This paper analyzes the complexity of the contraction fixed point problem: compute an e-approximation to the fixed point V * = Γ(V * ) of a contraction mapping r that maps a Banach space B d of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contractive Fredholm integral equations that arise in asset pricing applications and the contractive Bellman equation from dynamic programming. In the absence of further restrictions on the domain of Γ, the quasi linear fixed point problem is subject to the curse of dimensionality, i.e., in the worst case the minimal number of function evaluations and arithmetic operations required to compute an e-approximation to a fixed point V * e B d increases exponentially in d. We show that the curse of dimensionality disappears if the domain of Γ has additional special structure. We identify a particular type of special structure for which the problem is strongly tractable even in the worst case, i.e., the number of function evaluations and arithmetic operations needed to compute an e-approximation of V * is bounded by Ce -p where C and p are constants independent of d. We present examples of economic problems that have this type of special structure including a class of rational expectations asset pricing problems for which the optimal exponent p = 1 is nearly achieved.

Backus, Kehoe, and Kydland (1992), Baxter and Crucini (1995), and Stockman and Tesar (1995) find two major discrepancies between standard international business cycle models with complete markets and the data: In the models, cross-country correlations are much higher for consumption than for output, while in the data the opposite is true; and cross-country correlations of employment and investment are negative, while in the data they are positive. This paper introduces a friction into a standard model that helps resolve these anomalies. The friction is that international loans are imperfectly enforceable; any country can renege on its debts and suffer the consequences for future borrowing. To solve for equilibrium in this economy with endogenous incomplete markets, the methods of Marcet and Marimon (1999) are extended. Incorporating the friction helps resolve the anomalies more than does exogenously restricting the assets that can be traded.

We study the problem of identi cation of the long regression E(y j x � z) when the short conditional distributions P (y j x) and P (z j x) are known but the long conditional distribution P (y j x � z) is not known. This problem often arises when a researcher utilizes data from two separate data sets. (A leading example is the ecological inference problem of political science, where voting behavior across electoral districts is observed from administrative records, the demographic composition of voters within a district is observed from census data, and the researcher wants to infer voting behavior conditional on district and demographic attributes.) We isolate an identi cation region containing feasible values of the long regression, and show that this region forms a sharp bound on the long regression. The identi cation region can be calculated precisely when y has nite support. When y has in nite support we characterize two sets, one that contains the identi cation region, and one that is contained by it. Following this completely nonparametric analysis, we examine the identifying power yielded by exclusion restrictions across distinct covariate values. Such restrictions cause the identi cation region to shrink, in many cases to a single point. To illustrate the theory, we pose and address this hypothetical question: What would be the outcome if the 1996 U.S. presidential election were re-enacted in a population of di erent demographic composition, ceteris paribus? We have bene tted from the opportunity to present this research in seminars at Northwestern

This article concerns an infinite horizon economy where trade must occur pairwise, using a double auction mechanism, and where fiat money overcomes lack of double coincidence of wants. Traders are anonymous and lack market power. Goods are divisible and perishable, and are consumed at every date. Preferences are defined by utility-stream overtaking. Money is divisible and not subject to inventory constraints. The evolution of individual and economywide money holdings distributions is characterized. There is a welfare-ordered continuum of single price equilibria, reflecting indeterminacy of the price level rather than of relative prices.

This paper presents a new test for fractionally integrated (FI) processes. In particular, we propose a testing procedure in the time domain that extends the well–known Dickey–Fuller approach, originally designed for the I(1) versus I(0) case, to the more general setup of FI(d0) versus FI(d1), with d1<d0. When d0=1, the proposed test statistics are based on the OLS estimator, or its t–ratio, of the coefficient on Δd1yt−1 in a regression of Δyt on Δd1yt−1 and, possibly, some lags of Δyt. When d1 is not taken to be known a priori, a pre–estimation of d1 is needed to implement the test. We show that the choice of any T1/2–consistent estimator of d1∈[0 ,1) suffices to make the test feasible, while achieving asymptotic normality. Monte–Carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well, both in terms of power and size, when compared with others available in the literature. The paper ends with two empirical applications.