreign prices and interest rates can no longer serve as instruments for domestic prices and are replaced by domestic credit changes in partner countries, Ad t*, and lagged foreign output, y* t.i- The instrument list for interdependent economies is therefore given by: Ad t, Adt*, y t . i , y*t-it and e^  Final estimates of a 2 and p obtained under the assumptions of interdependence for the Canada, Germany, Japan, U.K., U.S.A., and their three largest trading partners, are summarized in Table 6.5. As the elasticity measure, TJ, varies over time when countries are interdependent, the mean elasticity estimate, T|, is reported in Table 6.5. 1 9 Quarterly income data was not available for the Netherlands so that for Germany, Tj was calculated using the estimated value of a 2 pertaining to the remaining two of the three largest trading partners, France and Italy. Similarly, due to lack of quarterly data for Saudi Arabia, the value of T| for Japan is calculated on the basis of the a 2 estimates obtained for Australia and U.S.A. 182 Quarterly estimates of the elasticity of the balance of payments with respect to the exchange rate are provided in Appendix 6.6, along with the final estimation results for equations (6.5') and (6.6'). Table 6.5 Interdependent Economies Final Estimates of a2, P, and f| A a2 1973(1) - 1978(IV) A P Tl a2 1979(1) - 1984(IV) A P Canada - 0.27958 - 23.0256 - 6.9619 (-1.4596) (-1.0614) 0.18044 - 23.0256 4.2735 (0.7370) (-1.0614) Germany - 0.17732 17.8330 0.0790 (-5.8796) (3.6177) - 0.17732 17.8330 0.2817 (-5.8796) (3.6177) Japan - 0.05227 9.0514 0.4536 (-1.3602) (1.2180) - 0.05227 9.0514 0.4507 (-1.3602) (1.2180) U.K. 0.08203 - 2.9782 - 0.0001 (0.2448) (-1.0921) - 0.10190 - 2.9782 (-0.7390) (-1.0921) 0.0006 U.S.A. 0.01055 - 9.9157 3.1771 (0.2846) (-4.2971) -0.15808 - 9.9157 (-4.1633) (-4.2971) - 0.0325 Australia - 0.40951 (-3.2929) - 0.40951 (-3.2929) France - 0.03030 (-0.4190) - 0.12741 (-2.8140) Italy - 0.02871 (-0.3752) - 0.76876 (-6.6067) 183 A comparison of the results reported in Tables 6.4 and 6.5 indicates that the estimated values of a 2 , p, and T) are quite sensitive to the structural differences between the small open economy and interdependent economy models. For all countries, the change in the underlying model causes fairly large changes in the A A magnitudes of a2 and p and in some cases also a change in sign. Germany and the A U.S.A. are the only countries for which p is significantly different from zero. In general, the estimation results reported in Table 6.5 do not compare favourably with those obtained on the basis of the small open economy model. Under the small open economy assumptions, significant coefficient pairs were obtained for Canada, Germany and Japan over the period 1973(1) - 1978(IV) and for Germany and U.S.A. over the period 1978(1) - 1984(IV). Under the assumptions of the interdependent economy model, by contrast, Germany is the only country for which both coefficient estimates are significant over the period 1973(1) - 1978(IV). A It is clear from Table 6.5 that estimation of P on the basis of the interdependent economy model has not yielded parameter values consistent with the theoretical bounds of 0 and 1. The failure to obtain a single p estimate within the predicted [0, 1] interval raises serious questions concerning the validity of the theoretical model developed in Chapter 5 since neither the small open economy nor the interdepencent economy version of the multiple partner model is supported by the data. A discussion of the possible sources of model misspecification responsible A for the unsatisfactory P estimates is taken up in Section 6.6. While there is no doubt that the model developed in Chapter 5 is not consistent with the data, it is not certain that the elasticity measures obtained are altogether A wrong. Even though they are indefensible, the estimates of T) obtained in this study may serve as useful benchmarks for future empirical work. For this reason, it seems worthwhile to use the estimates obtained to calculate and present graphically measures of exchange market pressure and exchange market intervention based on 184 the interdependent economy estimates reported in Table 6.4. The measures of exchange market pressure and exchange market intervention calculated using the quarterly elasticity estimates are provided in Appendix 6.7 and are presented graphically for each country in Figures 6.6(a) - 6.10(a) and 6.6(b) - 6.10(b), respectively. For purposes of comparison, measures of exchange market pressure and exchange market intervention obtained on the basis of the small open economy model are also included. The graphs clearly illustrate the extent to which the estimated measures of exchange market pressure and exchange market intervention are sensitive to the assumptions made about the degree of economic interdependence. 40-20+ 0+ -20 Figure 6.6(a) CANADA Exchange Market Pressure -401 l I l l l I I 1 I II l I I I I 1 I l I I I l I I 1 I I l l I l l l I I I 80 81 YEAR Figure 6.6(b) CANADA Exchange Market Intervention 12. 9-6-3-0--3--6 - l l I I l l I I l l l l I. I i i i I l I I I I I I I I i I i i I I i 78 79 YEAR 62 Erf K w K P u E—1 W PS <c SS • o z -< u X Figure 6.7(a) GERMANY Exchange Market Pressure - 1 2 - i I l I I I I l I l i I l I I I l I I I l l I I I I l l I l l l l I l I I l l l M l 74 75 76 77 78 78 YEAR 80 82 83 64 186 Z O E -Z > cc w E—' E -W DS O z - * X 60-40-20-Figure 6.7(b) GERMANY Exchange Market Intervention T_ r. - INT - SOE V; u V 'A 7 - 2 0 - i I I i i I I I I I I I I I I I I I I I I I I I I I I I I I I I i i I I i I I i i i i i - i 74 75 76 76 79 60 61 82 83 B4 YEAR Figure 6.8(a) 187 JAPAN Exchange Market Pressure 20 - 3 0 i i i l i r i l l i r i i i i i l l l l i l l l l l l l i i l i l i i l . l l i i l i i i i i 74 76 76 77 76 78 80 81 82 83 84 YEAR Figure 6.8(b) JAPAN Exchange Market Intervention 4 _ : , - 1 6 I I I 1 I I I I II I I I I I I II I I I I I I I I I I I 1 I I I I I I I M I I i I I I I 74 75 76 77 76 79 80 81 82 83 84 YEAR w cc C3 cn cn w cc 0 , E—' W . a: < s w o nc X Figure 6.9(a) UNITED KINGDOM Exchange Market Pressure 188 - 5 0 YEAR -1.5-Figure 6.9(b) UNITED KINGDOM " Exchange Market Intervention w >• cc to E—' E— S ' w o z < nc o X .5+ 0+ - . 5 + ii M 11 V V V \ / V r \ i \ I -\ • i • \ V - •/ —\ - INT - SOE - 1 II l I l I l l l l l l I I l l l I I I I I I I I •+- i l l I l l l I l I I 75 76 77 76 78 BO 81 82 83 _ 84 YEAR 400 w « 300 CO CO W « Cu E-I 200 w < w 100 o < W 0 Figure 6.10(a) UNITED STATES Exchange Market Pressure — INT — - SOE 4 J -•100 I l l M l I l l I M l l I l I l I l l l l l -i l l l l I I l I I I l l I I l l I i M l 74 76 76 77 78 79 60 81 82 63 84 YEAR 189 Figure 6.10(b) UNITED STATES Exchange Market Intervention - 1 2 I i i i i i i i i i i i i i i i i i i i i i i i i i i I I i i i i i i i i i i i i i i i i i 74 75 76 77 78 7S 80 81 B2 83 84 YEAR 190 6.6 Model Misspecification - Causes and Implications A It is clear from the p values reported in Tables 6.4 and 6.5 that neither the small open economy nor the interdependent economy version of the multiple partner model developed in Chapter 5 is supported by the data. This is evident from the failure of any of the p estimates to fall within the [0,1] interval predicted by the theory. The inevitable conclusion is that the underlying model is, in some fundamental way, misspecified and that any measures of exchange market pressure and exchange market intervention calculated on the basis of this model are unlikely to be very reliable.20 In order to measure exchange market pressure, and therefore also exchange market intervention, in the manner proposed in this study, it is important to obtain a reliable estimate of the elasticity of the balance of payments with respect to the A A exchange rate, Tl , since TJ determines the impact of observed exchange rate changes on the overall measure of exchange market pressure. In particular, with exchange A A market pressure measured as EMPt = Ar t-T)Ae t, the magnitude of T] becomes more important to the accurate measurement of exchange market pressure the larger are exchange rate changes relative to the balance of payments. In both the small open economy and interdependent economy models, a 2 and P are co-determinants of. T). Since a 2, the interest elasticity of the demand for money, can be expected to be negative and less than 1 in absolute value, the magnitude of P becomes a crucial factor in determining whether Tj is found to be relatively elastic or inelastic. In the case of the small open economy, values of p between 0 and 1 imply that TJ lies within the interval [0, -a2] and is therefore restricted to the inelastic range a priori.21 The 2 0 While it is true that the sources of measurement error, identified in Section 6.2, may be a contributing factor, the discussion in this section indicates that A measurement error is unlikely to be the primary cause of the unsatisfactory p values in this study. 2 1 A similar restriction is not imposed on the values of TI calculated on the basis of the interdependent economy model since, according to equation (6.12), p between 0 and 1 191 fact that the estimates of P consistently fall outside the [0,1] interval predicted by the theoretical model, indicates that the underlying model is misspecified. The most likely source of misspecification is the expectations formation process described by equation (5.16). According to this equation, economic agents form expectations about future exchange rate changes on the basis of contemporaneous deviations from purchasing power parity. Since the model does not allow exchange rate expectations to affect domestic price levels, causality is forced to run from price to exchange rate changes. In this framework, the assumption that P lies between 0 and 1 implies that exchange rates exhibit less volatility than domestic prices. The fact that, over the period under study, exchange rates were much more volatile than prices may account for the failure to obtain A values of p within the [0,1] interval. The original intention in employing the expectations formation process described by equation (5.16) was to provide the model with a tendency toward long run purchasing power parity while keeping the adjustment process as simple as possible. Simplicity was also the motivation for describing the domestic price level in terms of equation (5.13) rather than having the domestic price level endogenously determined by means of an explicity modeled goods sector. In the light of the empirical evidence, one is forced to conclude that the desired expositional simplicity is obtained at the cost of imposing undesirable restrictions on the range of the A A elasticity measure, Tj, and the inability to explain or interpret values of P outside the interval [0,1]. What this suggests is that a richer class of models is needed in order to obtain defensible elasticity estimates. In particular, the preliminary empirical work implies that for the interdependent economy TJ lies within the interval [0, Tlu] where n . n T| u = (- a2 £ FJJ_1Mj_1aJ2*wJ)/(a2 M t . j + £ E^jMj.ja^w*) which can exceed unity. 192 of this chapter indicates that the expectations formation process should be more flexible and that the goods market should be modeled explicitly in order to allow for simultaneous determination of domestic prices, output, and interest rates, and exchange rate expectations. &J Conclusion The fact that exchange rate practices are not limited by any formal international agreement, raises the question of what determines national exchange rate policy and, simultaneously, the problem of characterizing the wide variety of exchange rate practices that have developed since the breakdown of the Bretton Woods system. In this analysis, it is argued that exchange rate policy can be measured quantitatively as the proportion of exchange market pressure that is alleviated by a change in the domestic money supply. Since changes in the domestic money supply are readily observable, the problem of characterizing exchange rate policy then becomes one of measuring exchange market pressure. Girton and Roper proposed the difference between the change in reserve balances and exchange rate appreciation, both expressed as percentages, as a composite measure of exchange market pressure. In so doing, Girton and Roper assume that the elasticity of the balance of payments (change in reserves) with respect to exchange rate changes is equal to 1. In general, this elasticity will be model-specific. The measure of exchange market pressure developed in Chapter 5 is a model-consistent generalization of the Girton-Roper measure. In the context of the models employed in Chapter 5, the elasticity of the balance of payments with respect to the exchange rate was found to be determined by the magnitude of the interest elasticity of the demand for money, a2. and the expectations parameter, {$. 193 / In this chapter, measures of exchange market pressure and exchange market intervention were estimated for Canada, Germany, Japan, U.K., and U.S.A. over the period 1973(1) - 1984(IV) on the basis of the the multi-partner models developed in Chapter 5. In order to gain some insight into the sensitivity of these measures to the changes in the underlying structure of the model, preliminary estimations of the small open economy model were undertaken using a variety of restrictions and estimation techniques. The results indicate that while the magnitudes of &2 obtained on the basis of the small open economy model are relatively insensitive to the structural changes imposed, the values of p are not. Final estimates of the elasticity of the balance of payments with respect to the exchange rate were obtained for the small open economy using 2SLS estimation with a correction for first-order autocorrelation. Dummy variables were included in the estimation equation to allow for the possibility of structural shifts over the estimation period. Estimates of the interdependent economy elasticities were obtained in a similar manner. A comparison of the final results for the two models provides further evidence of the sensitivity of the elasticity estimates to changes in model specification. The results of this preliminary exploration suggest that a richer class of models than the one used in this study should be employed for estimation purposes. As stated in the preface to this study, and also in Chapter 4, the main objective of the analysis undertaken in Part II was to formulate a quantitative measure of exchange rate policy that can be used to classify exchange rate practices and to conduct empirical studies of exchange rate policy. The results of this chapter indicate that the present study has been, at best, only moderately successful in achieveing its stated objective. While this study does provide a general method by which model-consistent, quantitative measures of exchange rate policy can be obtained, it is not successful in ascribing to these measures index values that are 194 robust to a relatively large class of models. As a consequence, the practical application of this methodology must, for the present, be restricted to a narrower set of problems than was originally intended. It is clear that the measures of exchange market pressure and exchange market intervention proposed in this study can be employed to conduct empirical tests of theoretical propositions within the confines of a chosen analytical framework. Studies of this sort are quite limited in their objectives since they test whether the postulated economic structure and policy objective function are jointly consistent with the data. Using the intervention index, such studies can also be employed to construct model-specific classifications of exchange rate policy which are analogous to the MERM effective exchange rate index. Answers to more general questions, . such as whether exchange market intervention is, as the majority of thoeretical studies assume, widely employed by policy authorities as a tool of stabilization policy, require estimates of exchange market pressure, and therefore elasticity estimates, that are robust to a variety of model specifications. At this point it is difficult to know whether such estimates can be obtained and therefore also uncertain whether the proposed intervention index will be of use in general as a measure for classifying exchange rate policy. 195 Appendix 6.1 Partner Countries and Weights Country Partners % of Total Trade Canada U.S.A. 0.72 Japan 0.055 U.K. 0.04 0.82 Germany Netherlands 0.125 France 0.115 Italy 0.08 0.32 Japan U.S.A. 0.22 Saudi Arabia 0.075 Australia 0.045 0.34 U.K. U.S.A. 0.11 Germany 0.095 France 0.075 0.28 U.S.A Canada 0.20 Japan 0.12 Germany 0.05 0.37 Australia Japan 0.25 U.S.A. 0.16 U.K. 0.08 0.49 France Germany 0.35 Italy 0.20 Belgium 0.19 0.74 Italy Germany 0.37 France 0.29 U.S.A. 0.145 0.805 Netherlands Germany 0.41 Belgium 0.20 U.S.A. 0.14 0.75 Source: United Nations Trade Statistics. Weights were calculated as the average ratio of bilateral trade (exports plus imports) to total world trade over the ten year period 1973 - 1983. 196 Appendix 6.2 A. IPS Source Codes Data were obtained from the International Financial Statistics published by the IMF. The variables employed in the empirical analysis are identified below by IFS source code: m = 34 y = 99a.r i = 60c eJ = ef d = 32 r = 77f.d p = 64 e = amx I = 71 X = 70. As quarterly data on real GNP (y = 99a.r) was unavailable for U.K., Australia, France, and Italy, real GDP was used instead. The definition of real output, y, by IPS source code is therefore given by y = 99b.p, for U.K. and Australia, and y '=. 99b.r, for France and Italy. Quarterly treasury bill data was not available for Japan and France and was replaced by the money market rate so that for these two countries i = 60b. B. MERM Exchange Rate Index The MERM exchange rate index is constructed using the Multilateral Exchange rate Model developed by the IMF. The MERM-weighted effective exchange rate index is defined as: 18 ME(i) = n j = i j * i (R$(i) > W(i,j) x 100 where: ME(i) = MERM-weighted effective exchange rate index of country i R| = the cost of one unit of currency i in terms of the U.S. dollar relative to its cost in the base period, 1980 (i.e. R$(i) = 1 in 1980). W(i,j) = a measure of the effect of a 1 percent change in the price of currency i in terms of currency j, on the trade balance of country i, measured in its own currency and deflated by the induced change in the average of its export and import prices in its own currency (derived from MERM). source: IFS Supplement on Exchange Rates (1985). 197 Appendix 6.3 Small Open Economy Final Estimation Results Estimates of &2 were obtained for Germany using 2SLS and for Japan, U.K., and U.S.A. using 2SLS-A to estimate equation (6.5'). Exogenous dummy variables were included in the instrument list for Japan only. For Canada, estimates of a 2 were obtained on the basis of separate estimation of equation (6.5) over the periods 1973(1) - 1978(IV) and 1979(1) - 1984(1V) in order to allow the correlation coefficient to differ between the two sub-samples. Estimates of p were obtained for Japan and U.S.A. using 2SLS, and for Canada, Germany and U.K. using 2SLS-A to estimate equation (6.6') with exogenous dummy variables included in the instrument list for all countries except Canada. Canada: 1973(1) - 1978(IV) mt = - 8.5889 + 1.1311 y M (-3.8540) (2.0707) R 2 = 0.9904 0.18812 i t + 1.4629 pt (-3.5670) (7.2528) p = 0.4051 (2.17086) (6.5) pt = -0.03632 + 1.0510 p*t - 0.01829 et - 0.03507 i t + 0.11171 i* t (6.6') (-0.10948) (24.5140) R 2 = 0.9922 (-0.3481) (-2.3086) (1.0630) p = 0.9808 (34.4808) 1979(1) - 1984(IV) m t = - 18.3360 + 5.1879 y M - 0.00871 i t - 1.5677 pt (-1.6949) (2.2467) (-0.0344) (-2.4185) (6 .5) R2 = 0.5299 p = 0.6767 (4.5021) p t = -0.03632 + 1.0510 p* t - 0.01829 e t - 0.03507 i t + 0.11171 i* t (6.6") (-0.10948) (24.5140) (-0.3481) (-2.3086) (1.0630) R 2 = 0.9922 p = 0.9808 (34.4808) Germany: 1973(1) - 1978(IV) m t = - 13.3450 + 2.2466 y t_i - 0.14578 i t + 0.58055 p t (6.5') (-9.9467) (8.8593) (-7.9370) (5.1037) R 2 = 0.9742 DW = 1.8194 p t = 3.2264 + 0.09841 p* t + 0.21768 - 0.09101 i, + 0.00546 i* t (6.6*) (12.6110) (1.7366) (2.9869) (-4.7724) (0.5051) R 2 = 0.9899 p = 0.5805 (4.8877) 1979(1) - 1984(IV) m t = - 13.3450 + 2.24660 y t . i - 0.14578 i t + 0.58055 p t (6.5') (-9.9467) (8.8593) (-7.9370) (5.1037) R 2 = 0.9742 DW= 1.8194 p t = 3.2264 + 0.41105 p* t + 0.12608 6, - 0.09101 i t + 0.17559 i* t (6.6') (12.6110) (17.1265) (2.9869) (-4.7724) (4.6066) R 2 = 0.9899 p = 0.5805 (4.8877) Japan: 1973(1) - 1978(IV) m t = 0.24301 + 0.6241^^1 - 0.06297 ^ + 0.71644 p, (6.5') (0.1883) (4.7375) (-2.4516) (8.4347) R 2 = 0.9764 p = 0.1626 (1.1297) p t = 2.4716 + 0.75013 p* t (18.3190) (70.2580) 0.15354 e, R 2 = 0.9968 (5.0929) DW = 1.8805 0.13241 i t (-13.427) - 0.02031 i* t (-1.8738) 199 (6.6') 1979(1) - 1984(IV) m t = 0.24301 + 0.62411 y M (0.1883) (4.7375) (-2.4516) R 2 = 0.9764 0.06297 i t + 0.71644 p t (8.4347) p = 0.1626 (1.1297) (6.5') p t = 2.4716 + 0.42731 p* t (18.3190) (21.3740) + 0.08470 e R 2 = 0.9968 (2.2065) DW = 1.8805 0.02700 i t - 0.02031 i* t (-1.4220) (-1.8738) (6.6*) United Kingdom: 1973(1) - 1978(IV) m t = 5.0091 + 0.39297 y M (7.1695) (2.1344) R 2 = 0.9717 0.25662 i t + 0.95507 p t (-3.8528) (24.8330) p = 0.6040 (5.1962) (65 1 ) Pt - 1.7450 + 1.6744 p* t (-4.2652) (32.4890) R 2 = 0.9991 1979(1) - 1984(IV) m t = 5.0091 + 0.39297 y M (7.1695) (2.1344) 0.24470^ - 0.1868 i t - 0.12671 i* (5.0929) (-0.8677) (-4.9487) p = 0.6524 (5.9007) 0.25662 i t + 0.95507 p t (-3.8528) (24.8330) t (66 ' ) (6.5') R 2 = 0.9717 p = 0.6040 (5.1962) Pt = - 1.7450 + (-4.2652) R 2 = 0.9991 1.27338 p*t (25.1560) + 0.09358 ^ - 0.1868 i t + 0.03926 i* (1.4403) (-0.8677) p = 0.6524 (5.9007) (1.5668) 200 (6.6') United States: 1973(1) - 1978(IV) m t .= -3.8268 + 0.9085 y M (-2.17842) (4.4917) R 2 = 0.9877 0.02508 ^  + 0.59442 p t (-0.4803) (9.3263) p = 0.3261 (2.3651) (6.5') p t = 1.0250 + 0.86010 p*t - 0.10837 ^ + 0.02017 1 (9.1974) (101.42) (-5.2615) 0.01423 i* (3.3654) (-1.8435) R 2 = 0.9997 DW= 1.6455 (6.6') 1979(1) - 1984(IV) m t = -3.8268 + 0.9085 y M (-2.17842) (4.4917) R 2 = 0.9877 0.15805 i t + 0.68711 p t (-2.5918) (10.3549) p = 0.3261 (2.3651) (6.51) Pt = 0.8051 + 1.24885 p*t - 0.10837^ + 0.02017 i t (-18.3750) (51.367) (-5.2615) R 2 = 0.9997 DW= 1.6455 0.04280 i* (3.3654) (6.5918) (6.6') Appendix 6.4 Small Open Economy Exchange Market Pressure (Figures 6.1(a) - 6.5(a): EMP) Canada Germany Japan U.K. U.S.A. 9 .324011 - 6 . 3 2 7 4 9 9 - 4 . 0 2 1 5 3 8 - 1 . 9 2 2 7 6 2 - 5 . 8 0 7 0 2 4 5 .956665 - 9 . 8 6 2 1 2 4 0 .8611727 81 .75109 - 3 . 8 9 8 9 3 0 - 7 . 5 1 8 5 1 5 2 .204800 - 1 . 0 6 5 9 4 0 14 .81924 4 .997856 - 1 8 . 2 1 4 5 4 1.817530 1.628609 -6 .984408 6 .529731 - 1 . 5 0 3 9 5 2 - 6 . 1 6 8 7 6 5 - 0 . 1 0 4 3 4 7 1 - 2 8 . 9 5 9 2 2 -6 .347577 3 .213141 2 .495484 . 2 .397023 4 .261910 2 .529819 3.420424 - 4 . 0 1 0 8 2 3 0 .9712863 14 .47887 - 1 . 9 5 5 4 2 8 17 .10887 . - 1 . 6 2 5 0 3 3 - 0 . 4 5 9 2 6 0 1 E - 0 1 19 .90736 - 7 . 6 6 7 6 0 7 1 1 . 5 7 1 6 1 . 0 .5155988 0 .2482076 4 1 . 9 2 1 2 6 - 0 . 5 6 4 9 9 5 9 - 6 . 3 0 1 3 1 1 3 .141428 - 1 . 5 0 7 3 0 7 59 .17483 6 .594188 - 1 0 . 5 9 2 1 3 -0 .2390199E-- 0 1 0 .1256681 35 .49178 0 .8414234 - 1 3 . 5 5 7 9 1 1 .552921 0.3339704 11 .16712 0 .3714210 - 1 3 . 1 8 6 1 5 - 7 . 3 0 8 5 4 4 - 0 . 3 8 1 5 2 6 1 111 .5812 1.186477 0.4841CC4 0 .5069091 - 0 . 7 7 6 5 9 3 2 32 .42638 - 0 . 9 2 0 3 4 4 7 7 .680278 - 8 . 5 5 0 5 5 6 0.6816070 101 .8834 - 1 . 7 6 2 8 4 3 1 7 . 9 1 2 0 1 - 1 . 3 5 4 2 6 4 - 1 . 0 7 5 8 3 3 - 3 9 . 2 7 4 4 3 - 0 . 9 1 8 3 2 5 6 13 .26236 - 2 . 4 4 3 9 6 2 - 1 . 4 6 8 5 2 6 9 .565039 - 3 . 0 6 6 5 7 8 9 .332122 - 3 . 1 5 6 7 9 7 - 1 . 2 5 5 3 7 5 9 .112353 - 3 . 1 0 2 3 5 8 20 .46840 2 .067712 - 0 . 9 0 4 7 9 2 4 - 2 3 . 3 2 2 2 7 - 7 . 2 4 9 2 4 7 9.653624 - 3 . 6 0 7 8 4 5 1.659972 - 3 5 . 6 4 2 7 8 . - 8 . 3 7 5 0 7 9 7 .036480 - 0 . 1 7 8 9 0 5 9 - 4 . 2 5 9 3 4 8 76 .51693 - 0 . 1 6 5 7 2 9 0 12 .97846 4 . 4 0 3 8 2 1 - 5 . 0 5 1 5 2 8 - 1 2 . 3 0 1 6 8 - 7 . 3 3 5 4 3 9 20 .75847 - 1 . 8 4 5 3 4 9 1 .495481 ' - 1 . 6 5 6 0 6 8 - 7 . 5 0 4 0 0 7 0 .8379264 - 6 . 6 0 4 7 6 7 12 .25323 - 4 0 . 6 1 8 7 8 10 .90027 0 .6463633 - 0 . 8 5 8 6 1 9 8 15.47970 - 7 6 . 5 8 9 5 1 17 .94649 0 .9753373 1.257354 5.259024 - 7 7 . 9 0 1 4 9 - 1 7 . 3 7 4 7 4 0 .8379352 - 6 . 8 1 7 7 0 8 19.49382 35 .02862 11 .87413 - 1 . 3 5 3 1 4 6 - 4 . 7 3 0 5 3 2 4 .359779 - 6 4 . 4 6 7 6 1 . 4 .432458 1.313769 0.2406279 - 1 1 . 4 4 2 1 1 - 2 7 . 3 3 2 8 5 - 2 . 7 4 7 9 1 6 0 .8472086 - 0 . 7 2 5 4 5 7 6 - 9 . 6 7 9 5 4 5 - 3 3 . 0 8 1 3 8 - 2 2 . 2 3 7 8 5 - 1 . 4 0 7 8 8 9 2 . 1 5 0 4 3 1 - 1 5 . 9 2 6 1 0 - 4 4 . 1 4 4 6 9 2 0 . 5 6 8 9 3 0 . 2 6 6 1 1 5 2 E - 0 1 7 .647441 - 1 3 . 9 1 3 6 9 - 2 4 . 2 5 5 0 6 32 .26826 - 1 . 6 3 7 0 1 6 4 .877894 6.231554 55 .49413 54 .37862 - 1 . 3 5 7 4 9 6 1.698648 4 .675349 107 .2680 42 .38995 2 . 9 3 2 6 6 1 - 1 0 . 6 6 1 0 2 - 2 . 1 9 5 1 5 6 13 .17746 - 2 9 . 0 7 6 7 1 - 5 . 2 7 4 0 9 1 1.218829 3 .546599 - 2 0 . 8 1 4 4 5 31 .52469 - 1 2 . 0 7 0 0 2 - 2 . 5 2 3 6 3 2 6.086044 15 .31586 28 .08307 9 .081307 0 .5630524E - 0 1 6.993955 - 2 2 . 0 6 8 3 4 3 6 . 4 1 6 7 1 0 .9139511 -0 .9369435 - 3 . 4 5 3 4 6 6 44.58186 . 12 .80659 1.640115 2 .365102 - 2 0 . 1 4 4 1 6 137 .3712 - 2 1 . 7 2 0 6 0 0 .1915374 - 5 . 1 3 0 1 8 2 -2.516894 - 6 0 . 3 0 7 7 3 22.09058 0.2799004 2 .137224 - 0 . 9 7 6 5 4 2 1 - 1 3 . 8 1 3 3 3 27 .70350 - 2 . 5 3 4 9 9 5 0 .6728381 - 1 0 . 0 8 9 4 3 28 .16128 1 .465719 - 2 . 6 4 6 5 6 2 2 .390186 - 4 . 5 8 2 9 4 2 25 .08688 5 .838228 - 4 . 3 4 4 9 8 4 - 0 . 3 3 2 5 6 1 0 - 2 . 3 7 3 1 6 4 28 .56849 7 .500226 1.380784 . 0 .4587203 5.814519 21 .81857 45 .63155 0 .4873869 1.653532 - 1 . 9 8 7 5 4 4 46.78054 1 9 . 9 7 9 9 1 B. Girton-Roper Exchange Market Pressure (Figures 6.1(a) - 6.5(a): G-R) Canada 1.334754 0.7750769E-01 -1.2301S3 -2.283705 0.2109879 0.3253855 0.4908950 3.074022 0.7598517 -1.121199 -1.7176E1 -1.280997. -2.035744 C. 4841004 1.476166 1.702C51 2.445513 1.049264 3.256239 -1.185456 0.656£lie -2.061570 2.864695 0.5858267 -1.881779 .2.259379 0.6268961 -2.163909 1.695539 0.8472066 0.6612232 0.8250476 -3.553391 -2.185754 2.658591 -5.425123 -10.91887 7.843988 0.9781697 2.131588 0.6350979 0.7716926 -2.307936 -1.773244 -2.26635S 0.7457957 0.1261891 Germany -3.111156 -4.031105 0.2692887 0.8056229 -2.865841 0.4235377 -2.545274 -0.5369783E-01 -0.3965730 1.172701 -C.1720762 3.206421 -5.381095 1.C99339 -5.639423 -1.091572 -1.874159 • -2.080306 3.171123 -1.397301 -0.8681096 3.829782 0.9646494 -5.690849 -1.004879 2.361541 -4.827845 -4.759487 -0.7582223 -0.6079650 -0.. 2266617 5.528488 4.018976 0.8139972 -7.651966 0.8125392 -1.356053 0.3507621 -0.5018862E-01 3.345619 -5.088689 0.7402666 0.4905568 2.371927 -0.2778009 -0.7764687 0.7399159 Japan -5.972598 2.133526 -0.1219335 3.281141 -1.003051 5.220108 1.812374 -C.5281979 0.1749162 -2.300265 0.6196603 -0.2323134 -1.617750 -2.259754 1.369724 -2.620761 -3.342226 -2.933160 . -4.386235 0.7745969 -8.173350 -11.23024 1.847940 4.524356 5.879e08 2.306535 7.345648 1.528551 -4.172352 -3.934509 -6.514850 -5.662097 2.895504 2.036302 -0.8572108 1.365562 2.311715 2.737928 -1.656163 -8.477612 -0.9257067 -0.4275107 -4.369706 -1.876885 -C.9768365 2.562341 -0.6900412 U.K. 0.8591610E-4.001035 -2.477431 -4.482799 -5.881978 -3.346729 -8.395086 -2.105504 . 1.289195 5.239678 1.484694 -2.798025 2.081392 -0.4413157 6.823800 5.365953 5.016954 12.14488 5.872511 -2.623368 0.4460497 -0.5670109 -0.7462027 -13.62073 -9.805695 -14.57966 -3.054817 -2.884493 -5.292629 -5.202972 . 0.1090988 -2.931996 4.756690 8.110055 I . 910260 -0.5241976 3.586913 -6.186063 I I . 93C60 8.822272 -2.147767 -4.853016 1.971327 1.495788 -1.893507 -6.563699 -2.138617 U . S . A . 5.231855 3.774126 -1.915369 -4.324220 2.297353 -3.175099 -1.301375 4.465245 -0.7593699 -3.845056 -2.208064 -1.24 8954 -2.059367 C.1963722 -2.341636 -1.813616 -1.871794 -2.001522 -2.504352. -1.191068 2.709236 3.488011 -3.349654 1.205511 0.7945388 . -0.312C572 -1.503377 1.798619 -1.870842 0.9671623 -3.513148 -4.645442 -5.903438 -3.964259 1.477240 -2.970053 -3.542293 -5.111259 -1.756226 2.869994 -3.104427 -3.039526 -1.362552 0.4065650E -0.6602426 -5.531675 -3.772714 2 0 3 C Exchange Market Intervention (Figures 6.1(b) - 6.5(b): GAMMA) Canada Germany Japan U.K. U . S . A . - 0 . 5 3 1 8 7 7 6 E - 0 1 - 0 . 3 6 5 6 4 3 3 0.5599951 - 0 .1267059 - 0 . 5 3 5 9 9 4 0 E - 0 1 -0.2451358 - 0 . 5 8 8 4 7 7 3 - 0 . 3 3 9 9 7 5 1 - 0 .2572962E - 0 1 - 0 . 9 0 7 5 4 6 9 E - 0 1 - 0 . 2 8 0 2 9 5 3 E - 0 1 - 1 . 3 5 8 4 8 7 1.803196 - 0 .2588162 0.2333430 - 0 . 7 5 0 3 4 7 0 E - 0 1 - 0 . 4 9 5 7 7 4 5 0 . 7 9 7 3 6 3 5 E . - 0 1 0 . 6 1 3 7 0 8 0 0.7870923E - 0 1 - 0 . 5 6 7 0 7 2 0 E - 0 1 - 0 . 4 3 8 4 9 2 1 -6.811160 0 . 1 4 0 5 4 5 7 0.2451552 - 0 . 3 5 3 6 1 4 0 - 1 . 2 3 0 6 4 7 - 0 . 6 8 1 4 6 7 8 E . - 0 1 - 0 .9254331 - 0 . 2 4 9 8 6 7 9 - 0 . 5 2 7 3 7 3 6 E - 0 1 0 . 1 8 3 1 1 2 2 E - 0 1 0.2146324 - 0 .7038539 0.8146147 - 0 . 8 2 9 7 0 6 6 E - 0 2 - 1 . 5 9 7 8 4 8 -8.523846 - 0 .1925830 0 . 1 2 2 9 8 4 6 - 0 . 1 4 8 4 3 0 5 - 3 . 7 5 3 0 4 4 1.267804 - 0 .4534659E - 0 1 1.190676 - 0 . 1 0 4 3 9 7 2 E - 0 1 - 0 . 6 8 3 7 0 2 6 0 . 5 2 2 8 7 9 5 0 •1698390E - 0 1 0 . 1 2 2 5 7 1 2 - 0 . 2 9 8 1 7 6 0 E - 0 1 1 7 . 6 5 5 2 7 - 2 . 5 6 6 5 6 5 - 0 • 3 3 3 9 1 3 7 E - 0 1 - 1 . 0 0 8 7 1 9 - 0 . 1 1 3 0 0 8 8 3 . 8 6 4 0 9 1 2 . 5 3 7 8 1 9 - 0 . 3 4 8 7 4 5 5 - 1 . 4 1 7 9 8 4 -0.3938109E - 0 1 0 . 2 9 1 4 6 8 4 -1.938678 - 0 •5839570E - 0 1 - 0 . 5 1 6 2 5 6 1 1.000000 4.139885 -0.7671389 - 0 .9319222E - 0 1 0 . 3 2 7 4 9 3 1 0 . 7 4 2 1 5 1 0 E - 0 2 0 . 8 5 3 0 8 2 0 E - 0 1 0 . 8 4 3 9 6 9 1 E ' - 0 1 - 0 •6278728E - 0 2 1 . 1 8 2 0 3 9 - . 0 . 1 1 2 3 4 57. 0 . 4 7 8 8 3 1 4 - 0 . 3 0 2 3 9 4 3 - 0 . 2 2 5 8 6 8 2 1 . 5 4 0 4 6 6 - 0 . 2 4 9 4 6 3 3 E -02 0 . 3 7 3 6 2 0 3 - 0 . 1 5 7 1 7 0 6 0 . 4 8 7 4 0 2 4 0 . 7 8 4 0 5 6 9 - 0 . 9 0 9 4 0 1 4 E - 0 1 0 . 8 3 8 4 1 2 9 E - 0 1 - 0 . 2 1 2 1 2 4 6 1 . 3 5 8 9 2 2 0 . 8 0 3 3 3 1 4 - 0 . 3 3 4 8 2 6 6 E - 0 1 2 . 4 3 3 6 8 6 - 2 . 4 8 9 7 1 1 - 0 . 3 5 0 0 8 2 0 0 . 6 3 7 2 2 4 6 -0.3800800 - 0 . 6 4 6 1 0 8 0 1 . 4 8 3 7 3 3 0 . 8 6 6 5 0 4 5 E - 0 3 0 . 5 2 4 5 7 6 1 - 0 . 3 4 3 8 7 5 1 1 1 . 3 4 9 7 6 0 . 1 6 6 5 9 3 0 - 0 . 7 2 2 2 6 7 7 E - 0 1 - 8 . 6 1 4 7 5 5 - 0 . 4 2 4 3 8 6 1 0 . 6 4 9 7 9 8 0 - 0 . 1 0 9 3 1 3 4 - 0 . 2 8 8 0 2 8 7 E - 0 1 0 . 1 8 2 2 0 6 3 - 0 . 5 8 3 2 3 0 6 E - 0 1 - 3 . 0 9 1 0 4 8 0 . 7 8 6 2 4 9 8 0 . 4 0 7 4 5 0 4 0 . 6 9 3 1 5 8 4 1 . 0 9 9 4 3 3 0 . 6 2 8 2 4 5 2 - 0 . 1 0 4 2 3 6 0 0 . 2 8 3 1 4 5 2 0 . 2 1 1 2 3 5 7 2 . 2 9 2 6 7 6 1 . 4 5 7 6 4 7 - 0 . 8 5 6 7 5 7 2 E - 0 1 0 . 5 9 5 6 7 4 1 E - 0 1 0 . 1 5 2 4 1 8 4 0 . 5 6 5 2 9 2 2 3 . 4 0 2 0 8 2 0 . 1 7 8 3 3 2 7 E ' - 0 1 0 . 1 2 3 3 3 5 7 0 . 1 2 9 0 8 3 5 1 . 0 8 3 2 3 7 0 . 2 1 5 8 6 3 1 - 0 . 9 0 9 6 3 7 1 E ' - 0 1 - 0 . 1 7 2 5 7 0 2 0 . 8 7 2 4 8 6 1 E - 0 3 0 . 8 0 1 9 7 7 8 1 . 0 1 6 4 4 4 - 0 . 1 3 6 8 5 9 3 - 0 . 3 0 2 5 7 6 4 E - 0 1 0 . 4 7 3 0 2 2 5 0 . 9 0 3 9 6 0 8 - 1 0 . 1 5 2 2 2 - 0 . 1 1 2 2 6 9 7 0 . 1 3 0 3 3 3 3 0 . 7 1 6 9 3 8 8 1.000000 1 . 3 0 5 6 2 8 - 0 . 3 9 0 4 4 5 ' 4 E -- 0 1 0 . 9 1 1 1 2 5 6 E - 0 1 0 . 7 4 5 8 5 0 6 E - 0 1 1 . 1 7 5 2 7 6 -1.969303 - 0 . 3 4 5 0 S 7 7 E - C l -0 • 6 1 1 7 9 3 2 E - C . 3 3 3 1 6 4 9 E - C l 1 1 . 5 7 6 9 6 0 . 2 5 5 5 8 9 8 - 0 . 3 8 2 2 5 7 1 E - - 0 1 0 •5185882E - 0 1 - 0 . 1 4 5 1 7 5 4 E - 0 1 0 . 6 1 3 1 0 5 7 0 . 5 2 6 9 2 8 5 0 . 6 2 7 9 9 4 6 E - 0 1 0 . 1 3 9 3 1 1 3 E - 0 1 0 . 1 6 8 7 8 0 5 E - 0 1 0 . 7 9 8 3 5 3 1 - 0 . 3 9 9 1 8 6 1 0 . 1 1 8 3 4 8 4 E - 0 1 0 . 3 0 2 7 7 2 0 E - 0 2 0 . 3 0 2 1 8 7 8 E - 0 1 1 . 0 3 0 8 8 6 0 . 2 4 1 7 0 4 0 - 0 . 6 7 0 1 1 9 9 E ' - 0 1 0 .7783208E - 0 1 0.6809939E - 0 1 0 . 9 9 0 5 3 5 7 0 . 1 0 4 4 2 8 1 - 0 . 7 6 5 8 2 2 3 E - 0 1 - 0 •5135226E - 0 1 0.2960268E - 0 1 1 . 0 3 1 5 2 0 - 0 . 2 4 2 9 8 9 4 - 0 . 8 5 6 7 7 9 7 E - 0 1 0 .1740698 0.1292216E -02 1 . 0 4 5 0 3 0 1 5 . 0 5 0 1 2 - 0 . 6 5 3 1 4 6 5 E - 0 1 0 .2238095 - 0 . 1 1 3 1 7 4 1 E - 0 1 1 . 6 8 4 2 1 2 - 1 . 5 4 2 7 1 2 0 . 8 8 9 1 7 6 4 E - 0 1 0 . 2 1 0 1 1 3 3 - 0 . 8 4 6 1 7 2 4 E - 0 2 0 . 9 0 0 9 6 4 7 2 . 1 1 3 8 1 2 -0.1388695E - 0 1 - 0 . 9 2 4 9 4 3 3 E - 0 2 - 0 . 4 0 2 5 3 9 1 E - 0 2 2 . 4 2 6 3 4 7 0 . 9 7 8 2 7 0 7 - 0 . 1 0 6 7 5 8 2 - 0 . 4 0 1 0 4 2 7 E - 0 1 - 0 . 1 1 4 7 4 3 5 E - 0 1 2 . 2 4 1 6 7 8 - 0 . 7 5 6 0 6 3 3 0 . 1 5 7 5 6 4 2 E - 0 1 0 .3003987 0.1585416E - 0 1 1.029602 0 . 2 7 2 1 5 5 3 0.7558990E -02 - 0 .3016503E - 0 2 - 0 . 7 2 3 3 6 8 7 1 . 1 0 9 0 5 7 0 . 9 7 9 4 7 6 5 -0.3368667E - 0 1 - 0 . 1 4 2 0 8 2 4 E - 0 1 0 . 1 1 9 3 3 1 3 1 . 1 5 6 4 3 2 0 . 5 5 7 6 1 5 2 - 0 . 3 0 0 4 2 9 3 E - 0 1 - 0 . 1 4 9 9 9 7 3 0 . 3 2 7 2 1 9 4 E - 0 1 1 . 1 5 1 9 8 6 - 6 . 2 3 4 2 3 4 0.2083266E - 0 1 - 0 . 4 0 2 9 6 4 1 0 . 5 6 4 7 9 0 2 E - 0 2 1 . 4 1 7 4 1 9 - 0 . 4 8 4 4 2 4 7 - 0 . 1 4 2 8 4 6 4 - 0 . 1 2 7 8 1 9 2 - 0 . 5 4 3 0 3 2 6 E - 0 1 204 D. Girton-Roper Exchange Market Intervention (Figures 6.1(b) - 6.5(b): G-R) Canada Germany Japan U.K. U .S .A . - 0 . 3 7 1 5 4 6 6 - 0 . 7 4 3 6 4 8 7 0. 3770624 2 .835618 0 .5949190E - 0 1 18 .83932 - 1 . 4 3 9 7 1 3 - 0 . 1372269 -0.5257202 0 .9375579E - 0 1 . - 0 . 1 7 1 3 0 S 3 - 1 1 .12261 15 .76350 1.548160 - 0 . 6 0 8 8 7 2 1 - 0 . 5 9 8 4 6 7 1 - 1 . 1 1 8 4 9 5 0. 3957749E' - 0 1 0.9561856 - 0 . 1188538 - 0 . 4042170 - 0 . 9 4 3 8 6 1 0 - 0 . 7085628 0 . 6919601 - 0 . 6 7 7 3 6 2 9 3.491894 - 7 . 2 5 0 9 6 8 - 0 . 3129234E - 0 1 1.178498 0 .1990669 - 0 . 3674597 0 . 2 8 6 5 4 6 8 E - 0 1 0 . 1150257 1.213926 1.224C29 - 0 . 4 6 1 7 8 3 8 - -01 - 4 8 . 3 5 4 9 5 - 0 . 7411356 1.820856 - 0 . 2 1 1 1 8 6 2 - 2 . 260415 4 .879467 1 .799025 - 1 . 4 7 4 5 5 3 0 .8859020 -0 .5867262E -01 - 1 . 8 3 1 5 0 0 0 . 3426300 0 .1918094 - 0 . 2 1 0 2 0 6 9 - 0 . 1 8 3 8 7 1 2 2 .452350 - 0 . 5203354 - 0 . 7981170 0 .3843876 - 1 . 1 9 6 0 7 C 1 .670275 - 3 .648333 1.391866 0 .4216878 - 0 . 2 5 5 0 6 3 5 0 .3958693 - 0 . 4572130 - 3 . 1 3 0 5 3 0 0 .2974340 l.OOOOCO 1.908916. - 0 . 2601829 6.847447 - 1 . 5 3 4 6 7 4 0.38560E1E <-\ - 0.1293452 0 . 4199790E - 0 1 -0 .9374515E -01 0.8897926 • -1 .1823C1 0.594073.6 . - 0 . 1241341 1.653172 0 .7759295 -0 .1352675E - C l ' 0 .4872126 - 0 . 6905853E-- 0 1 0 .9268834 . 1.284528 -0.8088033 • C .1272264- -0 . 9078743E--01 1.0196C5 1.245163 - 0 . 2 1 0 3 3 5 5 1 .586871 - c . 5135775 1.39C326 1.644545 3.095134 - 1 . 6 6 8 2 5 7 3 .179661 0.1177290E 3.68E532 3.683963 2.339034 0. 8681599E--01 -12 .39003. 0-.5269805 2 .671690 0.747195C - 0 . 4917077E-- 0 1 - 0 . 6 2 4 8 9 7 7 - 0 . 3 8 3 1 8 7 7 - 0 . 4 1 9 6 6 7 6 5 .913095 0. 6362879 0 .9042658 1.552837 1.572554 0.7291377 -0. 2823004 0 .8443754 1.910000 -C.7675CC3 1 .245467 -0 . 2255574 0.4652642 3 . 442722 0 .2441525 1.796157 0. 4062559E - 0 1 0 .6590019 7 .167121 1.447899 0 .3048341 - 0 . 2413987 1.978808 - 0 .6691157E - 0 2 0 .5014966 1 .01C261 - 0 . 3903542 -0 .67624S5 1 .165701 0.7004234 3.221689 - 0 . 3078845 0.6730580 1 .053049 1.000000 1 .172271 - 0 . 9605605E - 0 1 0 .5793092 - 1 . 714925 2 . 5 0 2 4 2 1 18 .68832 - 0 . 8435958E - 0 1 3 2 . 8 4 7 6 1 , C.2243371 -0 .3734094 0 .3535521 - 0 . 9393349E - 0 1 0 .4290043 0 .1008420 0 .2824524 0 .6395415 0. 1351537 0 .1625282 - 0 . 1 5 5 4 6 9 6 0 .4958295 - 0 . 8 3 3 0 2 0 7 0. 2717280E - C l 0 .4004628E - C l - 0 . 3231304 1.137159 0 .3367517 - 0 . 1716051 0 .5369053 - 1 . 3 4 0 4 1 0 0 .9629598 0 .1566449 - 0 . 1988971 - 2 . 0 3 9 0 5 8 - 0 . 3 1 4 2 0 8 3 1 .140271 - 0 . 4 5 2 2 0 6 4 - 0 . 2255641 0 .7432653 - 0 . 1 0 2 4 4 6 1 E - 0 1 1.209674 2 .415664 - 0 . 1666443 0.796422C 0.8C63426E -01 - 1 . 5 7 3 6 4 0 - 2 8 . 8 0 0 0 4 0. 1854107 0 .7851309 0 .6170373E - 0 1 0.6932323 1.494307 - 0 . 3299761E - 0 1 - 0 . 1440225 0 .3046484E - 0 1 - 0 . 7317552 0 .9862474 - 0 . 2902638 - 1 . 1 2 6 0 9 9 0.8164955E - 0 1 - 0 . 8130784 -2 . ie2831 0. 3599164E - 0 1 0 .8550367 - 0 . 1 4 4 5 0 1 4 1.130897 0 .3732830 0. 1745332E -01 -0 .4309209E - 0 1 0 .7668823 1.655266 0.9870164 - 0 . 8225547E - 0 1 - 0 . 2 3 8 2 9 6 0 17 .13564 2 .195728 0.6675324 - 0 . 7298732E - 0 1 2 .263101 - 0 . 3 6 0 7 8 5 8 2 .132814 3 .683045 0 . 4727393E - 0 1 1.339504 -C .4659032E - C l - 5 . 3 8 9 1 6 0 - 1 . 0 8 2 5 7 1 - 0 . 4114441 2 .795943 0 .2875646 E. Holden, Holden, and Suss Inverse Flexibility Index (Figures 6.1(b) - 6.5(b): HHS) Canada Germany Japan U.K. U .S .A . 0 .4400646 0.7009290 - 4 . 7 0 5 7 4 3 2 .956047 - 0 . 4525184E - 0 3 2 .027779 1.011438 0 .9043607 0.6889867 - 0 . 7823846E - 0 3 0 .2316499 1.320925 6 .766832 4 .762098 0 . 2423147E - 0 2 0 .6236972 0.7606087 - 0 . 2 5 2 3 0 1 4 -33 .84062 0. 6439935E - 0 3 0 .4192863 0 .6215770 2.073199 -2 .937158 0. 2106974E - 0 2 2 .087165 1.180194 0 .1506214 9.041204 - 0 . 1323806E - 0 2 0 .3587171 -0 . 3829133E-01 - 0 . 5 7 2 9 1 8 9 7.535362 0 . 2691318E - 0 1 0.7098206E - C I 1 .582516 2 .497284 3 .247060 0 . 9314834E - 0 3 1.044705 1.814335 12 .81309 0 .8392646 - 0 . 4292825E - 0 1 0.1000536 1.048674 -3 .010338 -0.3626924 0. 9977297E - 0 3 0 .2615622 2 .474300 1.756238 0 .6476086 • - c . 3292725E - 0 2 0.9626474 3 .327310 4 .683803 5 .123260 - 0 . 3898374E - 0 2 0.3229606 - 0 . 9 1 2 2 7 1 4 1.705232 0 .9845569 - 0 . 2060264E - 0 2 O.OOOO0C0E + 00 3 .117340 1.128414 1.576906 0 . 2996357E - 0 2 -0 .7211557E - 0 1 -C .2009810 - 0 . 2 2 1 1 7 8 1 0 .1059039 - 0 . 3792986E - 0 1 0.9797534 - 2 . 1 1 9 5 2 5 . 0 .6469949 3 .042346 - 0 . 1703973E - 0 1 0.21292C2E r -- V - - 1 . 32C952. 0.35S7SEE - 1 4 . 8 2 5 5 7 0 . 2032696E — c-1 0.8687353 - 0 . 2 2 0 7 5 4 4 0 .4697976 63 .73416 0 . 2419461E n -w * 0.3119642 3 .781793 . 1 .852410 4 .708773 . c. 1C15047E - 0 1 • 2 .755451 0 .9999790 9.680760 - 0 . 1 6 0 2 5 2 2 E - 0 1 0 . 6480927E - 0 2 2 .089954 2 .616254 - 0 . 6 0 8 9 4 7 9 1.163622 - 0 . 4579427E - 0 2 2 .964665 - 4 . 9 3 1 5 1 5 0 .3401080 0.5256352 0. 1222775E - 0 2 0 .4719169 1.815823 - 1 2 . 0 6 0 9 2 - 1 2 . 6 7 7 5 0 0 . 1153095E - 0 1 4 .402965 - 4 . 4 1 8 0 6 6 1 .705151 - 8 . 2 2 5 9 0 4 0 . 8937525E -02 0 .6640743 7 .474382 1 .176121 - 1 . 0 8 8 7 1 0 0 . 5293651E - 0 2 -0 .547366 ' : 3 .450165 - 0 . 2 4 6 2 0 5 6 -2 .582464 0 . 4314575E -02 5 .089266 - 0 . 5 9 4 7 5 8 2 0 .9618283 2 .503383 0 . 2390853E -04 - 1 . 6 1 8 3 6 3 133.8527 1.423334 0 .4884947 0 . 2405597E-- 0 1 - 3 . 4 7 2 2 2 2 1.861625 . 1.064154 - 2 . 4 6 4 0 6 7 0 . 6493242E - 0 1 0.000C00CE + 00 9.607292 0 .4158503 - 1 . 8 2 7 6 9 7 0 . 2232081E' -02 2 .459402 1.370562 0 .3338454 1.342345 - 0 . 9903236E--03 0 .4147216 - 0 . 7 4 1 4 7 0 2 0 .4189329 - 1 . 0 6 2 0 7 3 - 0 . 3818845E--03 - 0 . 5 4 7 9 9 8 2 - 2 . 1 6 0 9 5 9 - 0 . 6 7 9 2 2 1 1 - 0 . 2 6 0 4 5 8 2 0 . 4405225E--03 - 1 . 6 8 2 6 4 0 0 .5648561 - 0 . 1 2 3 1 2 8 3 - 0 . 5 3 2 9 3 0 0 E - 0 1 0 . 8795300E--03 13 .19763 - 0 . 5 6 8 1 3 9 3 0 .6090361 - 1 . 3 8 4 9 3 4 0 . 2001138E--02 - 2 4 . 3 6 6 3 3 - 0 . 2 2 1 2 2 0 3 0.7988153 0.9187002 0 . 9240004E--03 6.337025 0 .3557281 0.8529514 - 3 . 8 1 4 8 1 9 0. 3804302E--04 5 .459464 2 .174802 0 .6704140 -5 .618115 - 0 . 3500965E--03 0 .5793552 1 .136331 - 1 . 0 2 2 2 9 9 - 4 . 9 4 0 3 6 3 - 0 . 2793053E--03 - 2 . 2 5 6 9 5 0 3 .948671 0 .1755354 0.1734392 - 0 . 1429176E--03 0 .3666431 - 9 1 . 1 1 6 0 5 1.156644 0.7295960 - 0 . 3814983E--03 0 .4539623 0 .9349940 - 0 . 1 8 6 3 9 0 9 - 8 . 5 2 0 7 1 6 0. 5610985E--03 7 .484335 - 0 . 7 1 3 9 0 4 3 - 0 . 8 0 0 1 4 8 5 E - 0 1 0.5430124E- - 0 1 - 0 . 1399771E--01 2 .145593 - 9 3 . 7 7 8 6 9 0 .3732763 0.2538103 0 . 4305008E--02 1.367250 - 2 . 4 1 8 1 9 7 0 .3180445 2 .364662 0 . 1035438E--02 1.647633 1.688394 - 0 . 2 2 2 1 7 1 1 5 .538405 0 . 1742907E--03 0 .7247502 0.5741384 1 .273071 1.916652 - 0 . 1636460E--02 206 Appendix 6.5 Interdependent Economies Final Estimation Results Estimates of &2 were obtained for Germany, Japan, and Australia using 2SLS-A to instrument list for Japan only. For Canada, U.K., U.S.A., France and Italy, estimates of 1973(1) - 1978(IV) and 1979(1) - 1984(IV) in order to allow the correlation coefficient to differ between the two sub-samples. Estimates were obtained using 2SLS-A in both periods for all countries except France, for which 2SLS was employed over the second sub-sample. Estimates of f$ were obtained for all principle countries using 2SLS-A to estimate equation (6.6'), with exogenous dummy variables included in the instrument list for Germany, Japan, and U.S.A. In general, 2SLS was employed whenever the correlation coefficient, p, estimated by the Cochrane-Orcutt method, was not significantly different from zero. In some cases, however, 2SLS-A was employed even though p* was not significantly different from zero because the autocorrelation correction yielded better t-statisics for the coefficients of interest. estimate equation (6.5'). Exogenous dummy variables were included in the &2 were obtained on the basis of separate estimation of equation (6.5) over the periods £ajiad_2.: 1973(1) - 1978(IV) mt = - 9.6537 + 1.8238 y M - 0.27958 i t + 0.84491 pt (-1.8963) (1.5277) (-1.4596) (1.9119) (6.5) R 2 = 0.9230 p = 0.9061 (10.2117) Pt = 0.43459 + 0.40341 p*t - 0.33890 ^ + 0.04343 4 - 0.05374 i* t (5.5369) (4.0768) (-2.1546) (1.0614) (-1.4840) (6.6') R 2 = 0.5714 p = 0.9967 (83.6668) 1979(1) - 1984(IV) m, Pt = - 11.254 + 2.6412 y t . j + 0.18044 i t - 0.08683 pt (-0.8206) (0.9768) (0.7370) (-0.1555) R 2 - 0.1206 p = 0.8452 (7.7465) 0.43459 + 0.05882 p*t + 0.00282^ + 0.04343 i t - 0.05374 i* (5.5369) (0.8917) (0.0167) (1.0614) (-1.4840) R2 = 0.5714 p = 0.9967 (83.6668) 207 (6.5) (6.6') Germany: 1973(1) - 1978(IV) m t = - 15.5040 + 2.6672 y M (-7.4914) (6.7934) R 2 = 0.9645 p t = 2.8186 + 0.15887 p*t (13.8520) (2.8838) R 2 = 0.9640 1979(1) - 1984(IV) m t = - 15.5040 + 2.6672 y M (-7.4914) (6.7934) R 2 = 0.9645 0.17732 i t + 0.39857 pt (-5.8796) (2.2910) p = 0.3097 (2.2328) + 0.27014 e. - 0.055921 t (3.3815) p = 0.2557 (1.8130) - 0.17732 i t + 0.39857 pt (-5.8796) (2.2910) p = 0.3097 (2.2328) 0.04772 i* (-3.6177) (-1.9735) (6.5*) (6.61) (6.5') Pt = 4.9803 + 0.42968 p*t - 0.42388 et (10.4967) (29.3842) (-4.6774) 0.05592 ^  (-3.6177) 0.04772 i* t (-1.9735) (6.61) R 2 = 0.9640 p = 0.2557 (1.8130) Japan: 1973(1) 1978(IV) m t = -0.44186 + 0.69327 y M (-0.2286) (3.4117) R 2 = 0.9758 - 0.05227 i t + 0.67453 pt (-1.3602) (4.8927) p = 0.2163 (1.5186) 208 (6.5') pt = 2.3101 + 0.41793 p*t (2.3306) (7.9878) R 2 = 0.9367 1979(1) - 1984(IV) 0.12707 - 0.11048 i t + 0.03855 i* t (0.5783) (-1.2180) (0.45752) p = 0.7732 (8.3581) (6.6') m t = -0.44186 + 0.69327 y M (-0.2286) (3.4117) (-1.3602) R 2 = 0.9758 0.05227 i t + 0.67453 pt (4.8927) p = 0.2163 (1.5186) (6.5') Pt 2.3101 + 0.41793 p* (2.3306) (7.9878) R 2 = 0.9367 t United Kingdom: 1973(1) - 1978(IV) m t 9.9970 (8.4702) R 2 = -0.0016 0.14643 y M (-0.3090) .+ 0.12707 e, - 0.11048 i t + 0.03855 i* t (0.5783) (-1.2180) (0.45752) p = 0.7732 (8.3581) 0.08203 i t + (0.2448) 0.06344 pt (0.3174) p = 0.9875 (30.6452) (6.6 1) (6.5) pt = 3.3897 + 0.37780 p*t - 0.32080 ^ + 0.33577 i t - 0.07629 i* t (2.2824) (2.2391) (-1.0966) (1.0921) (-0.7469) (6.6') R2 = 0.4027 p = 0.9895 (46.9531) 209 1979(1) - 1984(IV) mt = 7.9199 .+ 0.42047 y M - 0.10190 i t + 0.23767 (6 .5) (5.7905) (1,8274) (-0.7390) (1.8987) R 2 = 0.9993 p = 0.9783 (23.1382) p t = 3.3897 .+ 0.37780 p*t - 0 .32080^ + 0.33577 4 - 0.07629 i * t (6.6*) (2.2824) (2.2391) (-1.0966) (1.0921) (-0.7469) R2 = 0.4027 p =0.9895 (46.9531) United States: 1973(1) - 1978(IV) mt = - 1.8426 + 0.63538 y M + 0.010546 i t + 0.61272 pt (6.5 ' ) (-1.3688) (2,7867) (0.2846) (6.4700) R 2 = 0.9679 p = - 0.4488 (-2.4602) pt = -0.85122 + 0.9671 p*t + 0.14209 e t + 0.10085 ij + 0.03477 i * t (6.6 ') (-5.4699) (39.4380) (3.3789) (4.2971) (1.2211) R 2 = 0.9967 p = 0.22073 (1.5515) 1979(1) - 1984(IV) mt = - 5.2524 + 1.0141 y M - 0.19266 i t + 0.80454 ^ (6.5") (-2.7533) (3.9134) (-4.1633) (12.0990) R2 = 0.9637 p = 0.1330 (0.6575) pt = -0.85122 + 0.9671 p*t + 0.14209 e t + 0.10085 iy + 0.03477 i * t (6.6 ' ) (-5.4699) (39.4380) (3.3789) (4.2971) (1.2211) R 2 = 0.9967 p = 0.22073 (1.5515) Australia: 1973(1) - 1984(IV) m t = -3.5971 + 2.3705 y M (-0.7426) (1.8059) R 2 = 0.9599 0.40951 4 + 0.58921 pt (-3.2929) (1.9422) p = 0.5887 (4.9927) France: 1973(1) - 1978(IV) mt = 0.22531 + 0.23121 y M (0.0326) (0.2106) R 2 = 0.9683 0.03030 i t + 0.97510 pt (-0.4190) (2.6022) p = -0.0768 (-0.3773) 1979(1) - 1984(IV) m, - 1.3638 + 0.42203 yt.j (-0.1922) (0.4422) R 2 = 0.9741 0.12741 i t + 1.0409 pt (-2.8140) DW = 2.0712 (9.2946) Italy:. 1973(1) m t = - 1978(IV) 5.3502 - 1.7475 y M (2.7609) (-1.5414) R 2 = 0.2796 0.02871 i t + 0.82209 pt (-0.3752) (0.9794) p = 0.8265 (7.1938) 1979(1) - 1984(IV) m t = - 11.3960 + 3.8763 y M (-14.1570) (6.0200) R 2 = 0.8172 0.76878 4 - 0.84603 pt (-6.6067) (-1.7461) p = 0.0712 (0.3496) Interdependent Economies Quarterly Elasticity Measures Canada Germany Japan U.K. U.S.A. - 6 . 850346 0. .8375503E-- 0 1 0 .4564076 - 0 •5637491E. -04 0 . 8 4 2 3 8 8 3 - 6 . 822942 0. .8806423E--01 0 .4559270 - 0 .5775023E--04 1.278898 - 6 . 845749 0. .8425448E-- 0 1 0 .4566289 - 0 .6956213E--04 2.331466 - 6 . 874115 0. .8482211E-- 0 1 0 . 4 5 7 1 7 9 7 - 0 . 7 0 5 3 9 9 3 E - -04 2.149693 - 6 . 945656 0. 8716728E--01 0 .4579520 - 0 .6600318E--04 3.037438 -6. 904917 C. 7750787E--01 0 .4556093 -0 .7142487E--04 18.72782 -6. 894237 0. .7931302E--01 0 .4567066 - 0 .6831157E' -04 2.121256 -6. 894265 0. .8276988E--01 0 .4546287 - 0 •7448452E--04 55.90512 -6. 903344 0. .8008404E--01 0 .4559744 - 0 . 7 6 9 7 8 4 2 E - -04 - 1 . 8 5 3 3 9 1 -6. 89406S c. 630686CE--01 0 .4554023 -0 .7964484E' -04 -1.913470 -6. 931925 0. .8475918E--01 0 .4560221 -0 .7702414E' -04 -1.956939 -6. 966449 0. 8810880E--01 0 .4558761 - 0 .8223271E' -04 -1.241922 -6. 987071' G. .8705941E--01 0 .4561984 -0.7778205E' -04 -0.9095507 -7. 094625 0. .8186516E--01 0 .4541965 -0 .9068528E--04 -0.6638645 -7. 052£C: r v . ,7 64'5094'E-01 0 .4544631 -0 .87C9540E' -C4 -0.6325757 -7. 152707 0. .7573356E--01 0 .4531803 -0 .1000679E' -03 -0.6412163 -7. 094919 0. .7422406E' -01 0 .4522858 -0 .9404470E' -04 -0.6345041 -7. 106764 0, .7208940E' -01 0 .4507970 -0 .9693732E' -04 -0.5684161 -7. 051296 0. .7166861E--01 0 .4511517 -0 .9341207E' -04 -0.5757377 -6. 979905 0. .7162020E' -01 • 0 .4486392 -0 .9386481E' -04 -0.5129525 -6. 929485 0, .6511458E' -01 0 .4489837 -0 .9269774E -04 -0.4442965 -6. 980850 0, .6665948E' -01 0 .4455403 -0 .1013003E -03 -0.4072761 - 6 . 925055 0, .6897986E -01 0 .4432321 -0 .9725677E' -04 -0.3632571 4. 273501 0, .2598752 0 .4437247 -0 .6124438E -03 -0.4736890E -Cl 4 . 272356 0, .2661843 0 .4465370 -0 .5852932E' -03 -0.4324986E< -01 4 . 283739 0, .2676939 0 .4475578 -0 .5827526E--03 -0.3270010E -01 4 . 274C2E 0, .2691219 0 .4488912 -0 .5359182E--03 -0.3157270E' -01 4. 277321 0, .2748160 0 .4508477 -0 .5587583E--03 -0.2989189E' -01 4 . 271878 0, .2759832 0 .4518837 -0 .5328506E' -03 -0.2964535E' -01 4. 279996 0, .2778966 0 .4517897 - 0 .5233661E' -03 -0.2550530E' -01 4 . 270398 0 .2821269 0 .4530156 - 0 .5213469E - 0 3 -0.2644846E T O I 4 . 265469 0 .2842931 0 . 4 5 3 0 2 0 2 - 0 .5059345E - 0 3 - 0 . 3 0 3 9 2 1 7 E ' - 0 1 4 . ,270872 0 .2933980 0 .4525636 -0 .4889678E' -03 -0.2585467E' -01 4 . , 2 8 6 6 6 2 0 .2938045 0 .4523538 - 0 .5278349E -03 - 0 . 2 0 0 1 6 8 2 E ' - 0 1 4 . ,295780 0 .3166443 0 .4542061 - 0 • 5 8 3 5 0 6 1 E - 0 3 - 0 . 1 5 0 0 6 2 5 E ' - 0 1 4 . ,223333 0 .3053258 0 .4529160 - 0 .5487187E' -03 -0.4212865E' -01 4 . ,216628 0 .3042972 0 .4529610 - 0 .5398066E--03 -0.4137701E. -01 4 . .221932 0 .2961683 0 .4518657 - 0 .5589915E -03 - 0 . 3 8 3 8 0 8 0 E ' - 0 1 4 . ,219480 0 .2894989 0 .4520069 - 0 .5646324E -03 -0.3446605E' - 0 1 4 . ,225031 0 .2834772 0 .4512988 - 0 .5904852E -03 -0.3415544E' -01 4 . ,227259 0 .2781293 0 .4497010 - 0 . 6 1 9 1 1 7 6 E -03 - 0 . 3 7 6 6 3 6 2 E ' - 0 1 4 . .230384 0 .2657165 0 .4480290 - 0 . 6 1 3 9 1 5 1 E ' -03 -^0.3447186E-01_ 4 . .230594 0 .2708818 0 .4497103 - 0 .6246763E -03 -0.3114468E. -01 4 . .231048 0 .2737288 0 .4512166 -0 .6409560E -03 -0.3312603E' -01 4 , .228001 0 .2754814 0 .4504013 -0 .6167560E -03 -0.3387254E--01 4 , .232355 ' 0 .2771362 0 .4496247 -0 .6263281E' -03 -0.3175186E' -01 4 , .234952 0 .2793202 0 .4497166 -0 .6471849E -03 -0.2885785E' -01 Appendix 6.6 Interdependent Economies A. Exchange Market Pressure (Figures 6.6(a) - 6.10(a): INT) Canada Germany 3280 .014 - 3 3 . 3 6 8 4 0 - 1 0 . 8 9 4 1 7 4 .937547 10 .07494 - 2 . 7 2 0 1 4 5 26 .46018 -0.75631.86 2 .143094 • 2 .219364 - 6 . 7 3 4 8 9 9 - 2 . 8 0 0 2 0 0 - 4 . 8 0 8 3 4 1 - 0 . 2 6 9 4 9 1 5 - 2 2 . 3 1 3 7 5 - 2 .377194 - 1 8 . 8 2 0 1 5 - 1 . 8 1 1 8 5 6 8 .248925 - 1 . 8 7 1 9 7 3 14 .41200 - 0 . 4 0 0 8 1 3 4 21 .12990 5 .754611 .18.37145 - 2 . 4 1 3 2 3 0 - 0 . 4 8 4 1 0 0 4 2 .016745 - 1 0 . 0 2 3 0 5 - 1 . 1 1 4 6 2 6 - 2 8 . 5 8 0 2 6 - 0 . 6 8 2 0 3 1 1 - 1 7 . 6 1 8 5 4 - 0 . 9 8 4 4 4 6 4 - 1 4 . 3 3 6 9 8 - 0 . 3 9 5 5 5 8 1 - 2 8 . 4 9 2 6 6 4 .898785 - 2 1 . 0 0 5 0 9 2 .064032 - 1 4 . 6 3 5 3 7 - 1 . 9 5 4 8 4 7 - 2 9 . 5 6 6 0 2 . 2 .926133 - 2 9 . 5 7 2 9 0 5 .377139 0 .5121620 - 4 . 5 4 9 9 9 4 - 1 2 . 8 8 8 9 4 - 1 . 1 8 5 9 0 1 7 . 8 6 7 1 7 1 3 .770053 0 .2924065 - 2 . 3 7 4 9 0 6 - 5 . 6 9 9 2 0 8 - 4 . 7 9 4 9 0 1 3 .357470 - 1 . 9 7 7 9 6 3 - 0 . 8 4 7 2 ; : 6 - 0 . 9 0 8 4 9 6 5 2.5:;:o6 -3.10.4805 - 4 . 5 2 5 2 4 2 2 .970637 - 1 1 . 8 9 3 2 2 2 .995340 - 5 . 8 0 7 6 3 2 - 0 . 2 3 9 6 9 8 6 1.456790 - 4 . 1 8 3 8 3 1 - 6 . 0 7 2 8 4 4 0 .3365074 - 5 . 9 9 2 2 8 2 0 .1397281E-( 2 .539893 0.7003119 - 9 . 0 8 3 0 7 4 1.012453 4 .240444 4 .530578 - 4 . 1 8 4 5 4 8 - 5 . 0 3 8 1 7 1 - 5 . 2 9 1 4 5 0 - 0 . 9 8 9 8 1 0 5 - 1 . 3 3 1 9 7 0 0 .2663965 1.981060 2 .349560 6 .544360 - 0 . 2 1 0 8 8 4 5 - 1 . 9 8 5 0 5 7 - 2 . 2 8 2 4 1 1 - 2 . 7 7 7 6 8 2 - 0 . 3 7 0 5 9 9 5 Japan U.K. U . S . A . - 2 0 6 . 8 2 8 7 0 .2706414 - 3 9 2 . 9 0 4 1 0 .8134401 - 2 . 1 0 3 7 7 7 4 .728035 - 1 . 1 0 0 0 9 1 - 3 . 8 3 5 5 5 5 - 6 . 0 1 8 3 9 4 1.570562 - 4 . 2 8 6 3 7 4 . - 9 . 8 8 6 6 3 1 0.7410233E - 0 1 - 4 . 0 6 9 9 7 5 1 0 . 1 4 8 6 1 2 .289404 - 3 . 9 4 4 1 5 5 - 4 8 . 2 5 6 5 7 0 .9409831 - 1 0 . 1 9 1 1 3 - 0 . 9 7 4 4 7 8 0 0.2663947E - 0 1 - 3 . 8 3 3 9 4 8 301 .4055 0 .2509505 - 1 . 9 0 1 2 3 2 - 0 . 5 1 2 1 4 4 6 - 1 . 4 7 6 7 6 5 1.004682 9 .712232 0.1072179 - 1 . 1 8 5 3 2 5 1 .811354 0.3552696 - 3 . 8 9 4 5 7 3 0 .3703536 0.3357887 . • - 6 . 5 1 6 5 2 9 0 .7034497 0.7148333 - 3 . 0 2 2 1 2 0 - 0 . 6 3 1 8 6 4 3 0.6538713 - 0 . 6 4 0 3 4 8 1 - 1 . 9 2 0 3 8 5 - 1 . 0 0 9 7 6 3 8 .871195 - 1 . 1 5 8 6 9 7 ' - 1 . 3 3 5 2 2 4 4 .661990 - 2 . 7 4 2 2 9 4 . - 1 . 1 7 6 0 1 8 12 .38300 - 2 . 7 7 1 1 4 3 0.7424824 8 .164920 - 5 . 8 3 7 1 1 0 1 .705491 - 0 . 3 0 6 4 1 2 9 E - 0 1 - 6 . 0 3 5 9 8 3 - 4 . 0 6 0 6 9 0 - 5 . 5 2 7 1 2 4 0 .8583390 - 4 . 6 9 7 3 5 2 0 .3544171 - 3 . 3 0 1 4 9 7 1.473726 - 0 . 6 7 4 7 5 8 6 - 5 . 8 7 4 1 4 9 1.297078 - 1 1 . 4 9 9 7 1 2 .354490 1.891530 - 4 . 5 5 9 1 7 0 2 .819317 • 1 . 0 8 5 0 1 4 - 9 . 6 0 5 1 3 6 - 2 . 3 0 5 9 2 8 2 .320154 - 6 . 0 4 6 4 9 8 0 . 5 8 1 5 2 7 9 E -0.3614776 1.953339 2 . 1 0 5 5 6 1 - 1 . 1 8 1 3 0 6 - 3 . 5 6 1 4 5 9 - 1 . 9 7 3 0 3 0 - 1 . 5 7 0 3 8 4 - 3 . 0 1 2 9 8 4 - 1 . 7 2 5 5 8 2 - 2 . 6 5 0 7 1 1 3 .585447 - 0 . 7 1 6 0 5 6 9 - 2 . 2 7 4 1 2 7 - 1 . 2 5 6 9 9 2 - 0 . 3 4 1 5 0 8 0 1.524633 0 .7711482 1.094166 0 .9514311 0 .3206682 1 .385965 0.3090632 1.025113 - 2 . 0 3 1 9 8 8 0 .4698936 1.069743 1 .097655 0.7618687 2 . 6 6 5 5 3 1 0 .1843605 0.9867839 - 4 . 9 3 8 4 0 8 - 0 . 2 3 1 7 8 6 9 0.9168807 9 .365795 - 0 . 5 1 5 7 0 5 3 E -- 3 . 6 7 2 4 4 2 - 1 . 2 7 6 5 6 6 - 0 . 7 6 0 5 6 4 6 E -•0.2684264 2 .421425 - 0 . 1 4 6 0 9 7 9 •0.2000303 - 4 . 1 4 9 0 7 5 0 .5591344 - 2 . 0 0 7 0 7 0 - 0 . 8 6 2 3 3 1 0 E - 0 1 - 1 . 0 5 0 2 1 7 •0.7621583 - 0 . 3 5 7 6 2 7 5 0 .7184149 •0.4007847 - 4 . 2 8 6 6 7 2 0 .2767766 1.218760 - 8 . 7 9 3 4 9 8 0 .4415467 •0.1540902 - 5 . 9 8 1 9 3 6 - 1 . 0 0 7 4 1 2 B. Exchange Market Intervention (Figures 6.6(b) - 6.10(b): INT) 213 Canada . Germany Japan U.K. U.S.A. - 0 . 1 5 1 1 9 5 5 E - 0 3 - 0 . 6 9 3 3 5 2 7 E - 0 1 0.1088844E--01 0.9001773 - 0 . 7 9 2 1 8 5 7 E --03 0.1340343 1 . 1 7 5 4 0 9 -0.3599248 0.9998324 0 . 7 4 8 4 0 0 1 E ' -01 0 . 2 0 9 1 7 3 0 E - 0 1 1 . 1 0 1 1 1 5 1 . 7 4 7 2 1 8 0 . 9 9 9 9 7 5 4 -0 . 1 9 3 7 7 5 1 0 . 5 1 6 5 2 0 4 E -01 1 . 1 9 1 4 1 0 0.8268338E--01 1.000003 -0.5198435E' -01 0 . 3 9 7 9 5 2 2 E - 0 1 1 . 2 1 8 7 9 7 -9 . 5 9 1 1 2 6 1.000029 - 0 . 1 5 3 3 3 5 4 0 . 1 6 8 7 0 5 1 1 . 0 9 6 7 2 8 - 0 . 7 1 3 5 0 2 0 E --01 0.9999892 0.1309916E -01 0 . 3 7 5 1 4 8 4 E -01 0 . 2 7 2 5 2 4 7 0 . 2 2 1 5 4 4 4 0.9999880 1.634640 0 . 6 3 6 1 7 0 2 E - 0 2 1 . 0 9 2 2 7 7 -14.69497 0.9999664 - 0 . 3 1 2 8 6 6 9 E -02 0.9126287E -01 1.068001 1.253947 0.9998708 1;313549 0.7974846E - 0 2 1 . 1 4 7 3 4 7 0.5336934 1 . 0 0 0 3 3 6 0.8322058E -01 0 . 2 1 9 1 4 5 2 E -01 1.052850 -3.008221 0.9998265 -0 . 4 6 8 5 7 7 5 0 . 7 2 5 1 1 6 0 E - 0 1 1 . 0 4 2 7 5 1 2.385671 0.9999768 - 1 . 4 2 2 0 7 0 0.2826586E - 0 1 0.8827215 -2.202744 0.9998974 - 0 . 8 7 0 7 4 5 7 1.000000 1 . 0 4 0 5 6 1 -0.8334179 0.9999226 0 . 4 7 7 0 1 1 6 - 0 . 5 6 8 6 8 1 7 E ' - 0 2 0 . 6 5 4 4 1 9 2 0.8797683E--01 0.9989850 1.085068 0 . 7 0 4 1 0 0 1 E - 0 1 0 . 9 5 0 7 9 7 9 - 0 . 3 2 2 1 7 4 0 0 . 9 9 9 9 6 0 5 1 . 2 2 0 8 9 7 0 . 1 8 7 7 8 3 6 E - 0 2 0 . 9 2 7 5 4 0 3 -0.1666223 1.000007 0 . 8 7 6 7 7 3 8 0.5919411E - 0 1 0 . 6 6 9 1 0 5 1 - 0 . 2 2 6 4 3 8 5 0 . 9 9 9 9 9 8 1 0 . 8 9 9 3 4 7 8 0.2405308E - 0 1 1 . 0 2 7 2 2 7 - 3 . 0 3 3 9 7 3 0 . 9 9 9 9 7 3 8 0 . 7 9 1 3 8 4 5 0 . 1 7 4 67 9 1 1 . 1 2 9 3 7 1 . 1 . 4 4 4 1 3 2 1 . 0 0 7 9 4 2 0 . 7 2 7 8 6 2 6 0 . 1 6 5 3 3 0 3 1 . 0 3 8 7 2 C 0 . 1 7 4 7 4 3 1 0.9998998 1.663346 0 . 1 8 6 2 9 0 7 0 . 9 7 7 9 4 4 0 - 0 . 1 1 7 5 5 5 5 0.9997367 0 . 4 0 4 8 3 5 5 0 . 4 0 9 3 9 4 3 E -01 1 . 0 6 0 7 9 9 0 . 7 9 7 8 5 6 4 1.000010 0 . 8 8 5 4 8 4 1 - 1 . 7 9 8 7 3 6 0 . 9 1 1 9 6 0 1 - 0 . 9 8 4 6 9 5 7 1 . 0 0 0 1 1 3 0 . 9 7 7 9 2 9 7 - 0 . 1 1 4 9 7 4 7 1 . 0 5 5 3 7 0 - 0 . 7 0 1 1 4 3 6 1 . 0 0 0 6 7 3 0 . 9 7 0 2 2 6 5 0 . 7 0 1 1 8 3 6 E -01 1 . 1 3 4 6 3 2 0 . 8 6 4 3 7 2 2 E -01 1 . 0 0 0 3 0 2 0 . 9 7 2 6 2 0 5 - 3 . 1 0 4 1 8 1 0 . 6 1 9 6 8 4 2 - 0 . 7 6 4 2 7 2 5 0 . 9 9 9 7 3 5 0 0 . 1 7 8 1 5 1 6 0 . 1 9 0 4 1 1 2 1 . 0 0 2 7 9 9 - 1 . 6 5 0 6 6 0 0.9986169 0 . 9 9 5 7 6 8 9 0 . 3 5 3 7 1 7 3 1 . 2 3 5 0 6 3 - 1 . 0 8 7 4 4 2 1.000259 0.9985088 1 . 0 0 0 0 0 0 1 . 0 4 2 5 7 7 - 0 . 2 4 0 6 6 3 1 1.000380 0 . 9 6 1 1 8 9 3 - 0 . 6 3 9 4 3 0 6 1 . 3 6 4 3 1 3 - 0 . 2 0 7 3 3 6 8 0 . 9 9 9 4 9 4 8 1 . 1 0 0 6 5 2 - 0 . 6 8 0 8 0 4 6 E -01 0 . 6 5 7 9 7 6 0 - 0 . 2 3 3 8 7 4 6 1 . 0 0 0 6 7 4 1 . 3 7 1 7 2 7 0 . 8 4 3 8 9 5 6 E -01 0.8581002 0 . 2 5 6 6 7 7 1 1.002526 0 . 8 3 8 8 1 7 0 0.1866099 2 . 8 2 8 8 7 2 0 . 5 8 1 5 6 6 2 E ' -01 1 . 0 1 2 8 1 5 . 0 . 9 2 4 2 4 5 7 2 . 0 7 5 2 7 6 0 . 6 1 5 8 9 7 9 - 0 . 4 7 5 9 6 0 3 1 . 0 0 0 5 0 4 0 . 9 7 4 4 6 7 5 0 . 8 6 0 2 5 2 0 0 . 3 7 8 2 3 8 7 -0 . 5 7 8 0 1 6 9 0.9991828 0 . 8 5 0 1 9 0 2 2 . 0 7 7 7 5 1 43 . 88637 - 0 . 6 8 4 4 2 2 3 1.000186 0 . 1 9 6 8 3 9 4 3 . 7 3 6 4 70 1 . 2 1 0 0 3 3 -0 . 4 6 2 9 2 5 8 1 . 0 0 0 1 4 1 1 . 7 7 8 1 1 1 - 0 . 1 6 9 4 6 7 7 1 . 4 2 7 6 5 6 0 . 3 3 4 9 1 1 7 1 . 0 0 0 1 5 5 2.101313 0 . 3 4 8 4 7 4 3 1 . 1 0 3 4 7 6 - 0 . 7 6 1 7 2 9 9 E -01 0.9953315 - 1 1 . 4 9 5 9 2 - 0 . 1 1 1 0 6 0 1 0 . 9 9 6 1 3 6 7 -1.001016 0.9988325 1.734967 - 0 . 1 1 8 5 7 7 4 1 . 6 3 2 5 1 1 0 . 7 6 9 2 2 4 2 E -01 1 . 0 0 0 1 0 4 0 . 7 8 5 5 2 8 0 1.959532 0.6873833 0.3799861E -01 0.9851043 1.009558 - 1 . 4 8 1 6 2 6 0.9964122 - 0 . 2 0 2 5 6 1 7 0.9966804 0 . 9 6 9 7 5 0 7 - 0 . 7 6 7 7 8 7 6 0 . 8 7 9 3 4 9 1 - 0 . 1 7 7 8 9 3 1 0.9996559 0 . 8 8 6 7 1 5 1 -0.8013089 1.252960 0.9938950E -01 0 . 9 9 9 8 4 1 3 0 . 5 8 3 6 8 1 3 - 0 . 2 4 8 7 0 8 0 2 . 1 6 1 3 9 5 - 1 . 8 4 2 5 1 5 0 . 9 9 9 5 8 4 5 1 . 0 7 6 9 9 2 214 BIBLIOGRAPHY Aizenman, Joshua. 1983. 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