(Edited with Roger W. Dimand) Irving Fisher (1867-1947), economist, Yale University teacher, inventor, mathematician and activist reformer, was one of the most important American economists of the first half of the 20th century. On the 50th anniversary of his death in May of 1998, a large gathering of economists met at Yale to reassess Fisher’s enormous scientific contribution. Such a reevaluation was facilitated by welcomed republication of all of Fisher’s books and articles in 14 volumes the previous year. The offices of the Cowles Foundation at Yale University were made available for the presentations and the Cowles Foundation directors and administrators assisted with the preparation of this important volume.
This book consists of original papers explaining Fisher’s technical contributions to econometrics, a reassessment of his prescient and much neglected textbook on economics, his theories of capital and interest, his debt-deflation theory of depression, the various financial devices that he developed to improve governance and policy-making, and finally his eugenic crusades that included the prohibition of alcoholic beverages and healthy diets. Fisher’s ideas were so advanced for his time that many of the contributors to these volumes delight in pointing out how the recent financial inventions in the world economy are catching up to the insights that Fisher provided decades earlier. This volume consists of the major papers from that conference including written versions of the comments that were presented at that time. The contributions include original essays by Nobel Laureate, James Tobin. Other contributions include analytic essays by distinguished economics such as, A. J. Auerbach,William J. Barber, W. C. Brainard, W. E. Diewert, Robert Dimand, Victor R. Fuchs, John Geanakoplos, M. J. Graetz, Robert E. Hall, William D. Nordhaus, Peter C. B. Phillips, John Rust, Herbert E. Scarf, M. D. Shapiro, J. B. Shoven, Robert J. Shiller, Martin Shubik, T. N. Srinivasan, John Whalley, and others. In addition, the editors have included several already published biographical essays on Fisher so that the collection will be thorough and complete. A useful scholarly index has been prepared especially for this volume.
We show that very little is needed to create liquidity under-supply in equilibrium. Credit constraints on demand by themselves can cause an under-supply of liquidity, without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. We show that the under-supply is a non-monotone function of the demand distortion that causes it, a result that may have interesting implications for emerging markets economies. Finally, when we make the credit constraint endogenous, the inefficiency can be large due to the presence of a multiplier.
We define liquidity as the flexibility to move goods (money) from one project (investment) to another. We show that credit constraints on demand by themselves can cause an under-supply of liquidity, without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. In this respect liquidity is like a commodity: according to our offsetting distortions principle, a distortion in the demand for any good can often be understood as an inefficiency of supply.
We show that the liquidity under-supply is a non-monotone function of the credit constraint. This result is also a particular case of a more general principle applying to any commodity with supply alternatives: second best supply inefficiency is non-monotone in the demand distortion. Defining liquidity as flexibility ensures that there will be alternatives, and thus non monotonicity. If we interpret the credit constraints as the degree of financial development in the economy, our second proposition suggests that when financial markets are very undeveloped, as in some emerging markets, financial innovation may paradoxically make government intervention (taxation) more necessary.
Finally, we think about the magnitude of the under-supply in the context of a specific demand distortion. We model the credit constraint by assuming that borrowers will default unless their promises are covered by collateral. Further, we assume that only an exogenous proportion beta of a durable good can serve as collateral. This parameter will represent the degree of financial development of the economy. We show that when the price of the collateral is endogenous, the magnitude of the under supply can be much larger. Any policy intervention that affects the interest rate in equilibrium will have two effects on the borrowing constraint: a direct effect, also present in the case when the credit constraint is exogenous, and an indirect effect through the price of the collateral. We explore our findings by solving and simulating a particular case in which utilities for the consumption good and collateral are quadratic.
During a crisis, developing countries regret having issued dollar denominated debt because they have to pay more when they have less. Ex ante, however, they may be worse off issuing local currency debt because the equilibrium interest rate might rise, making it more expensive for them to borrow. Many authors have assumed that lenders and borrowers have contrary goals, and that local currency (peso) debt is better for the borrower (Bolivia), and dollar debt is better for the lender (America).
We show that if each country is represented by a single consumer with quadratic utilities, in perfect competition, then both will agree ex ante on whether dollar debt or peso debt is better. (In fact all assets can be Pareto ranked). But we show that it might well be dollar debt that Pareto dominates. In particular, if the lender is sufficiently risk averse and the borrower sufficiently impatient, and the lender’s endowment is sufficiently riskless, then dollar debt Pareto dominates peso debt. However, if there are persistent gains to risk sharing between the countries, then peso debt Pareto dominates dollar debt.
In the special case where utilities are linear in the first period and quadratic in the second period, we can completely characterize the Pareto ranking of any asset by a formula depending only on marginal utilities at autarky.
In the more general case where utilities are linear in the first period and have positive third derivative in the second period, we show that when persistent gains to risk sharing hold, America must gain from Peso debt but Bolivia might lose. Thus the presumption that peso debt is more favorable to Bolivia than to America is false.
Our framework of optimal security design can be used to demonstrate one rationale for credit controls. If the purchasing power of a dollar overseas varies with the quantity of debt issued, then both America and Bolivia can gain from capital controls, because a tax that reduces the quantity of Bolivian debt might make the real dollar payoffs in Bolivia more `peso-like’, and therefore under persistent gains to risk pooling, better for America and Bolivia.
During a crisis, developing countries regret having issued dollar denominated debt because they have to pay more when they have less. Ex ante, however, they may be worse off issuing local currency debt because the equilibrium interest rate might rise, making it more expensive for them to borrow. Many authors have assumed that lenders and borrowers have contrary goals, and that local currency (peso) debt is better for the borrower (Bolivia), and dollar debt is better for the lender (America).
We show that if each country is represented by a single consumer with quadratic utilities, in perfect competition, then both will agree ex ante on whether dollar debt or peso debt is better. (In fact all assets can be Pareto ranked). But we show that it might well be dollar debt that Pareto dominates. In particular, if the lender is sufficiently risk averse and the borrower sufficiently impatient, and the lender’s endowment is sufficiently riskless, then dollar debt Pareto dominates peso debt. However, if there are persistent gains to risk sharing between the countries, then peso debt Pareto dominates dollar debt.
In the special case where utilities are linear in the first period and quadratic in the second period, we can completely characterize the Pareto ranking of any asset by a formula depending only on marginal utilities at autarky.
In the more general case where utilities are linear in the first period and have positive third derivative in the second period, we show that when persistent gains to risk sharing hold, America must gain from Peso debt but Bolivia might lose. Thus the presumption that peso debt is more favorable to Bolivia than to America is false.
Our framework of optimal security design can be used to demonstrate one rationale for credit controls. If the purchasing power of a dollar overseas varies with the quantity of debt issued, then both America and Bolivia can gain from capital controls, because a tax that reduces the quantity of Bolivian debt might make the real dollar payoffs in Bolivia more `peso-like’, and therefore under persistent gains to risk pooling, better for America and Bolivia.
Keywords: Dollar debt, Currency, Indexed bonds, Security design, Capital controls
Irving Fisher long advocated inflation indexed bonds. I prove in the context of a multicommodity CAPM world that the best welfare improving bond pays the minimum money needed to achieve the same utility, and not the minimum needed to buy an ideal commodity bundle.
Irving Fisher also developed and advocated the impatience theory of interest. But in OLG economies, the rate of interest is determined by population growth, not impatience. I reconcile this contradiction by proving that in stationary OLG economies with land, the interest rate at the unique steady state does depend on impatience. Indeed, the proposition that greater impatience creates higher interest rates holds more generally in OLG with land than in Fisher’s two-period model.
Arrow’s original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can move some alternative from the bottom of the social ranking to the top), thereby simplifying both steps in Arrow’s proof.
My first proof is the most straightforward, and the second uses Condorcet preferences (which are transformed into each other by moving the bottom alternative to the top). The third (and shortest) proof proceeds by reinterpreting Step 1 of the first proof as saying that all social decisions are made the same way (neutrality).
We build a finite horizon model with inside and outside money, in which interest rates, price levels and commodity allocations are determinate, even though asset markets are incomplete and asset deliveries are purely nominal.
The classical Fisher equation asserts that in a nonstochastic economy, the inflation rate must equal the difference between the nominal and real interest rates. We extend this equation to a representative agent economy with real uncertainty in which the central bank sets the nominal rate of interest. The Fisher equation still holds, but with the rate of inflation replaced by the harmonic mean of the growth rate of money. Except for logarithmic utility, we show that on almost every path the long-run rate of inflation is strictly higher than it would be in the nonstochastic world obtained by replacing output with expected output in every period. If the central bank sets the nominal interest rate equal to the discount rate of the representative agent, then the long-run rate of inflation is positive (and the same) on almost every path. By contrast, the classical Fisher equation asserts that inflation should then be zero. In fact, no constant interest rate will stabilize prices, even if the economy is stationary with bounded i.d.d. shocks. The central bank must actively manage interest rates if it wants to keep prices bounded forever. However, not even an active central bank can keep prices exactly constant.
We build a finite horizon model with inside and outside money, in which interest rates, price levels and commodity allocations are determinate, even though asset markets are incomplete and asset deliveries are purely nominal.