The simple analytics of information and experimentation in dynamic agency

Summary. The dynamics of a stochastic, two–period principal–agent relationship is studied. The agent's type remains the same over time. Contracts are short term. The principal designs the second contract, taking the information available about the agent after the first period into account. Compared to deterministic environments significant changes emerge: First, fully separating contracts are optimal. Second, the principal has two opposing incentives when designing contracts: the principal ‘experiments,’ making signals more informative; yet dampens signals, thereby reducing up–front payments. As a result, ‘good’ agents' targets are ratcheted over time. Received: November 28, 2000; revised version: December 1, 2000     

Stochastic technology shocks in an extended Uzawa–Lucas model: closed-form solution and long-run dynamics

We add stochastic technological progress, modelled as a geometric Brownian motion with drift, to an augmented Uzawa–Lucas growth model. Under a particular combination of parameters we derive a closed form solution to the model and analytical expressions which show that uncertainty reduces the optimal levels of consumption and increases the proportion of human capital devoted to producing new human capital.     

Basic Stochastic Dynamic Systems of Growth and Trade

Uncertainties are intrinsic features of dynamic economic systems, and this paper considers the dynamic implications of factor endowment (labor, capital) uncertainties for a small growing trading economy. The stochastic growth models presented extend the open neoclassical two-sector growth model (Deardorff) to a stochastic environment in continuous time, and extend the diffusion dynamics of one-sector growth models (Merton; Bourguignon) to a trading two-sector economy. It is demonstrated that the basic propositions of deterministic steady-state growth and endogenous growth theory, under some specifications and certain parametric restrictions, are preserved within a stochastic framework.     

On discounted dynamic programming with unbounded returns

In this paper, we apply the idea of k-local contraction of Rincón-Zapatero and Rodriguez-Palmero (Econometrica 71:1519–1555, 2003; Econ Theory 33:381–391, 2007) to study discounted stochastic dynamic programming models with unbounded returns. Our main results concern the existence of a unique solution to the Bellman equation and are applied to the theory of stochastic optimal growth. Also a discussion of some subtle issues concerning k-local and global contractions is included.     

Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.This paper is dedicated to Professor Mukul Majumdar on his 60th birthday. His research with various co-authors in the late 70s and the 80s pioneered innovative techniques for the analysis of nonconvex dynamic optimization models – both deterministic and stochastic. Roy considers himself particularly fortunate for having had the opportunity to learn economic theory and mathematical economics from Professor Majumdar. This paper has benefited from helpful comments and suggestions by an anonymous referee. Financial support from the 21st Century COE Program at GSE and RIEB, Kobe University, is gratefully acknowledged.     

Stationarity without degeneracy in a model of commodity money

We develop a model of macroeconomic heterogeneity inspired by the Kiyotaki–Wright (J Polit Econ 97:924–954, 1989) formulation of commodity money, with the addition of linear utility and idiosyncratic shocks to savings. We consider two environments. In the benchmark case, the consumer in a meeting is chosen randomly. In the auctions case, the individual holding more money can be selected to be the consumer. We show that in both environments socially optimal trading decisions (that are individually acceptable) are stationary and solve a tractable static optimization problem. Savings decisions in the benchmark case are remarkably invariant to mean-preserving changes in the distribution of shocks. This result is overturned in the auctions case.     

Optimal climate change mitigation under long-term growth uncertainty: Stochastic integrated assessment and analytic findings

Economic growth over the coming centuries is one of the major determinants of today׳s optimal greenhouse gas mitigation policy. At the same time, long-run economic growth is highly uncertain. This paper is the first to evaluate optimal mitigation policy under long-term growth uncertainty in a stochastic integrated assessment model of climate change. The sign and magnitude of the impact depend on preference characteristics and on how damages scale with production. We explain the different mechanisms driving optimal mitigation under certain growth, under uncertain technological progress in the discounted expected utility model, and under uncertain technological progress in a more comprehensive asset pricing model based on Epstein–Zin–Weil preferences. In the latter framework, the dominating uncertainty impact has the opposite sign of a deterministic growth impact; the sign switch results from an endogenous pessimism weighting. All of our numeric scenarios use a DICE based assessment model and find a higher optimal carbon tax than the deterministic DICE base case calibration.     

On capital accumulation paths in a neoclassical stochastic growth model

Summary. Boldrin and Montrucchio [2] showed that any twice continuously differentiable function could be obtained as the optimal policy function for some value of the discount parameter in a deterministic neoclassical growth model. I extend their result to the stochastic growth model with non-degenerate shocks to preferences or technology. This indicates that one can obtain complex dynamics endogenously in a wide variety of economic models, both under certainty and uncertainty. Further, this result motivates the analysis of convergence of adaptive learning mechanisms to rational expectations in economic models with (potentially) complicated dynamics. Received: June 21, 1996; revised version: October 31, 1996     

A note on Johansen's cointegration procedure when trends are present

This note discusses some issues that arise when Johansen's (1991) framework is used to analyze cointegrating relationships among variables with deterministic linear time trends. We cistinguish “stochastic” and “deterministic” cointegration, arguing that stochastic cointegration is sufficient for the existence of an error correction representation and that it is often the hypothesis of interest in empirical applications. We show that Johansen's (1991) method, which includes only a constant term in the estimated regession system, does not allow for stochastic cointegration. We propose to modify Johansen's method by including a vector of deterministic linear trends in the estimated model. We present tabulated critical values of the maximal eigenvalue and trace statistics appropriate for this case. We discuss the circumstances under which our modification may be useful.