Contributions published at Financial Economics (Felix Kübler)

This paper studies an overlapping generations model with stochastic production and incomplete markets to assess whether the introduction of an unfunded social security system leads to a Pareto improvement. When returns to capital and wages are imperfectly correlated a system that endows retired households with claims to labor income enhances the sharing of aggregate risk between generations. Our quantitative analysis shows that, abstracting from the capital crowding-out effect, the introduction of social security represents a Pareto improving reform, even when the economy is dynamically effcient. However, the severity of the crowding-out effect in general equilibrium tends to overturn these gains.

We examine the effects of collateralized borrowing in a realistically parameterized life-cycle portfolio choice problem. We provide basic intuition in a two-period model and then solve a multi-period model computationally. Our analysis provides insights into life-cycle portfolio choice relevant for researchers in macroeconomics and finance. In particular, we show that standard models with unlimited borrowing at the riskless rate dramatically overstate the gains to holding equity when compared with collateral-constrained models. Our results do not depend on the specification of the collateralized borrowing regime: the gains to trading equity remain relatively small even with the unrealistic assumption of unlimited leverage. We argue that our results strengthen the role of borrowing constraints in explaining the portfolio participation puzzle, that is, why most investors do not own stock.

We construct a life cycle model that delivers realistic behavior for both equity holdings and borrowing. The key model ingredient is a wedge between the cost of borrowing and the risk-free investment return. Borrowing can either raise or lower equity demand, depending on the cost of borrowing. A borrowing rate equal to the expected return on equity-which we show roughly matches the data-minimizes the demand for equity. Alternative models with no borrowing or limited borrowing at the risk-free rate cannot simultaneously fit empirical evidence on borrowing and equity holdings. Copyright Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

In a comment, Peter Bossaerts and William R. Zame [2006. Finance Research Letters. This issue] claim that the main result of our paper [Judd, K.L., Kubler, F., Schmedders, K., 2003. The Journal of Finance 58, 2203–2217], namely the no-trade theorem for the dynamic Lucas infinite horizon economy with heterogeneous agents, is an artifact of the assumption that asset dividends and individual endowments follow the same stationary finite-state Markov process. In this reply, we clarify our assumptions and contrast them with the examples in Bossaerts and Zame.

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents' first-order conditions are approximately satisfied ("approximate equilibria"), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close-by economies; that is, for economies with close-by individual endowments and preferences. Copyright The Econometric Society 2005.

Bill and Herb have provided an illuminating and interesting presentation of Irving Fisher's Ph.D. dissertation Mathematical Investigations in the Theory of Value and Prices. They correctly emphasize that Fisher's fundamental contribution to the early theory of general equilibrium was the construction of a machine to compute the equilibrium quantities in a Walrasian model of competitive markets. As Fisher notes, Walras deserves priority for deriving a system of equations that characterize equilibrium in competitive markets. Even in this area, however, Fisher makes a subtle and interesting contribution in his system of equilibrium equations, discussed later. The first modern treatment of computing equilibrium prices in Walrasian economies is due to Herb, as everyone in this audience knows. His seminal paper, “On the Computation of Equilibrium Prices,” appears, most appropriately, in Ten Essays in Honor of Irving Fisher. The modern treatment of the existence question in the general equilibrium model, due to Arrow and Debreu, converts the equilibrium conditions into a fixed point of a continuous map, say from the price simplex into itself. It follows from Brouwer's fixed point theorem that this map will have a fixed point. The Scarf algorithm computes approximate fixed points of any continuous map of the simplex into itself. Hence the Scarf algorithm can be used to compute equilibrium quantities. Subsequent to Scarf's research, a more direct method of solving nonlinear systems of equilibrium equations was suggested by Eaves. The so-called homotopy method deforms a set of equations whose solution we know into the equilibrium equations, tracing out a path of solutions terminating in a solution for the equilibrium equations. Unfortunately, there is no price-adjustment interpretation of the disequilibrium prices along the homotopy path. In this way they are similar to the prices generated by the Fisher machine out of equilibrium. Below we give a system of equations characterizing equilibrium in an exchange economy with two agents and three goods. Agents are assumed to be endowed with money income and additive separable utility functions, which are monotone, strictly concave, and smooth. The unknowns in our equations are the state variables of Fisher's machine, in other words, prices, individual consumptions, expenditures, marginal utilities of income, and marginal utilities of the consumptions implied by expenditures and prices. Equilibrium values are computed using the homotopy method.

Kreps–Porteus preferences constitute a widely used alternative to time separability. We showin this paper that with these preferences utility maximization does not impose any observable restrictions on a household’s savings decisions or on choices in good markets over time. The additional assumption of a weakly separable aggregator is needed to ensure that the assumption of utility maximization restricts intertemporal choices. Under this assumption, choices in spot marketsare characterized by a strong axiom of revealed preferences (SSARP).Under uncertainty Kreps–Porteus preferences impose observable restrictions on portfolio choice if one observes the last period of an individual’s planning horizon. Otherwise there are no restrictions.

Is general equilibrium theory empirically testable? Our perspective on this question differs fromthe standard, Sonnenschein–Debreu–Mantel (SDM) viewpoint. While the SDM tradition considersaggregate (excess) demand as a function of prices, we suppose that what is observable is the equilibriumprice vector as a function of the fundamentals of the economy.We apply this perspective to anexchange economy where equilibrium prices and individual endowments are observable.We derivenecessary and sufficient conditions that characterize the equilibrium prices, as functions of initialendowments. Furthermore, we show that, if these conditions are satisfied, then the economy cangenerically be identified. Finally, we show that when only aggregate data are available, observablerestrictions vanish.We conclude that the availability of individual data is essential for the derivationof testable consequences of the general equilibrium construct.

At a stationary Markov equilibrium of a Markovian economy of overlapping generations, prices at a date-event are determined by the realization of the shock, the distribution of wealth and, with production, the stock of capital. Stationary Markov equilibria may not exist; this is the case with intra-generational heterogeneity and multiple commodities or long life spans. Generalized Markov equilibria exist if prices are allowed to vary also with the realization of the shock, prices and the allocation of consumption and production at the predecessor date-event. (Stationary) Markov $ \epsilon $ -equilibria always exist; as $ \epsilon \rightarrow 0, $ allocations and prices converge to equilibrium prices and allocations that, however, need not be stationary.

We consider an infinite-horizon exchange economy with incomplete markets and collateral constraints. As in the two-period model of Geanakoplos and Zame (2002), households can default on their liabilities at any time, and financial securities are only traded if the promises associated with these securities are backed by collateral. We examine an economy with a single perishable consumption good, where the only collateral available consists of productive assets. In this model, competitive equilibria always exist and we show that, under the assumption that all exogenous variables follow a Markov chain, there also exist stationary equilibria. These equilibria can be characterized by a mapping from the exogenous shock and the current distribution of financial wealth to prices and portfolio choices. We develop an algorithm to approximate this mapping numerically and discuss ways to implement the algorithm in practice. A computational example demonstrates the performance of the algorithm and shows some quantitative features of equilibria in a model with collateral and default.