International Finance and Debt

Jerome L. Stein
Division of Applied Mathematics, Brown University

April 17, 1999

I. The Yale Influence

Jim Tobin wrote an autobiographical sketch which made a profound impression upon me. He explained that he was attracted to economics for several reasons. Born on March 5,1918 he was sufficiently close to the period of the Great Depression and wanted to understand how the economic system functioned and how its performance could be improved. His considerable analytical and mathematical skills plus originality would be invaluable in helping to achieve those objectives.

Born ten years later, I was attracted to economics for much the same reasons: how could I use my mathematical, analytical skills to solve significant economic problems which could eventually lead to the improvement of the economic conditions. It was no surprise that I was most influenced at Yale by Jim, Henry Wallich and Robert Triffin. I’ll explain below what Jim’s influence was. But I want to start by describing my relations with Henry Wallich and Robert Triffin.

Henry asked me to be his Research Assistant. My function was to walk with him on Saturday mornings -- to East Rock, West Rock, or through the cemetery. During these walks he would pose economic problems, ask me what I thought of various current articles in the areas that interested him. He wanted my mathematical/theoretical analysis so that he could decide whether the theses were logical or consistent, what were the underlying processes -- the transmission mechanisms -- what were their strengths, weaknesses and implications. Often he would call me to have a drink with him at a bar where we could finish the earlier discussions. He drank beer and I drank Coca Cola. In all of our discussions, there was an interplay between the theory and the economic reality, between the mathematics and the substantive problem. I could not just say that the system is not stable because one eigenvalue has a positive real part. I had to explain what was the economic interpretation of that condition within the context of the model. Moreover, each equation had to be explored and justified in terms of its correspondence with reality. The discussions between the senior professor who came from a banking family in Germany and the naive 21 year old red head who had never been outside of the US, were vigorous dialogues, with no distinctions of rank or eminence.

Many years later when he was a Governor of the Federal Reserve and I was giving a talk in DC, Henry would come for the lunch, attend the talk and then ask me to return to the Fed with him for further discussion. He would pose extremely relevant and difficult problems concerning the subject of my talk. Generally, I did not know the answers off-hand and had to think hard concerning either the implications of my work or see that there were important lacunae in my presentation. Again there was the use of mathematical analysis/theory to solve significant real world problems.We stopped when it was time for his driver to take me to the airport.

Robert Triffin was different from Henry Wallich. He shared Nurkse’s distrust of free capital markets and exchange rates, and was engaged in devising international financial institutions in the spirit of the Keynes plan. Triffin’s course was intellectually challenging. He would pose problems concerning his projects in international finance and the subsequent discussions were the responses. When I approached the problems analytically, I found myself in disagreement with him. I argued that his arrangements were weak substitutes for a regime of free exchange rates and free capital movements and that Nurkse’s work lacked a clear cut design. Nurkse made no distinction between the stability of a system and the character of the forcing term -- the government policies undertaken which produce the undesired fluctuations. Triffin did not accept my arguments. Nevertheless, when he invited a seminar speaker, he asked me to come to his home afterwards and discuss the issues with the speaker. Both Triffin and Wallich made sure that I would participate in the post seminar discussion. Again there was the interaction between theory/mathematical models and important international problems. I did not own a car and Triffin made sure that someone would drive me back to our modest apartment on George and Orchard Streets. At that time it was a safe middle class area, and my wife and I could walk back home from the library late at night.

I left Yale and was instructor at Wesleyan for a year and then went to Brown on a series of one year contracts. Except for many leaves and sabbaticals, I was in the Brown economics department for 40 years until my retirement. I then was invited to move over to Applied Mathematics as an unpaid visiting professor (research). I am convinced that being away from Yale was influential in my development along an independent path. Despite our occasional divergent approaches, I consider myself strongly in the Tobin mold. Jim told my younger son, who was an Archaeology major at Yale, that I was in-between him and Milton Friedman in orientation and approach. I agree. The research that I am engaged in, described next, shows the direct connection with Jim Tobin, Henry Wallich and Robert Triffin.

II. Real Exchange Rates and Stochastic Optimal Control

Bill Brainard suggested that our common theme should be: How has the US economy, and our understanding of it, changed since our graduate student days - “what I learned in graduate school that is still relevant, what have I learned since, and what is in store. Each panelist should talk about aspects of the US economy that they are interested in.”

Two exciting subjects that were developing during my graduate student days were portfolio selection under uncertainty, and dynamic stock flow interactions. The first was Jim Tobin’s liquidity preference as behavior towards risk. Keynes’s concept of liquidity preference was that the interest rate followed a mean reversion process. When the interest rate deviates from the longer term mean, investors expect it to return, and adjust their portfolios between safe and risky assets accordingly. This approach did not explain why the adjustment of the portfolio was a smooth -- rather than a discontinuous -- function of the interest rate. Second, it did not explain how one can derive a smooth relation between the interest rate and portfolio composition if the interest rate did not follow a mean reversion process. Jim’s contribution was to show how the maximization of the expectation of a concave utility function would generate smooth liquidity preference. This article became one of the foundations of finance theory, especially the work of Robert Merton.

The second subject that was being developed was the dynamic stock-flow interactions. Hicks and Goodwin employed that approach in their business cycle theories, and Jim Tobin’s Dynamic Aggregative Model used that approach to generate cycles and growth.

My current work in international finance and debt has these concepts as integral components. One topic concerns the fundamental determinants of exchange rates. The second topic is a stochastic optimal control approach to international finance and debt.

A. Fundamental Determinants of Exchange Rates

The questions that motivated the research are the following. (1) What determines real exchange rates, such as the real value of the $US relative to the rest of the G7? What will determine the value of the Euro relative to the $US? (2) How can we evaluate if currencies are misaligned? What produces misalignment? The answers will influence the approporiate reactions to crises. (3) What are the effects of controllable and uncontrollable variables upon the real exchange rate and the current account? For example, the Mundell-Fleming type of analysis claims that a rise in the high employment budget deficit appreciates the exchange rate. That was consistent with the rise in the $US in the first half of the 1980s. When the dollar then fell, Greenspan and others attributed it to the budget deficits.

As a result of the dissatisfaction with the explanatory power of the existing models, we take a very different approach to explaining the real exchange rate. We call our model the NATREX, an acronym for the Natural Real Exchange Rate. The underlying equations are very much in the spirit of the work on uncertainty and stock-flow dynamics that I mentioned above.

Instead of focusing upon the short run, where anticipations are crucial, we devote our attention to the medium to longer run trends in the real exchange rate. The NATREX is a generalization of the Purchasing Power Parity (PPP) hypothesis and the macroeconomic balance approach. Whereas the macroeconomic balance approach just looks at flows, we have an endogenous stock-flow interaction where the foreign debt and capital are state variables. Whereas the PPP hypothesis is that the equilibrium real exchange rate is a constant, the NATREX[1] explains how the equilibrium real exchange rate depends upon real fundamentals: the ratio of social consumption/.GDP which we call time preference, the productivity of capital, the terms of trade and world real rate of interest in economies where the latter are exogenous. If a linear combination of these exogenous fundamentals is stationary, the equilibrium real exchange rate will be constant. But the PPP is a special case.

The NATREX or equilibrium real exchange rate is not a point but a trajectory: an attracting set.

In the medium run, the NATREX real exchange rate equates the current account to saving less investment, when the rate of capacity utilization is at its longer run mean and there is portfolio balance. The real rate of interest at home adjusts until the investors are indifferent between holding domestic and foreign securities. In this respect, the medium run NATREX is like the macroeconomic balance models.

The most important fundamental is the ratio of social consumption/GDP. The logic of the NATREX model can be shown by explaining the effect of changes in this fundamental. A rise in social consumption/GDP produces the Mundell-Fleming effects in the medium run. Saving less investment declines: there is a smaller capital outflow or larger inflow. The real exchange rate appreciates, and produces a decline in the current account -- say a deficit. The macroeconomic balance models stop here, and the NATREX continues.

The current account deficit is the rate of change in the foreign debt. The rate of investment is the rate of change of capital. This opens up stock-flow dynamics, and leads to the generalization of PPP.

The current account and saving depend upon the foreign debt and capital, which are state variables. As the foreign debt rises, the current account declines because of the flow of interest payments abroad. Saving is positively related to the foreign debt, in a dynamically stable system. As net worth declines due to the rise in the debt, the economy must increase its saving. Otherwise, the debt will explode. This is our intertemporal budget constraint.

Investment raises capital which affects the productivity of the economy which in turn changes both the current account and saving.

The new level of the foreign debt and productivity feed back into the macroeconomic balance equation for the real exchange rate. The trajectory of the equilibrium real exchange rate towards the longer run, resulting from a rise in the ratio of social consumption/GDP is medium term appreciation and in the longer run there will be a depreciation below its initial level. The Mundell-Fleming macroeconomic balance type models neglect the effects of endogenous variations in the stocks of capital and foreign debt. The PPP hypothesis ignores the mechanism whereby equilibrium real exchange rates are determined.

Misalignment is the deviation between the actual real exchange rate, defined as the nominal exchange rate times the ratio of domestic/foreign unit labor costs (or prices), and the NATREX. The NATREX is an attracting set. Misalignment tends to be eliminated. The convergence to the NATREX is faster when the exchange rates are free. When there are adjustable pegs, misalignment produces exchange rate crises. Misalignment can occur either because the nominal exchange rate or relative nominal unit labor costs rise relative to theNATREX, or that changes in the fundamentals depreciate the NATREX.

The dynamic stock-flow analysis, which is the medium to longer run trajectory, fits in nicely with the coinintegration error-correction approach. Each of the fundamentals is objectively measurable and the paths of convergence are deducible. The NATREX model has explained the medium to longer term movements of the $US relative to the rest of the G7, the real value of the DM, the real value of the Yen. We have been using the NATREX model to explain the French franc/DM and Italian lira/DM. The movements in these curencies are explained quite well by the real fundamentals. Moreover, before the 1992-93 crises, the French franc was not overvalued but the Italian lira was overvalued by two standard deviations. We see objective reasons why the Italian lira had to be devalued, but that the French franc could withstand the attacks.

The NATREX approach is being used by several research groups in Europe -- one in Rome and other based in Paris -- to evaluate the evolution of the Euro relative to the US dollar. The Deutsche Bank-Deutsche Morgan Grenfell adapted the NATREX model to its own needs and calls it the DMG-NATREX model. This adoption by a profit making institution gave the authors of the NATREX model psychic satisfaction.

B. A Stochastic Optimal Control to International Debt

The recent crises in south-east Asia are agreed to be debt crises. There is therefore a need for a way to monitor international debt and the current account to know when they are “excessive” and may impend difficulties. Institutional investors, banks and the governments should have some benchmark measure of excessive debt to evaluate whether an economy is unduly vulnerable to shocks arising from the productivity of capital, the real interest rate and their correlation.

Shocks arise from the productivity of capital, the real interest rate and their correlation. Our objective is to select the optimal controls -- the ratio of debt/net worth and consumption/net worth -- that will maximize the expectation of the discounted value of a concave utility function of consumption in a dynamic stochastic environment. The resulting ratio of debt/net worth and current account deficit/net worth are our benchmarks to evaluate whether a debt or current account deficit is excessive and that the economy is unduly vulnerable. This is a problem in stochastic optimal control.

The Division of Applied Mathematics (DAM) at Brown is a leading group in stochastic optimal control, and I am doing joint research[2] on optimal debt and curent account with Wendell Fleming in the DAM.

Wendell and I already have already derived operational clear cut equations for the optimal values of the debt/net worth and curent account/net worth. The optimal risk-return relationships are clearly seen in this context. Currently we are examing how the results are varied as we change the nature of the stochastic processes and the criterion function. For example, mathematicians in the DAM are using concepts of risk-sensitive and robust control in stochastic optimization. We are examining the strengths and weaknesses of alternative approaches.

Along with an economist in Rome, we are embarking upon a study which applies the Fleming-Stein theoretical results to the evaluation of country risk. We are asking: To what extent are our results more useful in analyzing debt problems of countries than are the conventional measures?

These two research projects are applications of mathematical model building to significant real world economic problems.

[1] Jerome L. Stein, Polly R. Allen et al, Fundamental Determinants of Exchange Rates, Oxford: Oxford University Press, 1997.

[2] Wendell H. Fleming and Jerome L. Stein, A Stochastic Optimal Approach to International Finance and Debt, Division of Applied Mathematics, Brown University, April 1999.