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.     

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.     

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.     

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.     

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.     

Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

Pareto improving interventions in a general equilibrium model with private provision of public goods

Most of the literature on government intervention in models of voluntary public goods supply focuses on interventions that increase the total level of a public good, which is considered to be typically underprovided. However, an intervention that is successful in increasing the public good level need not benefit everyone. In this paper we take a direct approach to welfare properties of voluntary provision equilibria in a full blown general equilibrium model with public goods and study interventions that have the goal of Pareto improving on the voluntary provision outcome. Towards this end, we study a model with many private goods and non-linear production technology for the public good, and hence allow for relative price effects to serve as a powerful channel of intervention. In this setup we show that Pareto improving interventions generally do exist. In particular, direct government provision financed by “small” , or “local” , lump-sum taxes can be used generically to Pareto improve upon the voluntary provision outcome.     

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.     

Voluntary contributions to multiple public goods in a production economy with widespread externalities

In a production economy, multiple public goods are produced by firms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers’ consumption and contributions and all firms’ production enter into utility functions. Public goods can be imperfect substitutes or complements, and they can be local public goods or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the differentiable approach. Applying the transversality theorem for smooth economies in a regular parameterization, we obtain the existence of equilibrium in such an economy, and generically equilibria are regular and locally unique.     

Satiation and existence of competitive equilibrium

In this paper, we introduce a new assumption concerning the (non)satiation property of preferences and establish the existence of a competitive equilibrium under it. The assumption is weaker than the standard nonsatiation assumption and “weak nonsatiation” introduced by Allouch and Le Van (2008). In particular, it allows preferences to be satiated only inside the set of individually rational feasible consumptions, while the two nonsatiation assumptions do not. It is also worth noting that just like the two nonsatiation assumptions, our new assumption depends solely on the characteristics of consumers.     

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.     

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

The graph of Lindahl correspondence as the unique von Neumann-Morgenstern abstract stable set

In this paper, we consider a continuum economy with a finite number of types of agent, and several private and public goods. The main result of the paper is that the graph of the equal-treatment Lindahl equilibria mapping is the unique abstract stable set with respect to the dominance relation in economies with crowding effects introduced by Vasil'ev et al. in 1995. The external stability of this mapping implies that, for any equal-treatment allocation x in , that is not a Lindahl equilibrium, there exists a subeconomy of such that one of its equal-treatment Lindahl allocations blocks x. This result is a counterpart of the theorem of Mas-Colell for Aumann's atomless market with private goods.     

The business cycle model with a unique stable limit cycle

This paper provides the mathematical foundation to the long-standing academic belief that Goodwin's 1951 nonlinear business cycle model has a unique stable limit cycle. In spite of the asymmetric nonlinearity of investment function, the model has certainly a unique stable limit cycle in an economically meaningful region. Once solution paths start from any initial point in the region, they all tend to the limit cycle without escaping from the region or hitting the ceiling or floor of investment during a transition period. The structural stability of the model prevents the limit cycle from vanishing in the face of small perturbations.     

Defining efficient policies in a general equilibrium model: a multi-objective approach

Macroeconomic policy makers are typically concerned with several indicators of economic performance. We thus propose to tackle the design of macroeconomic policy using Multicriteria Decision Making (MCDM) techniques. More specifically, we employ Multi-objective Programming (MP) to seek so-called efficient policies. The MP approach is combined with a computable general equilibrium (CGE) model. We chose use of a CGE model since it has the dual advantage of being consistent with standard economic theory while allowing one to measure the effect(s) of a specific policy with real data. Applying the proposed methodology to Spain (via the 1995 Social Accounting Matrix) we first quantified the trade-offs between two specific policy objectives: growth and inflation, when designing fiscal policy. We then constructed a frontier of efficient policies involving real growth and inflation. In doing so, we found that policy in 1995 Spain displayed some degree of inefficiency with respect to these two policy objectives. We then offer two sets of policy recommendations that, ostensibly, could have helped Spain at the time. The first deals with efficiency independent of the importance given to both growth and inflation by policy makers (we label this set: general policy recommendations). A second set depends on which policy objective is seen as more important by policy makers: increasing growth or controlling inflation (we label this one: objective-specific recommendations).     

The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance

This paper focuses on the analysis of size distributions of innovations, which are known to be highly skewed. We use patent citations as one indicator of innovation significance, constructing two large datasets from the European and US Patent Offices at a high level of aggregation, and the Trajtenberg [1990, A penny for your quotes: patent citations and the value of innovations. Rand Journal of Economics 21(1), 172–187] dataset on CT scanners at a very low one. We also study self-assessed reports of patented innovation values using two very recent patent valuation datasets from the Netherlands and the UK, as well as a small dataset of patent licence revenues of Harvard University. Statistical methods are applied to analyse the properties of the empirical size distributions, where we put special emphasis on testing for the existence of ‘heavy tails’, i.e., whether or not the probability of very large innovations declines more slowly than exponentially. While overall the distributions appear to resemble a lognormal, we argue that the tails are indeed fat. We invoke some recent results from extreme value statistics and apply the Hill [1975. A simple general approach to inference about the tails of a distribution. The Annals of Statistics 3, 1163–1174] estimator with data-driven cut-offs to determine the tail index for the right tails of all datasets except the NL and UK patent valuations. On these latter datasets we use a maximum likelihood estimator for grouped data to estimate the tail index for varying definitions of the right tail. We find significantly and consistently lower tail estimates for the returns data than the citation data (around 0.6–1 vs. 3–5). The EPO and US patent citation tail indices are roughly constant over time, but the latter estimates are significantly lower than the former. The heaviness of the tails, particularly as measured by value indicators, we argue, has significant implications for technology policy and growth theory, since the second and possibly even the first moments of these distributions may not exist.