In this paper, we examine the influence of monetary policy on the speed of convergence in a standard monetary growth model à la Sidrauski allowing for differences in the elasticity of substitution between factors of production. The respective changes in the rate of convergence and its sensitivities to the central model parameters are derived both analytically and numerically. By normalizing the constant elasticity of substitution (CES) production functions both outside the steady state and within the steady state, it is possible to distinguish between an efficiency and a distribution effect of a change in the elasticity of substitution. We show that monetary policy is the more effective, the lower is the elasticity of substitution, and that the impact of monetary policy on the speed of convergence is mainly channeled via the efficiency effect.

If private sector agents update their beliefs with a learning algorithm other than recursive least squares, expectational stability or learnability of rational expectations equilibria (REE) is not guaranteed. Monetary policy under commitment, with a determinate and E-stable REE, may not imply robust learning stability of such equilibria if the RLS speed of convergence is slow. In this paper, we propose a refinement of E-stability conditions that allows us to select equilibria more robust to specification of the learning algorithm within the RLS/SG/GSG class. E-stable equilibria characterized by faster speed of convergence under RLS learning are learnable with SG or generalized SG algorithms as well.

Using a two-sector endogenous growth model, the speed of convergence is determined primarily by the gap in rates of return between physical and human capital. In closed economies, for a typical situation of having relatively less physical capital than in a steady state, the return on physical capital will be significantly high, whereas the return on human capital will be relatively low. This gap in rates of return is quite large when the economy is not at its steady state. In open economies, where human capital is nontradable, the gap in rates of return is small, as is the gap between the international interest rate (which is less than the closed economies return on physical capital) and the return on human capital. Convergence in open economies will be relatively slow, and convergence in closed economies will be relatively fast, and therefore there is little gain from financial liberalization.

We derive results that show the impact of aggregation in a queueing network. Our model consists of a two-stage queueing system where the first (upstream) queue serves many flows, of which a certain subset arrive at the second (downstream) queue. The downstream queue experiences arbitrary interfering traffic. In this setup, we prove that, as the number of flows being aggregated in the upstream queue increases, the overflow probability of the downstream queue converges uniformly in the buffer level to the overflow probability of a single queueing system obtained by simply removing the upstream queue in the original two-stage queueing system. We also provide the speed of convergence and show that it is at least exponentially fast. We then extend our results to non-i.i.d. traffic arrivals.

Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∫0∞[limu→∞E(X(u))-E(X(t))]dt as a measure of the speed of convergence towards stationarity of the process {X(t), t≥0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t), t≥0} is an ergodic birth-death process on {0,1,….} starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

We consider the many-server Poisson queue M/M/c with arrival intensity λ, mean service time 1 and λ/c < 1. Let X(t) be the number of customers in the system at time t and assume that the system is initially empty. Then pn(t) = P(X(t) = n) converges to the stationary probability πn = P(X = n). The integrals ∫0∞[E(X)-E(X(t))]dt and ∫0∞[P(X≤n) − P(X(t)≤n)]dt are a measure of the speed of convergence towards stationarity. We express these integrals in terms of λ and c.