Yaw Nyarko

Learning by Doing and the Choice of Technology

This paper explores a one-agent Bayesian model of learning by doing and technological choice. To produce output, the agent can choose among various technologies. The beneficial effects of learning by doing are bounded on each technology, and so long-run growth in output can take place only if the agent repeatedly switches to better technologies. As the agent repeatedly uses a technology, he learns about its unknown parameters, and this accumulated expertise is a form of human capital. But when the agent switches technologies, part of this human capital is lost. It is this loss of human capital that may prevent the agent from moving up the quality ladder of technologies as quickly as he can, since the loss is greater the bigger is the technological leap. We analyze the global dynamics. We find that a human-capital- rich agent may find it optimal to avoid any switching of technologies, and therefore to experience no long-run growth. On the other hand, a human-capital-poor agent, who because of his lack of skill is not so attached to any particular technology, can find it optimal to switch technologies repeatedly, and therefore enjoy long-run growth in output. Thus the model can give rise to overtaking.

The transfer of human capital

Most of our productive knowledge was handed down to us by previous generations. The transfer of knowledge from the old to the young is therefore a cornerstone of productivity growth. We study this process in a model in which the old sell knowledge to the young - - old workers train the young, and charge them for this service. We take an information-theoretic approach in which training occurs if a young agent watches an old worker perform a task. This assumption has plenty of empirical support -- in their first three months on the job, young workers spend about five times as long watching others work as they do in formal training programs. Equilibrium is not constrained Pareto optimal. The old have private information, and this gives rise to an adverse selection problem: some old agents manage to sell skills that the young would not buy (if only they knew exactly what they were buying). We derive the implications for the lifetime of technological lines, and we show that the model generates a negative relation between a firms productivity and its probability of failure.

Stepping stone mobility

People at the top of an occupational ladder earn more partly because they have spent time on lower rungs, where they have learned something. But what precisely do they learn? There are two contrasting views: First, the Bandit model assumes that people are different, that experience reveals their characteristics, and that consequently an occupational switch can result. Second, in our Stepping Stone model, experience raises a workers productivity on a given task and the acquired skill can in part be transferred to other occupations, and this prompts movement. Safe activities (where mistakes destroy less output) are a natural training ground.

OPTIMAL CONTROL OF AN UNKNOWN LINEAR PROCESS WITH LEARNING

Optimal control of a linear process with unknown parameters is considered when the horizon is infinite and rewards are discounted. Active learning strategies are considered, i.e., agents consider the information value of possible actions, as well as current reward. Distributional assumptions are minimal in that no restriction to conjugate families is made. Convergence of beliefs and actions is established. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Is the Brain Drain Good for Africa

We build upon recent literature to do several exercises to assess benefits and costs of the brain drain to Africa. Contrary to a lot of the worries expressed in the media and in aid agencies, the brain drain is probably a net benefit to the source countries. We make several arguments: (1) the African brain drain is not large enough to have much effect on Africas skill gap relative to the rest of the world. Since other regions had a larger brain drain, the skill gap between Africa and the rest would actually be larger in a counterfactual world of NO brain drain with the same amount of skill creation. (2) The gains to the migrants themselves and their families who receive indirect utility and remittances more than offset the losses of the brain drain. According to one of our calculations, the present value of remittances more than covers the cost of educating a brain drainer in the source country. (3) Brain drain has a positive effect on skill accumulation that appears to offset one for one the loss of skills to the brain drain. Hence it is not surprising that we fail to identify any negative growth effect of the brain drain. Although some of our exercises are reliant on special assumptions and shaky data that require further investigation, we conclude based on what we can know in this paper that the brain drain is on balance good for Africa.

Dynamic Optimization Under Uncertainty: Non-convex Feasible Set

An editorial note in the Economic Journal (May 1930) reported the death of Frank Ramsey, and his 1928 paper was described as ‘one of the most remarkable contributions to mathematical economics ever made’. In the same issue the editor organized a symposium on increasing returns and the representative firm. This symposium seems to be a natural follow-up of a number of papers published by the Journal during 1926–8, including the well-known article of Allyn Young (1928) that is still available, and duly remembered. The problems of equilibrium of a firm under increasing returns, or more generally, of designing price-guided resource allocation processes to cope with increasing returns, has since been a topic of continuing interest. Ramsey’s contribution was enshrined as a durable piece with a resurgence of interest in intertemporal economics in the fifties. But neither John Keynes, the editor of the Economic Journal who was most appreciative of Ramsey’s talents, neither the subsequent writers on ‘growth theory’ in Cambridge, England (nor, for that matter, those in Cambridge, Massachusetts), have made any precise suggestion towards incorporating increasing returns in a Ramsey-type exercise.

LEARNING IN MIS-SPECIFIED MODELS AND THE POSSIBILITY OF CYCLES

Abstract I study the problem of a monopolist maximizing a sum of discounted profits facing a linear demand curve whose slope and intercept are unknown. I show that if the monopolist has a mis-specified model, i.e., if the true slope and intercept lie outside of the support of the monopolists prior beliefs, then actions and beliefs may cycle on every sample path. This behavior is shown to be robust to perturbations in the prior, true parameter, and actions. Such behavior is not possible if the agents model is correctly specified; instead actions and beliefs necessarily converge.

Bayesian Learning Leads to Correlated Equilibria in Normal Form Games

SummaryConsider an infinitely repeated normal form game where each player is characterized by a “type” which may be unknown to the other players of the game. Impose only two conditions on the behavior of the players. First, impose the Savage (1954) axioms; i.e., each player has some beliefs about the evolution of the game and maximizes its expected payoffs at each date given those beliefs. Second, suppose that any event which has probability zero under one players beliefs also has probability zero under the other players beliefs. We show that under these two conditions limit points of beliefs and of the empirical distributions (i.e., sample path averages or histograms) are correlated equilibria of the “true” game (i.e., the game characterized by the true vector of types).

Bounded rationality and learning* Introduction

Many have objected to the use of the Nash equilibrium (or more generally, Bayesian Nash equilibrium) concept in game theory, and similarly to the use of the rational expectations concept in the theory of competitive markets, on the grounds that the theory assumes too much sophistication and coordination of beliefs on the part of decision-markers. The papers in this volume are among those which study the implications of relaxing those assumptions. To provide a suitable context to describe the papers in this symposium, we will begin with a slight digression. Consider a repeated stage game where at each stage there are finitely many players, each with finitely many actions. First consider the case where each player seeks to maximize his expected utility at each date (i.e., he has a zero discount factor) given specified beliefs about the play of his opponents. Let us suppose that we have eliminated all dominated actions within the stage game. This means, in particular, that for each of the actions of each player there is a set of beliefs that a player could have on the actions of the other players which would rationalize that action as a best response for that player. If the stage game were to be played only once, each outcome to the game could be rationalized as the outcome of maximizing behavior under some beliefs of agents. Maximizing behavior by itself imposes absolutely no restriction on the outcome of the oneshot stage game! This is true even when the payoff matrices of the players are common knowledge. Introducing imperfect information over the payoffs does not diminish the set of possible utility maximizing outcomes. Indeed, by allowing type-dependent correlations in behavior, the introduction of imperfect information over payoffs may actually increase the set of possible (probability distributions of) outcomes. Instead of a zero discount factor, let us now suppose that the players have a positive discount factor and seek to maximize the expected sum of their discounted payoffs. Then, even without eliminating strategies which are dominated in the normal form game, we may show via folk-theorem-type arguments that without placing restrictions on the beliefs of players we can rationalize just about a n y

Optimal Growth with Unobservable Resources and Learning

Abstract This paper examines the problem of choosing optimal resource consumption from an imperfectly observable aggregate capital, wealth or resource stock which the decision-maker learns about over time. Learning is complicated by the fact that the planner receives information about an object (the true resource stock) which is a moving target. Under the assumption that the utility of zero consumption is − ∞ we show that the optimal policy follows a completely deterministic ‘cautious’ or ‘minmax’ policy that assumes the worst in each period and optimizes against that. When this model is compared to a model with completely observable wealth levels the following insights are obtained: (1) there is ‘over-saving,’ (2) investment and output processes are more volatile than consumption, and (3) regressions underestimate the risk aversion of agents. Information about the wealth or stock level is only valuable if it alters the support of the agents beliefs. Thus, information may be statistically informative yet economically valueless. If information changes the support of the agents beliefs then the optimal solution features an endogenous resource ‘discovery’ process.