# 1996

96-01. Mena, H.,*"International Trade in Middle Products and the Transfer Problem"*

**Abstract:**** **For several decades, the Theory of International Trade has elaborated its models and propositions using mostly (what we can refer to as) a classical assumption regarding the type of commodities which represent the world trade pattern: international trade takes place in final consumption goods. Of course, "extensions" to such a paradigm have been pursued in the international trade literature. These extensions have incorporated other categories of traded goods as well, such as capital goods and intermediate goods. Nontraded goods have also been incorporated as part of the individuals' consumption opportunities. Also, models have been developed in which labor is regarded as an internationally mobile factor. However, for the most part, all of these theoretical extensions have a "common denominator"; namely, they have mostly preserved such a classical assumption in the following essential sense: the commodities exchanged in the world market are formally incorporated in the countries' final demand functions; in open economies, the individuals' utility functions incorporate commodities traded in the world market.

96-02. Santos, M., and Vigo, J., *"Accuracy Estimates for a Numerical Approach to Stochastic Growth Models" *

**Abstract:** In this paper we develop a discretized version of the dynamic programming algorithm and derive error bounds for the approximate value and policy functions. We show that under the proposed scheme the computed value function converges quadratically to the true value function and the computed policy function converges linearly, as the mesh size of the discretization converges to zero. Moreover, the constants involved in these orders of convergence can be computed in terms of primitive data of the model. We also discuss several aspects of the implementation of our methods, and present numerical results for some commonly studied macroeconomic models.

96-03. Renero, J.M., *"Unstable and Stable Steady-States in the Kiyotaki-Wright Model" *

**Abstract:** Provide new results concerning dynamics for the Kiyotaki-Wright model (1989). I permit mixed strategies, but only those that restrict agents to play a unique strategy for each opportunity set. My results demonstrate the importance of examining stability in such models, because they show that many steady states focused on in the literature are not stable. One counterintuitive result is that very often there does exist a locally-stable steady state with highest acceptance rate of the most costly to-store good, while the steady state with universal acceptance of the least costly to-store good i generically unstable.

96-04. Antinolfi, G., and Huybens, E., *"Capital Accumulation and Real Exchange Rate Behavior in a Small Open Economy with Credit Market Frictions"*

**Abstract:** We consider the nature of the relationship between the real exchange rate and capital formation. We present a model of a small open economy that produces and consumes two goods, one tradable and one not. Domestic residents can borrow and lend aborad, and costly state verification (CSV) is a source of frictions in domestic credit markets. The real exchange rate matters for capital accumulation because it affects the potential for investors to provide internal finance, which mitigates the CSV problem. We demonstrate that the real exchange rate must monotonically approach its steady state level. However, capital accumulation need not be monotonic and real exchange rate appreciation can be associated with either a rising or a falling capital stock. The relationship between world financial market conditions and the real exchange rate is also investigated.

96-05. Hernández, A., and Zapatero, F., *"Exchange Rate Determination and the Collapse of a Target Zone with Stochastic Capital Flows"*

**Abstract:** We develop a model of exchange rate determination for a small open economy under a target zone regime. The driving force of the model is an exogenous stochastic capital flow that is invested in a domestic securities market. Equilibrium exchange rates are the result of equilibrium in both the domestic securities market and a money market. Within the band, interest rates increase as exchange rates depreciate. At the limits of the band the central bank is forced to intervene and can do so through two alternative policies -''sterilization'' and ''non-sterilization''-. Our model allows us to study the effects on interest rates, reserves and exchange rate dynamics of both types of intervention. Furthermore, ''speculative attacks'' arise naturally in our model and seem to mimic the actual dynamics of currency crises. For a given set of parameters, our model allows to predict the sustainability of the regime depending on the type of central bank intervention.

96-06. Azariadis, C., **"The Economics of Poverty Traps Part One: Complete Markets"**

**Abstract: **This essay lists theoretical reasons why neoclassical models of one-sector growth imply that nations with identical economic structures need not converge to the same steady state or balanced growth path, and outlines the empirical significance and policy implications of conditional non-convergence. We survey poverty traps in both convex and non-convex economies with complete market structures (Part One) and incomplete ones (Part Two). Among the potential causes of traps are subsistence consuption; distorted international trade in intermediate inputs; demographic transitions when fertility is endogenous; technological complementarities in the production of consumption goods, financial intermediation services, manufactures, or human capital; coordination failures among voters; various restrictions on borrowing, indivisibilities in human capital formation or child rearing; and monopolistic competition in product or factor markets.

96-07. López, G., *"Equilibrium Behavior in an All-Pay Auction with Complete Information"*

**Abstract: **A widely used sealed-bid auction is the first-price auction. In this auction, the highest bidder wins the item and pays the price submitted; the other bidders get and pay nothing. The all-pay auction is similar to the first-price auction, except that losers must also pay their submitted bids. The Nash equilibria of the all-pay auction involves the use of randomized strategies, which protect bidders from being overbid by a small amount. This paper generalizes the standard Nash equilibrium analysis of the all-pay auction to allow for endogenously determined decision ''errors''. Such errors may either be due to mistakes or to unobserved random variations in payoff functions. The error distributions depend on equilibrium expected payoffs, which in turn determine the error distributions as a fixed point. A striking result derived in this paper is that for any structure of the error terms the generalized Nash equilibrium and the nash equilibrium of the all-pay auction are equivalent if the error terms are identically and independently distributed. In addition, this paper shows how the generalized Nash equilibrium can be computed for two particular parametrizations, which we call the power function and the logit equilibrium. It is also shown how Nash-mixed equilibria for the all-pay auction with discrete bid choices can be computed. In the process, we derive theoretical results for the symmetric and asymmetric models with discrete choices. The results derived in this paper are appealing since can be used to establish differences in the qualitative properties of Nash and the generalized Nash equilibrium in games.

96-08. Huybens, E., and Smith, B., *"Financial Market Frictions, Monetary Policy and Capital Accumulation in a Small Open Economy"*

**Abstract:** We consider a small open economy where domestic residents combine their own income with credit obtained either at home or abroad in order to finance capital investments. These investments are subject to a costly state verification (CSV) problem. In addition, lenders to domestic residents confront a binding reserve requirement. Under one technical condition, the presence of these credit market frictions leads to the existence of two steady state equilibria: one with a relatively high and one with a relatively low capital stock. The low-capital-stock steady state is a saddle, while the high-capital-stock steady state may be either a sink or a source, depending on the rate of domestic money creation, the world interest rate and the level of domestic reserve requirements. An increase in the rate of money creation, the world interest rate or the level of reserve requirements acts to raise (lower) the level of real activity in the high (low)-capital-stock steady state. At the same time, sufficiently large increases in the rate of money growth or the world interest rate can transform the high-capital-stock steady state from a sink to a source. Thus, while small increases in the rate of interest or the money growth rate may be conducive to higher long-run levels of real activity, excessive increases can induce a kind of ''crisis''. This finding accords well with an array of empirical evidence. Finally, the model delivers a set of prescriptions for what a small open economy can do to protect itself against a ''crisis'' induced by rising world interest rates.

96-09. Ortigueira, S.,*"Fiscal Policy in an Endogenous Growth Model with Human Capital Accumulation"*

**Abstract:** In this paper we present an endogenous growth model with physical and human capital accumulation and study the effects of labor and capital income taxation on the transitional dynamics to the balanced path. Our results amount to an extension of those in Caball\'{e} and Santos (1993) and offer conditions on the parameters in the model to characterize the three growth cases (normal growth, exogenous growth and paradoxical growth). We show that parameters on preferences, technologies and depreciation rates, as well as fiscal policy parameters, are relevant to determine qualitatively the dynamic behavior of the economy. We also offer a measure of the inefficiency derived from the taxation of capital earnings. The associated welfare cost is closely related to the short-run behavior of human capital investment, which characterizes the three possible growth cases.

96-10. Cuoco, D., and Zapatero, F., **"On the Recoverability of Preferences and Beliefs in Financial Models"**

**Abstract:** We examine the extent to which an investor's preferences and beliefs are uniquely determined from knowledge of the equilibrium prices and of his/her consumption strategy. More precisely, we assume that the investor's preferences admit an expected utility representation, but with subjective probabilities, and investigate what joint restrictions can be placed on utility functions and beliefs. If the investor has preferences for wealth or consumption at a single future date, then the problem is indeterminate. In fact, for any given ''well behaved'' assets' price dynamics, utility function and consumption choice, we can construct investor's beliefs that would support the given consumption choice. On the other hand, if the investor draws utility from intertemporal consumption, we show that the set of utility functions and beliefs that are consistent with a given price and consumption process can be characterized by a martingale condition. In the Markovian case, this characterization can be reexpressed in terms of a partial differential equation that must be satisfied by the investor's relative risk aversion function. To each solution of this differential equation is associated a unique set of beliefs. Some general implications of time-homogeneous price and consumption processes are discussed.