Knowledge that Transforms

The neoclassical growth model focuses on factor accumulation as an engine of growth, while the neo-Schumpetarian growth model stresses innovation. This paper argues that these two views of growth may capture different phases of a single growth experience. In the model presented below, the balanced growth path is unstable and the economy achieves sustainable growth through cycles under an empirically plausible condition, perpetually moving back and forth between two phases. One phase is characterized by higher output growth, higher investment, no innovation, and a competitive market structure. The other phase is characterized by lower output growth, lower investment, high innovation, and a more monopolistic market structure. Both investment and innovation are essential in sustaining growth indefinitely, and yet they move in an asynchronized way; only one of them appears to play a dominant role in each phase. The economy grows faster along the cycles than along the Zunstable. balanced growth path.

This paper examines the sharing of risks between generations in the framework of an overlapping generations model of social security with shocks to the productivity of labor and capital and demographic shocks. The study focused on stationary long run allocations. The concept of interim optimality was utilized, which amounts to standard Pareto optimality once the state of the world in which the agents are born is known. The set of interim optimal allocations was characterized and the equilibria associated with various institutional forms of social security from the point of view of the optimal criterion were also studied. In addition, the analogs of two traditional welfare theorems of microeconomic theory were obtained.

A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form μ = ∫ Θ μ θ dλ(θ). Among these, a natural representation is one whose components (μ θ 's) are learnable (one can approximate μ θ by conditioning μ on observation of the process) and sufficient for prediction (μ θ 's predictions are not aided by conditioning on observation of the process). We show the existence and uniqueness of such a representation under a suitable asymptotic mixing condition on the process. This representation can be obtained by conditioning on the tail-field of the process, and any learnable representation that is sufficient for prediction is asymptotically like the tail-field representation. This result is related to the celebrated de Finetti theorem, but with exchangeability weakened to an asymptotic mixing condition, and with his conclusion of a decomposition into i.i.d. component distributions weakened to components that are learnable and sufficient for prediction.

I provide a systematic treatment of the asymptotic properties of weighted M-estimators under variable probability stratified sampling. The characterization of the sampling scheme and representation of the objective function allow for a straightforward analysis. Simple, consistent asymptotic variance matrix estimators are proposed for a large class of problems. When stratification is based on exogenous variables, I show that the unweighted M-estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality. When population frequencies are known, a more efficient weighting is possible. I also show how the results carry over to multinomial sampling.

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We analyze under which conditions a given vector field can be disaggregated as a linear combination of gradients. This problem is typical of aggregation theory, as illustrated by the literature on the characterization of aggregate market demand and excess demand. We argue that exterior differential calculus provides very useful tools to address these problems. In particular, we show, using these techniques, that any analytic mapping in Rn satisfying Walras Law can be locally decomposed as the sum of n individual, utility-maximizing market demand functions. In addition, we show that the result holds for arbitrary (price-dependent) income distributions, and that the decomposition can be chosen such that it varies continuously with the mapping. Finally, when income distribution can be freely chosen, then decomposition requires only n/2 agents.