امور مالی بین المللی در توازن کلی

Our purpose in this paper is to unify international trade and finance in a single general equilibrium model. Our model is rich enough to include multiple commodities (including traded and nontraded goods), heterogeneous consumers in each country, multiple time periods, multiple credit markets, and multiple currencies. Yet our model is simple enough to be effectively computable. We explicitly calculate the financial and real effects of changes in tariffs, productivity, and preferences, as well as the effects of monetary and fiscal policy. We maintain agent optimization, rational expectations, and market clearing (i.e. perfect competition with flexible prices) throughout. But because of the important role money plays, and because of the heterogeneity of markets and agents, we find that fiscal and monetary policy both have real effects. The effects of policy on real income, long-term interest rates, and exchange rates are qualitatively identical to those suggested in Mundell-Fleming (without the small country hypothesis), although our equilibrating mechanisms are different. However, because the Mundell-Fleming model ignores expectations and relative price changes, our model predicts different effects on the flow of capital, the balance of trade, and real exchange rates in some circumstances.

International trade is most commonly analysed via general equilibrium theory (see e.g. Bhagwati and Srinivasan, 1983;86 J.D. GEANAKOPLOS AND D.P. TSOMOCOS Frenkel and Razin, 1992; Svensson and Razin, 1983), with its three-legged apparatus of agent optimization, market clearing (i.e. perfect competition with flexible prices), and rational expectations. International finance, on the other hand, has traditionally been studied via a potpourri of models and methodologies (see e.g. Blanchard and Fisher, 1989; Dornbusch, 1976; Dornbush, 1988; Flemming, 1962; Mundell, 1968), in which some markets clear and others do not, some prices are flexible and others are not, some expectations are rational and others are formed as if prices were flexible even when they are not, and agent activity is described not by optimization but by behavioural equations. The traditional international finance literature following Mundell and Fleming recognizes the fundamental importance of interactions among multiple markets, and its general equilibrium character. But, like the mainstream, Keynesian macroeconomics literature from which it derives, it usually repudiates one (and sometimes all) of the three legs of a genuine, full-bodied general equilibrium approach. The alternative international finance literature inspired by Lucas (Grilli and Roubini, 1991; Grilli and Roubini, 1992; Lucas, 1982) does maintain all three hypotheses of agent optimization, market clearing, and rational expectations. But by adopting the auxiliary hypothesis of an exchange economy with a single ‘‘representative agent’’ who is obliged to put his entire endowment up for sale (to himself!), this literature apriori eliminates many interactions between the financial and real sectors of the economy. Our purpose in this paper is to unify international trade and finance in a genuine general equilibrium model. Our model is rich enough to include multiple commodities (partly to allow for relative price changes and partly in order to distinguish between traded and nontraded goods), heterogeneous consumers in each country, multiple time periods, short-term and long-term assets, and multiple currencies. Yet our model is simple enough to be effectively computable. We believe that international finance cannot properly be separated from international trade because the most interesting financial questions invariably turn on the interactions of real and financial variables. For example, if a country reduces its tariffs, or becomes more productive, or more impatient, will its currency appreciate or depreciate? What will happen to income, to short- and long-term interest rates, to price levels and to the rate of inflation, to the real terms of trade, and to the balance of trade? What will happen if a country’s government, or a trading partner’s government, spends more, or prints more money, or increases the rate at which it expands its money supply?INTERNATIONAL FINANCE IN GENERAL EQUILIBRIUM 87 If the real sector is important, then international finance depends on international trade, and if the latter requires a general equilibrium analysis, then logically speaking, so must the former. Moreover, there are direct advantages to a full- bodied general equilibrium approach to international finance. Foremost among these is the accounting clarity which comes from explicitly modelling every transaction: we understand the demand for money better when we see where and why each agent spends each dollar he obtains. By deriving behaviour from utility maximisation with rational expectations, we ensure that the model will specify behaviour that is logical, even if policy essentially changes the regime in which an agent acts. In contrast, models which exogenously specify behaviour that is not derived from underlying preferences can seem plausible in some regimes and absurd in other regimes. By deriving behaviour from utility maximization, general equilibrium also makes welfare analysis, and especially distributional questions, amenable to rigorous analysis. Finally, without general equilibrium one must resort to reduced form behavioral equations in which various indirect effects are apriori ignored. In general equilibrium one sees all the indirect effects and can judge whether, and under what conditions, they can safely be ignored. The mainstream literature in international finance deriving from the Mundell–Fleming extension of the Keynesian IS-LM model has avoided what we call full-bodied general equilibrium for the same reasons that Keynesian macroeconomics has. First, there is a powerful Keynesian intuition that goods markets are slower to clear than asset markets, and therefore in the short- run goods market do not clear. In Keynesian macroeconomics this meant that commodity and labor prices were taken to be sticky in the short run. Although we do not wish to dogmatically reject the hypothesis of fixed prices (and we are glad to see others investigate its consequences), we feel that it is also worthwhile to fully analyse the consequences of flexible prices. Second, it seems more convenient to work with a single period model, as in IS-LM, rather than with a multi-period general equilibrium model. This, however, leaves expectations about future price levels and exchange rates to arbitrarily pre- specified behavioral rules. Some theorists are comfortable knowing that expectations can be systematically biased; this outlook is represented by temporary equilibrium models, such as Grandmont (1983); Grandmont and Laroque (1973); Grandmont and Younes (1972) and Grandmont and Younes (1973). By contrast, we work with an explicit multi-period model so that expectations (particularly resulting from policy changes) must conform to the subsequent reality. The effects of policy, if there are any, cannot then be attributed to irrational expectations. The effect of policy88 J.D. GEANAKOPLOS AND D.P. TSOMOCOS changes on long-term interest rates, inflation, and exchange-rate trajectories is one of the most important features of our model.† Third, and most importantly, it has not been clear how to maintain agent optimization and a positive value for fiat money in a finite horizon general equilibrium model. In the last period no optimizing agent will accept worthless fiat money, and therefore optimizing agents calculating backward to the beginning will immediately set the price of money equal to zero. This puzzle is not avoided at all by postulating cash-in-advance constraints. We overcome the problem by also adding the possibility of borrowing (selling bonds) to the central bank; then we prove that in our model money always has positive value, if there are enough potential gains to trade. Thus in spite of these Keynesian doubts, we present a finite horizon model in which all prices (including exchange rates) are flexible and all markets clear, in which expectations are rational, and in which money always has positive value. We work out an elaborate example to show that our model is easily computable. We have not tested our comparative statics predictions by estimating parameters, but we believe our conclusions are sensible and generally in accordance with the stylized facts without being obvious at first glance. Indeed there are so many endogenous variables, including trades in multiple commodities, exchange rates, real exchange rates, inflation rates, short and long nominal interest rates, and commodity prices, that it is inconceivable that one could automatically work out all their changes without any analysis. Our model resembles the real business cycle literature in the sense that all markets clear all the time. But our comparative stat- ics results are compatible with Keynesian analysis. In particular, monetary and fiscal policy are not neutral. Expansionary mone- tary policy leads to higher income and a fall in nominal interest rates, higher domestic prices, a currency depreciation, a fall in the real terms of trade and an increase in net exports. All these effects (except the price changes) are consistent with the Mundell- Fleming model. A short burst of expansionary fiscal policy leads to higher domestic economic activity, higher long-term real and nom- inal interest rates, a temporarily higher exchange rate, and higher expected inflation following a temporary drop in prices. Again, most of these effects are consistent with the Mundell-Fleming model. Though most of the effects of monetary and fiscal policy in our model are identical to the Mundell-Fleming model, importantdifferences remain because the Mundell-Fleming model implicitly assumes that expectations about future exchange rates never change, and that the real terms of trade move in lock step with the exchange rate. In the Mundell-Fleming story, expansionary fiscal policy tends to increase output and interest rates; the latter causes an influx of foreign capital, which tends to appreciate the domestic currency; this in turn encourages imports and discourages exports, increasing the balance of trade deficit. In our multi-period model, however, we notice at once that this story misses several important elements. In the first place, when the expansionary fiscal policy eventually reverts to its normal levels, the currency will also tend to revert to its previous exchange level. Rational investors therefore expect a currency depreciation following the appreciation, and hence it is no longer clear that there will be an influx of foreign capital, despite the higher long-term interest rates. ‘‘Overshooting’’ of exchange rates is a fundamental property of our equilibrium, as it must be in any flexible exchange rate model where short-run policy has short- run effects on exchange rates.† In the second place, government expenditures might be proportioned quite differently from private demand, and this too could affect the balance of trade. In our model the effect of expansionary fiscal policy on the balance of trade therefore depends on a more precise description of the policy. For instance, if the government expenditures are financed by contemporary taxes (a balanced budget expansion), and if the government spends its money exclusively on domestic nontraded goods, which does not seem a completely unreasonable assumption, then we find that the balance of trade improves rather than worsens. The reason is clear: the balanced budget multiplier (with flexible prices) turns out to be less than 1 (in our example it is 0 4). Hence the government expenditure crowds out some domestic expenditure, part of which would have been on foreign goods. Even if the real terms of trade move in the same direction as the exchange rate, this is a sign of flagging demand for imports, not a stimulus to extra imports. If on the other hand, the government buys all goods in the same proportion as the economy as a whole, then we find ambiguous effects on net imports in our example. If in addition we suppose the expenditures are financed by new bonds, which will be paid off much later by raising taxes on agents not active at the time of the government expenditures, then our example confirms an increase in the balance of trade deficit depending on how the taxrevenue to pay off the bonds is raised. The only program which is guaranteed to yield the Mundell-Fleming effects on output, interest rates, exchange rates, real terms of trade, and the balance of trade is government expenditure that is targeted entirely at domestic goods that are also exported. (In this case the extra demand raises their prices relative to imports, which is the real terms of trade, and chokes off exports). The domestic effects of monetary policy are also identical in our model and in Mundell-Fleming, but again the underlying mechanisms are different and so are some of the international effects. In Mundell-Fleming, short-term open market operations raise output and lower interest rates, so capital flees, depreciating the currency and thus causing an increase in net exports. In our model we again observe overshooting, so that with rational expectations, the fall in the exchange rate is accompanied by an expected appreciation, rendering the direction of capital mobility ambiguous. Furthermore, in our example, the real terms of trade turn against the domestic country because the increased economic efficiency stemming from lower interest rates increases the demand for imports and the willingness to export. The real balance of trade, as it were, is thus not much different, but measured in (depreciated) dollars, starting from an original deficit position, the balance of trade deficit increases in our example, rather than decreasing as predicted by Mundell-Fleming. As with fiscal policy, the effect of monetary policy depends on the precise nature of the policy. Does the open market operation involve long-term bonds or short- term bonds? Is the policy instantaneous, or is it anticipated? Is it expected to continue into the future, or will the government allow the money supply to contract (compared to what it would have been absent the open market operations) when it comes time for the bonds to pay off? We defer our discussion of these topics to Section 11. A fundamental reason why the international effects of fiscal and monetary policy are different in our model and in the Mundell- Fleming model is that in the latter model there is essentially one channel by which policy affects the currency exchange rates: they are determined largely by the flow of capital controlled by agents who weigh the marginal benefits of money invested domestically against money invested abroad. In our model agents also weigh the marginal benefits of money spent on commodities domestically or abroad. This opens an entirely new channel for the determination of exchange rates. For example, if there is a burst of domestic economic activity, so that the same money chases more transactions (and if velocity does not change to make up all of the difference), domestic prices for commodities will go down, attracting foreign money aimed at domestic commodity purchases, and the currency will appreciate.INTERNATIONAL FINANCE IN GENERAL EQUILIBRIUM 91 In summary, our model of flexible prices, rational expectations, and explicit agent optimization makes exactly the same qualitative predictions about output, interest rates, and currency exchange rates as the Mundell-Fleming model (modified to allow for two equal-sized countries), while it differs with respect to expectations, and possibly also with respect to real terms of trade, and the balance of trade. We believe any sensible general equilibrium model should agree with Keynesian predictions about the effects of policy on output and interest rates. Balanced budget fiscal policy transfers wealth (say via lump sum taxes) from private agents who would have transacted only a portion of it and places it in the hands of the government who transacts all of it. This action is bound to stimulate economic activity and measured income, even if it does not raise welfare. Moreover the government spends this wealth on markets that meet earlier than the agents would on average have spent the wealth themselves, raising the relative price of current consumption over future consumption. Expansionary fiscal policy is thus also bound to raise interest rates. Expansionary open market operations make it easier to borrow money, and thus reduce nominal interest rates. Lower nominal interest rates on money must improve the efficiency of trade in any economy where money plays a fundamental role in trade. Keynesians often wave the banner of involuntary unemployment and variable velocity to argue for their view that policy matters. We do not wish to discount the importance of either. But our analysis shows that the qualitative features of domestic Keynesian policy analysis hold in a world which has no involuntary unemployment and a fixed velocity of money. Involuntary unemployment (or more generally fixed prices), variable velocity of money, and irrational expectations might increase the magnitude of domestic Keynesian effects, but they are not responsible for their qualitative features. We might well ask, why did Lucas not detect these Keynesian features in his general equilibrium analysis of the macroeconomy and international finance? The answer is surprisingly simple. In his early papers, Lucas postulated a world in which each agent is obliged to sell the whole of his endowment in each period. Real income, which by definition is the aggregate of sales in a period, is thus exogenously fixed, independent of any government monetary or fiscal policy that does not directly create new commodities. In cash-in-advance economies, trade is usually inefficient because the positive interest rate on money discourages transac- tions (assuming the nominal interest rate exceeds the real interest92 J.D. GEANAKOPLOS AND D.P. TSOMOCOS rate). Agents cannot always time their sales so as to instanta- neously deposit the money and earn the maximal rate of interest. As a result they make fewer transactions. In our stylized model, agents who sell goods in period 0 cannot spend the money or deposit it in banks until period 1. An agent who has no cash and wishes to trade his $1 apple in period 0 for a $1 orange in period 0 must go to the bank and borrow the $1 to buy the orange, but since the interest rate is positive, he will need to sell more than 1 apple in order to repay the loan. If he values the orange only slightly more than the apple, he will forego the entire set of transactions; in particular, he will not sell the apple. A similar effect obtains for intertemporal trade if it is costly to make trips to the bank, even if sales receipts can be used for contemporaneous purchases. An agent who wants to trade his apple today for an orange tomorrow could sell the apple today, but if there were inflation so that the orange tomorrow cost more than $1, he would have to go to the bank to deposit the $1 in order to have enough to pay for the orange. But if it were costly to go to the bank, he might forego the entire set of transactions. Keynesian IS-LM models with variable velocity implicitly incorporate similar effects. When interest rates go up, agents are assumed to demand less money. The implicit justification is that each agent makes more frequent trips to the bank, partially mitigating the trading inefficiency from higher interest rates but substituting ‘‘shoe leather’’ costs. In the early Lucas model these inefficiencies do not affect the number of transactions because the agent is obliged to sell all his apples anyway, no matter what the interest rate. Our methodological approach has parallels in the overlapping generations literature and in the work of Lucas and his followers. Both of these literatures maintain all three legs of the general equilibrium paradigm. But both avoid the backward induction value of money puzzle by working in an infinite horizon which has no last period from which to start the backward induction. The infinite horizon introduces several inconvenient features to the modelling which we have sought to avoid. In overlapping generations models, there can be a continuum of different equilibria, and one country can run a balance of trade deficit for all time (see Kareken and Wallace, 1981). A further difficulty is that the infinite horizon makes the model almost completely intractable from a computational point of view. Indeed, in order to make his model tractable, Lucas makes the heroic assumption that each country is represented by a single agent, and that all these representatives are identical. In order to motivate trade inside each country, the representative agent is given a split personality that trades with itself at some moments, and pools all its resources at other moments. By contrast, we develop a computationally tractable model in which there is genuine diversity between agents.INTERNATIONAL FINANCE IN GENERAL EQUILIBRIUM 93 Thus although our methodological approach is akin to Lucas, our policy conclusions are not. Our closest methodological precursor is Martin Shubik (1973); Shubik and Wilson (1977) who introduced a central banking sector with exogenously specified stocks of money, and cash-in-advance constraints. Shubik (1973); Shubik (1993) also emphasized the virtues of modelling each transaction. Grandmont (1983); Grand- mont and Laroque (1973); Grandmont and Younes (1972); Grand- mont and Younes (1973) also introduced a banking sector and emphasized the inefficiency of trade with money. (The cash-in- advance constraint can be traced at least as far back as Clower, 1967 and has been used by Lucas.) Though they had most of the individual ingredients, neither Grandmont nor Shubik com- bined a central bank which makes loans, with cash in advance constraints and with private money. It is this triple combi- nation which is crucial to make equilibrium determinate and to separate our international monetary equilibrium from com- petitive equilibrium. Neither Grandmont nor Shubik saw the need for a gains to trade hypothesis, and neither proved the existence of a monetary equilibrium distinct from competitive equilibrium in a finite horizon. Neither focused on international finance. Our analysis owes much to the framework developed by Dubey and Geanakoplos (1992) in a one-period general equilibrium model, and then extended by them (Dubey and Geanakoplos, 1993) in unpublished work to multiple periods in order to combine macroeconomics and general equilibrium. In particular we owe to Dubey and Geanakoplos (1993) the proof that monetary and fiscal policy are not neutral and to Dubey and Geanakoplos (1992) the proof that money can have positive value in a finite horizon model. We extend those models by considering many countries and international finance (though we drop uncertainty). In the Dubey- Geanakoplos framework, as in ours, agents begin with stocks of cash which they own free and clear with no obligations. But they also have the option of voluntarily borrowing more money from the central bank, at endogenously determined interest rates, which, if positive, will cause them to owe more money than they borrowed. (These bank loans are available at different moments and for different periods of time, and therefore agents will be re-paying them throughout the time horizon of the model.) In equilibrium all the money left in the agents’ hands in the last period (including their private endowments) will be owed to the bank, so money will have value (i.e. some agents will give up goods for money) in the last period because they need the cash to pay off their debts. The central bank is regarded as an arm of the government which provides exogenously fixed quantities of money for loans of varying lengths at various time periods, and94 J.D. GEANAKOPLOS AND D.P. TSOMOCOS then collects on its debts.† Equivalently, the bank executes open market transactions, buying bonds from the public. By varying the quantities of money available at the bank (i.e. the value of the open market purchases), the government can control the stocks of money in the economy. We show in our model that under a gains to trade hypothesis, ‘‘international monetary equilibrium’’ (IME) always exists, and money has value, and exchange rates are well defined. (If there were no gains to trade, there would be no reason to obtain money, and money would have no value.) Moreover, although we do not prove it here, there are typically only a finite number of equilibria, so one can speak of the exchange rate or price level determined in equilibrium, in contrast to models of international trade based on overlapping generations economies. IME allocations are typically not Pareto efficient because purchases must be made with money, and money is scarce. The scarcity of money gives money value (i.e. it makes the relative price between commodities and money less than infinity) and it makes interest rates positive (i.e. it makes the relative price of future money, or bonds, to present money less than 1). In Sections 2–4 we describe the model. In Section 5 we note that the Keynesian sources of demand for money apply even though we derive behaviour from utility maximization. We also observe that our simple choice of the order of markets requires the velocity of money to be 1. However, in our model the ‘‘real’’ velocity of money, by which we mean the stock of money divided by the amount of real transactions (somehow aggregated) is variable and endogenous. If we allowed for simultaneous markets the velocity would also be variable and endogenous. In Section 6 we state our existence theorem and note that it depends on potential gains to trade. It is curious that previous authors have not found it necessary to invoke such a hypothesis in discussing money. We note that if the ratio of government deficits to central bank loans and open market operations exceeds the gains to trade, then equilibrium will not exist. At some finite level of debt, prices will explode in a hyperinflation. In Section 7 we note that as government expenditures and private money shrink to 0, our international monetary equilibrium approaches competitive equilibrium. In Section 8 we show that in the presence of private money or government deficits, international monetary equilibrium is not Pareto efficient, and monetary policy necessarily has real effects.INTERNATIONAL FINANCE IN GENERAL EQUILIBRIUM 95 In Sections 9 and 10 we derive straightforwardly many of the standard relationships of international finance, including the uncovered interest rate parity, purchasing power parity, the Fisher effect, long-run international trade balance, and a version of the quantity theory of money. Armed with these general principles we turn in Section 11 to analysing concrete comparative statics changes in computable general equilibrium models. Often the general principles can point us to the correct directions of change, but other times it is only after tracing out the new equilibrium that we can rationalize the outcome. For example, in general equilib- rium the exchange rate must simultaneously satisfy purchasing power parity, uncovered interest parity, and it must guaran- tee a long-run trade balance. Some shocks to the economy will move these three requirements in different directions, appar- ently leaving the direction of change of the exchange rate ambiguous. Only by simultaneously equilibrating all the equa- tions and variables can one determine the direction of movement of each. The comparative statics conclusions we come of course to depend on the parameterization of tastes and endowments that we have chosen. It has been suggested that general equilibrium is not useful because in such models anything can happen when policy parameters are changed, if the initial data of the economy is chosen fortuitously. We regard this not as a criticism of general equilibrium, but as its vindication. One cannot hope to fully understand any policy change until one knows how all its effects depend on the behaviour of the agents. In order to give a more comprehensive treatment of issues arising in international finance, we would need to extend the model we have described here to incorporate production, uncertainty, and incomplete markets. Such an elaborate frame- work might also permit us to reconsider some of the tradi- tional international trade results in a financial context. We believe that incorporating money is the crux of the prob- lem, and therefore that this extension is within our grasp.† Finally, it seems evident that after we gain some experi- ence with these models, we will be able to derive our com- parative statics results in a more general context than our example