Stochastic growth with social-status concern: The existence of a unique stable distribution

This paper extends Kurz’s (1968) growth model to a stochastic growth framework with social-status concern and unbounded production shocks. Using the stochastic monotonicity of a stochastic dynamic system and the methods adopted in Zhang (2007), the existence, uniqueness, and stability of invariant distribution are investigated. Different from the existence of multiple steady states under certainty, it is shown here that there exists a unique stable invariant distribution under uncertainty.     

Stochastic optimal growth with nonconvexities

This paper studies optimal investment and dynamic behavior in stochastically growing economies. We assume neither convex technology nor bounded support of the productivity shocks. A number of basic results concerning the investment policy and the Ramsey–Euler equation are established. We also prove a fundamental dichotomy pertaining to optimal growth models perturbed by standard econometric shocks: either an economy is globally stable or it is globally collapsing to the origin.     

Stochastic optimal growth with a non-compact state space

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [Brock, W.A., Mirman, L., 1972. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory 4, 479–513] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.     

Equivalence of utilitarian maximal and weakly maximal programs

For a class of aggregative optimal growth models, which allow for a non-convex and non-differentiable production technology, this paper examines whether the set of utilitarian maximal programs coincides with the set of weakly maximal programs. It identifies a condition, called the Phelps–Koopmans condition, under which the equivalence result holds. An example is provided to demonstrate that the equivalence result is invalid when the Phelps–Koopmans condition does not hold.     

Trip-timing decisions with traffic incidents

This paper analyzes traffic bottleneck congestion when drivers randomly cause incidents that temporarily block the bottleneck. Drivers have general scheduling preferences for time spent at home and at work. They independently choose morning departure times from home to maximize expected utility without knowing whether an incident has occurred. The resulting departure time pattern may be compressed or dispersed according to whether or not the bottleneck is fully utilized throughout the departure period on days without incidents. For both the user equilibrium (UE) and the social optimum (SO) the departure pattern changes from compressed to dispersed when the probability of an incident becomes sufficiently high. The SO can be decentralized with a time-varying toll, but drivers are likely to be strictly worse off than in the UE unless they benefit from the toll revenues in some way. A numerical example is presented for illustration. Finally, the model is extended to encompass minor incidents in which the bottleneck retains some capacity during an incident.     

Existence of a competitive equilibrium in the Lucas (1988) model without physical capital

This paper considers an endogenous growth model with human capital accumulation. It gives sufficient conditions and a necessary condition for the existence of a unique competitive equilibrium with externalities. These conditions are more stringent than those which prevail for the existence of an equilibrium defined as the solution to a fixed-point problem.     

Local and global indeterminacy in two-sector models of endogenous growth

We consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors. We also show that for any value of the elasticity of intertemporal substitution in consumption, poverty traps may occur when the final good sector is capital intensive in human capital.     

A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

A unified theory of structural change

This paper uses dynamic general equilibrium and computational methods, inspired by the multi-sector growth model structure in Stephen Turnovsky's work, to develop a theory that unifies two of the traditional explanations of structural change: sector-biased technical change and non-homothetic preferences. The theory is based on an overlapping-generations growth model with endogenous technical change and non-homothetic preferences. An expanding-variety setup with two different R&D technologies, agricultural, and non-agricultural, is employed. The analysis, based on numerical simulations, shows that the biased technical change hypothesis finds most support in the data. It also points to production-side specific factors, such as asymmetries in cross-sector knowledge spillovers, as explanatory factors of the bias in technical change.     

Estimation and inference in two-stage,semi-parametric models of production processes

Many papers have regressed non-parametric estimates of productive efficiency on environmental variables in two-stage procedures to account for exogenous factors that might affect firms’ performance. None of these have described a coherent data-generating process (DGP). Moreover, conventional approaches to inference employed in these papers are invalid due to complicated, unknown serial correlation among the estimated efficiencies. We first describe a sensible DGP for such models. We propose single and double bootstrap procedures; both permit valid inference, and the double bootstrap procedure improves statistical efficiency in the second-stage regression. We examine the statistical performance of our estimators using Monte Carlo experiments.     

The core can be accessed with a bounded number of blocks

We show the existence of an upper bound for the number of blocks required to get from one imputation to another provided that accessibility holds. The bound depends only on the number of players in the TU game considered. For the class of games with non-empty cores this means that the core can be reached via a bounded sequence of blocks.     

Mean-variance portfolio selection of cointegrated assets

This paper considers the continuous-time mean-variance portfolio selection problem in a financial market in which asset prices are cointegrated. The asset price dynamics are then postulated as the diffusion limit of the corresponding discrete-time error-correction model of cointegrated time series. The problem is completely solved in the sense that solutions of the continuous-time portfolio policy and the efficient frontier are obtained as explicit and closed-form formulas. The analytical results are applied to pairs trading using cointegration techniques. Numerical examples show that identifying a cointegrated pair with a high mean-reversion rate can generate significant statistical arbitrage profits once the current state of the economy sufficiently departs from the long-term equilibrium. We propose an index to simultaneously measure the departure level of a cointegrated pair from equilibrium and the mean-reversion speed based on the mean-variance paradigm. An empirical example is given to illustrate the use of the theory in practice.