learning and control in a changing economic environment abstract in this paper we investigate optimal bayesian learning and control with lagged dependent variables and time varying unknown parameters we assess both the performance of alternative decision rules as in the computationally oriented dual control literature as well as the dynamics of learning and convergence of beliefs as in the more theoretically oriented bayesian learning literature our numerical results indicate that the optimal decision rule involves a noticeable degree of experimentation for moderate to large levels of uncertainty in most situations though the optimal rule will remain less activist than a certainty equivalent rule and induce gradualism exceptions occur when the process to be controlled is near the deterministic steady state in this situation we find that the decision maker will repeatedly undertake costly experiments the extent of optimal experimentation is lower if the unknown parameter is perceived to vary over time in contrast to the fixed parameter case however parameter uncertainty is continually renewed and the incentive to experiment never ceases

price formation in a matching market with targeted offers abstract we model a market where the surpluses from seller buyer matches are heterogeneous but common knowledge price setting is synchronous with search buyers simultaneously make one personalized offer each to the seller of their choice with impatient players efficient coordination is not possible and both temporary and permanent mismatches occur nonetheless for patient players efficient matching with monopsony wages is an equilibrium the setting is inspired by a labor market for highly skilled workers such as the academic job market but it can be easily adapted to for example the housing market or internet advertising auctions

active learning and optimal climate policy this paper develops a climate economy model with uncertainty irreversibility and active learning whereas previous papers assume learning from one observation per period or experiment with control variables to gain additional information this paper considers active learning from investment in monitoring specifically in improved observations of the global mean temperature we find that the decision maker invests a significant amount of money in climate research far more than the current level in order to increase the rate of learning about climate change this helps the decision maker make improved decisions the level of uncertainty decreases more rapidly in the active learning model than in the passive learning model with only temperature observations as the uncertainty about climate change is smaller active learning reduces the optimal carbon tax the greater the risk the larger is the effect of learning the method proposed here is applicable to any dynamic control problem where the quality of monitoring is a choice variable for instance the precision at which we observe gdp unemployment or the quality of education

price dispersion and incomplete learning in the long run abstract in each period a seller chooses a price and the customer for that period buys either one unit or nothing the relationship between price and purchase probability is one of two linear functions it is shown that the seller behaving optimally does not necessarily learn which function is the actual relationship since there can be a positive probability of sequences of prices converging to the price at which the two functions give the same purchase probability

the stability of macroeconomic systems with bayesian learners we study abstract macroeconomic systems in which expectations play an important role consistent with the recent literature on recursive learning and expectations we replace the agents in the economy with econometricians unlike the recursive learning literature however the econometricians in the analysis here are bayesian learners we are interested in the extent to which expectational stability remains the key concept in the bayesian environment we isolate conditions under which versions of expectational stability conditions govern the stability of these systems just as in the standard case of recursive learning we conclude that bayesian learning schemes while they are more sophisticated do not alter the essential expectational stability findings in the literature

actively learning about demand and the dynamics of price adjustment by observing the quantity demanded at particular prices a firm may learn about the parameters of its demand curve in such an environment price changes obstruct the learning process by inducing additional noise the authors paper constructs a dynamic model where a price setting firm endogenously controls the speed of learning the model provides a possible explanation for price inertia as a stable pricing policy allows the firm to learn more rapidly which improves future expected profits furthermore even in the long run learning continues to affect the firm s optimal price copyright 1990 by royal economic society

learning about variable demand in the long run this paper studies the problem of a monopoly who is uncertain about the demand it faces and learns about it over time through its pricing experience the demand curve facing the monopoly is not constant it changes over time in a markovian fashion we characterize the monopoly s optimal policy and inquire how it differs from an informed monopoly s policy it turns out that even when the rate at which the demand varies is negligible the stationary probability with which the monopoly s policy deviates from its informed counterpart is nonnegligible as long as the discount factor is below 1

the invariance of market innovation to the number of firms this article provides a set of conditions under which the r d undertaken in a market economy is invariant to the number or size distribution of firms and the market s allocation is efficient i e given the aggregate expenditure the market chooses socially optimal projects as in several patent race studies we assume that a winner takes all competition determines firms gains but our model differs from earlier studies in that firms are not restricted to undertake only one research project our analysis shows that how one characterizes a firm s choices and innovation technologies has a strong influence on the conclusions one draws from economic analyses of r d

the ignorant monopolist optimal learning with endogenous information economics lacks a good theory of the pricing and output decisions of a monopolist which does not know its demand we inevitably assume that the monopolist knows much more about demand conditions than is reasonable i present a model in which demand information is generated endogenously when information is endogenous the monopolist has an incentive to experiment with price and quantity i derive the direction of experimentation characterize an important value function arising from dynamic programming problems with learning and relate the results to blackwell s comparison of experiments copyright 1993 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

learning under fear of floating in recent years a large fraction of economies overcame the fear of floating we study a model that describes the policy of a central bank uncertain about whether currency depreciations cause output to expand textbook model or contract balance sheet model we conclude that the movement away from fear of floating may not be explained by bayesian or robust policies when the private sector anticipates the central bank s policy and endogenously determines the model central banks may fall in a learning trap an increase in financial volatility provides an escape to such trap that replicates patterns in the data

learning and optimal monetary policy to conduct policy efficiently central banks must use available data to infer or learn the relevant structural relationships in the economy however because a central bank s policy affects economic outcomes the chosen policy may help or hinder its efforts to learn this paper examines whether real time learning allows a central bank to learn the economy s underlying structure and studies the impact that learning has on the performance of optimal policies under a variety of learning environments our main results are as follows first when monetary policy is formulated as an optimal discretionary targeting rule we find that the rational expectations equilibrium and the optimal policy are real time learnable this result is robust to a range of assumptions concerning private sector learning behavior second when policy is set with discretion learning can lead to outcomes that are better than if the model parameters are known finally if the private sector is learning then unannounced changes to the policy regime particularly changes to the inflation target can raise policy loss considerably

a dynamic duopoly investment game without commitment under uncertain market expansion abstract we model capacity building investments in a homogeneous product duopoly facing uncertain demand growth capacity building is achieved through the addition of production units that are durable and lumpy and whose cost is irreversible while building their capacity over time firms compete a la cournot in the product market given their installed capacity there is no exogenous order of moves no commitment regarding future decisions and no finite horizon we investigate markov perfect equilibrium mpe paths of the investment game which may include episodes during which firms invest at different times a preemption pattern and episodes in which firms invest simultaneously a tacit collusion pattern these episodes may alternate and are typically several when firms have yet to invest in capacity the sole pattern that is mpe compatible is a preemption episode firms invest at different times but have equal value the first such investment may occur earlier and therefore be riskier than socially optimal when both firms hold capacity tacit collusion episodes may be mpe compatible firms invest simultaneously at a postponed time hence holding back production in the meantime thereby generating an investment wave in the industry such investment episodes are more likely with higher demand volatility faster market growth and lower cost of capital discount rate

martingales nonlinearity and chaos abstract in this article we provide a review of the literature with respect to the efficient markets hypothesis and chaos in doing so we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices and report some evidence moreover we look at the controversies that have arisen about the available tests and results and raise the issue of whether dynamical systems theory is practical in finance

central bank misperceptions and the role of money in interest rate rules research with keynesian style models has emphasized the importance of the output gap for policies aimed at controlling inflation while declaring monetary aggregates largely irrelevant critics however have argued that these models need to be modified to account for observed money growth and inflation trends and that monetary trends may serve as a useful cross check for monetary policy we identify an important source of monetary trends in form of persistent central bank misperceptions regarding potential output simulations with historical output gap estimates indicate that such misperceptions may induce persistent errors in monetary policy and sustained trends in money growth and inflation if interest rate prescriptions derived from keynesian style models are augmented with a cross check against money based estimates of trend inflation inflation control is improved substantially

learning by doing and learning from others human capital and technical change in agriculture household level panel data from a nationally representative sample of rural indian households describing the adoption and profitability of high yielding seed varieties hyvs associated with the green revolution are used to test the implications of a model incorporating learning by doing and learning spillovers the estimates indicate that i imperfect knowledge about the management of the new seeds was a significant barrier to adoption ii this barrier diminished as farmer experience with the new technologies increased iii own experience and neighbors experience with hyvs significantly increased hyv profitability and iv farmers do not fully incorporate the village returns to learning in making adoption decisions

stochastic control for economic models past present and the paths ahead abstract on the 30th anniversary of a meeting between engineers and economists at princeton university to discuss the potential application of stochastic control methods to economics this paper provides a review of past present and paths ahead the events surrounding some of the key developments of the past are described along with a discussion of the present state of the research and of paths for future research the paper is structured around the primary methods for solving quadratic linear economic stochastic control models namely open loop classical control handcrafted feedback rules optimal feedback min max control optimal feedback rules with parameter uncertainty and dual control the paper also includes a discussion of software developments in economic stochastic control modeling

caution and probing in a macroeconomic model abstract this paper reports on the application of an adaptive dual control technique to a small macroeconometric model of the u s economy both monetary and fiscal policy variables are used in the model the experiments find that probing and active learning will occur in small macroeconometric models but that unrealistically high terminal period penalties on state deviations are required before it appears

an equilibrium model of child maltreatment we propose a dynamic equilibrium model of human capital development of a child that can explain why a parent child relationship might lead to child maltreatment assuming that a parent cannot observe a child s human capital accumulation or effort and that the child s time preference develops endogenously an unstable path of the parent s beliefs regarding the child can persist in equilibrium when the parent faces a high degree of uncertainty in inferring the child s human capital the parent with an initial high estimate of the human capital then tends to underestimate the child s effort which results in persistently punitive abusive nteractions

learning experimentation and monetary policy abstract we present a model of monetary policy where the policymaker faces uncertainty about which he is learning in a bayesian fashion a fixed money supply rule is not optimal since the learning leads to adjustments in the monetary action we present cases in which it is optimal to bear some cost in terms of current output performance in order to gain information that can be used in the formulation of future monetary policy experimentation therefore pays we also show that even passive learning without experimentation still leads to an activist monetary policy i e one that is responsive to new information

bayesian economist bayesian agents i an alternative approach to optimal learning we generalize the results on bayesian learning based on the martingale convergence theorem to the sequential framework we show that the variability in the sequential framework is sufficient under mild conditions to circumvent the incomplete learning results that characterize the optimal learning literature we then give an alternative approach whereby the economist is bayesian with a prior on the space of agent priors we illustrate the usefulness of our approach by applying it to two popular economic examples a monopolist who does not know the demand curve he faces and the stochastic single sector growth model with an unknown production function

optimal monetary policy and model selection in a real time learning environment abstract we investigate how real time parameter learning optimal policies and the volatility of exogenous shocks affect the policymakers ability to distinguish across competing models of the economy the detection speed of model misspecification depends only on the relative volatility of supply and demand shocks

the learning cost of interest rate reversals abstract many central banks in many time periods have sought to avoid interest rate reversals but at present there is no good explanation of this phenomenon our analysis identifies a new learning cost associated with reversing the interest rate in a standard monetary model with forward looking expectations data uncertainty and parameter uncertainty a policy that frequently reverses the interest rate makes learning the key parameters of the model more difficult optimal monetary policy internalises this learning cost and therefore has a lower number of interest rate reversals

leaders and followers perspectives on the nordic model and the economics of innovation abstract what kinds of social and economic systems are most conducive to innovation we formulate a simple model in which countries can close the gap with the technological leader but where the cost of doing so may be so high that the country chooses to remain laggards observed disparities in productivity may be the result of a recognition that the cost of closing the gap exceeds benefit and there may therefore exist an international equilibrium in which there are leaders and followers even if it is granted that the united states is the leader and scandinavia are followers there are theoretical grounds for arguing that the nordic model may in fact be better for innovation suggesting that if the us adopted some of the nordic institutions innovations would be higher and societal welfare would be improved even more

inflation variability and gradualist monetary policy this paper considers the optimal approach to reducing inflation when the cost of inflation is its conditional variability inflation is stochastically related to money growth with unobservable time varying autonomous and induced components a sharp reduction in money growth provides information about the responsiveness of inflation to money but also induces variability as the economy heads into unknown territory gradual policy is always optimal and the model explains why moderate inflation countries adopt a much more gradual money growth reduction than high inflation countries additionally the analysis sheds light on the more general problem of learning with two unobservable parameters

strategic entry deterrence in analyzing deterrence of large scale entry two classes of entry barriers may be distinguished an innocent entry barrier is unintentionally erected as a side effect of innocent profit maximization in contrast a strategic entry barrier is purposely erected to reduce the possibility of entry two types of innocent barriers may also be distinguished a postentry absolute advantage has the property that if entry did occur the established firm would be at a profit advantage over the entrant examples are superior technology or product design patents and lower input prices a preentry asymmetry advantage arises from the fundamental preentry asymmetry between established firm and potential entrant before the entrant makes his entry decision the established firm has already committed resources this prior existence gives first move advantages the preentry asymmetry is independent of symmetry or asymmetry in the rules the equilibrium concept of the postentry game that might ensue even if the postentry game will be played according to nash cournot or entrant as leader rules the preentry leadership

optimal monetary policy when agents are learning abstract we derive optimal monetary policy in a sticky price model when private agents follow adaptive learning we show that this slight departure from rationality has important implications for policy design the central bank faces a new intertemporal trade off not present under rational expectations it is optimal to forego stabilizing the economy in the present in order to facilitate private sector learning and thus ease the future intratemporal inflation output gap trade offs the policy recommendation is robust the welfare loss entailed by optimal policy under learning if the private sector actually has rational expectations is much smaller than if the central bank mistakenly assumes rational expectations when in fact agents are learning

a value function arising in the economics of information abstract the value function for a problem in the economics of the optimal accumulation of information is calculated as a fixed point of a contraction mapping by direct numerical iteration the optimal policy function is obtained as is the function defined as the sum of current expected reward and the discounted expected value of following the optimal policy in the future the optimal policy function is shown to be sensitive to the discount factor indeed for large values of the discount factor weighting the future heavily the policy function has a break and the value function is apparently not differentiable

invention and innovation under alternative market structures the case of natural resources this paper examines the interactions between market structure and resource allocation over time when there is endogenous technical progress the structures considered are a planned economy pure monopoly and competition with patent rights in an efficient allocation the date of invention coincides with the date of innovation the date at which technology is used this is also true with a pure monopoly but monopoly retards technical progress relative to the efficient level competition for patents rights to a new technology results in excessively rapid technical progress if the resource endowment of the economy is sufficiently large also competition may lead to sleeping patents where invention strictly precedes the date of innovation

actively learning by pricing a model of an experimenting seller this article presents a model of a rational seller who is actively learning the slope of his demand curve via his pricing strategy consequently this seller optimally experiments with his price resulting price patterns show a tendency for discreteness as observed in the data which has proved to be a major challenge to most price setting models the experimentation motive can also replicate the observation that prices are more volatile than costs as well as the presence of many idiosyncratic price changes in the data it can do so without a need to assume the existence of large idiosyncratic shocks

contestable markets an uprising in the theory of industry structure presents a transcript of the presidential address delivered at the 94th meeting of the american economic association on december 29 1981 discussion of developments in the theory of industry structure welfare attributes of contestable markets behavior characteristics of oligopoly equilibrium intertemporal vulnerability to inefficient entry ebsco

the impact of disaggregated energy on productivity abstract the issue of the productivity slowdown of the 1970s and 1980s has received considerable analysis in the literature however the issue of the impact of energy on productivity is still debated this study contributes to the debate with the hope that some sight could be provided through disaggregating the factor input energy into two components a petroleum component and a non petroleum component by analysing labour productivity growth total factor productivity growth and labour intensity ratios the disaggregated energy component can be viewed as a major influence in explaining the productivity decline

entrepreneurial learning and the existence of credit markets abstract i explore the economic implications of learning by doing by borrower entrepreneurs who are initially imperfectly informed about their innate abilities it is shown how entrepreneurial learning worsens the adverse effects of moral hazard causing the possible disappearance of otherwise viable credit markets and thereby decreasing social welfare the reason is that learning reduces subjective uncertainty about risky future outcomes thus encouraging excessive risk taking behaviour

active learning a correction these changes stem from a bug which we discovered recently in the measurement error section of the passive learning part of our adaptive control code dual thus the results for the macrae model in section 2 of the paper are not affected because it does not include measurement error also the mean values in the first table above are not altered for the active learning and certainty equivalence solutions but rather only for the passive learning solution the modified results reported above show that the passive learning solutions to the single control variable abel model performed relatively worse than in our earlier report

insurance policies for monetary policy in the euro area in this paper we aim to design a monetary policy for the euro area that is robust to the high degree of model uncertainty at the start of monetary union and allows for learning about model probabilities using the data that has become available since then to this end we compare and ultimately combine bayesian and worst case analysis using four reference models developed at the ecb and estimated with pre emu synthetic data we start by computing the cost of insurance against model uncertainty that is the relative performance of worst case or minimax policy versus bayesian policy we find that maximum insurance across this range of models can be obtained at moderate costs costs are measured in terms of lower expected performance relative to a bayesian policy with flat priors further scrutiny however highlights three shortcomings of this worst case insurance policy i prior beliefs that would rationalize the minimax policy from a bayesian perspective indicate that such insurance is strongly oriented towards the model with highest baseline losses ii the minimax policy is not as tolerant towards small perturbations of policy parameters as the bayesian policy and iii the minimax policy offers no avenue for incorporating posterior model probabilities derived from data available since monetary union thus we propose preferences for robust policy design that reflect a mixture of the bayesian and minimax approaches these preferences referred to as intermediate ambiguity aversion incorporate model probabilities while still giving extra weight to the worst uncertain outcomes we show how the incoming emu data may then be used to update model probabilities and investigate the implications for policy design

strategic deterrence of sequential entry into an industry industrial entry deterrence is typically studied in a setting where an established firm or firms confront and attempt to deter a single potential competitor during the evolution of most industries however a sequence of firms enters or attempts to enter at distinct points in time consideration of issues arising from sequential entry fundamentally alters the qualitative nature of the deterrence decision undertaken by incumbent firms within a sequential setting counterintuitive behavior may be observed specifically numerous government policies designed to decrease industrial concentration penalties for anticompetitive practices subsidization of entry consent decrees restructuring industries may have the opposite effect

preemptive patenting and the persistence of monopoly this article takes a different tack and inquires whether institutions such as the patent system create opportunities for firms with monopoly power to maintain their monopoly power the results apply to other situations such as brand identification spatial location and capacity expansion which share the characteristic that early or preemptive actions may lower the returns to potential competitors

a dynamic model of bertrand competition with entry abstract this paper analyzes a simple repeated game of simultaneous entry and pricing we report a surprising property of the symmetric equilibrium solution if the number of potential competitors is increased above two the market breaks down with higher probability and the competitive outcome becomes less likely more potential competition lowers welfare another bertrand paradox the model can also be applied to auctions to explore whether a revenue maximizing auctioneer should restrict the number of bidders if bidder participation is costly

a density projection approach for non trivial information dynamics adaptive management of stochastic natural resources abstract we demonstrate a density projection approximation method for solving resource management problems with imperfect state information the method expands the set of partially observed markov decision process pomdp problems that can be solved with standard dynamic programming tools by addressing dimensionality problems in the decision maker s belief state density projection is suitable for uncertainty over both physical states e g resource stock and process structure e g biophysical parameters we apply the method to an adaptive management problem under structural uncertainty in which a fishery manager s harvest policy affects both the stock of fish and the belief state about the process governing reproduction we solve for the optimal endogenous learning policy the active adaptive management approach and compare it to passive learning and non learning strategies we demonstrate how learning improves efficiency but typically follows a period of costly short run investment

learning uncertainty and central bank activism in an economy with strategic interactions abstract in this paper we examine the optimal level of central bank activism in a standard model of monetary policy with uncertainty learning and strategic interactions we calibrate the model using g7 data and find that the presence of strategic interactions between the central bank and private agents creates an additional motivation for caution in the optimal monetary policy an activist policy designed to help learning and reduce future uncertainty creates extra volatility in inflation expectations which is detrimental to welfare

experimentation with accumulation abstract we study signal dependent experimentation in the presence of accumulation and show that the passive learner s action surprisingly coincides with the experimentor s when the unknown term is the one determining the decay rate of the stock while they differ when the parameter being learned is the one measuring the accumulation rate these results highlight the importance of the dynamic structure of the problem in signal dependent experimentation moreover they have important consequences for the pollution accumulation debate currently in progress

benefits from u s monetary policy experimentation in the days of samuelson and solow and lucas a policy maker knows two models of ination unemplo yment dynamics one implies an exploitable trade o the other does not the policy maker s prior probability over the two models is part of his state vector bayes law converts the prior probability into a posterior probability at each date and gives the policy maker an incentive to experiment for two models calibrated to u s data through the early 1960s we isolate the component of government policy that is due to experimentation by comparing the outcomes from two bellman equations the rst of which experiments and learns the second of which learns but doesn t experiment we interpret the second as an anticipated utility model and study how well its outcomes approximate those from the experiment and learn bellman equation the approximation is good for our calibrations the benets from purposeful experimentation are small

active learning monte carlo results abstract the revival of interest in learning in stochastic control models invites the examination of some unanswered issues from earlier work following in the tradition of prescott and macrae we consider active learning to examine the question of when these methods are superior to passive learning in the earlier literature it was not possible to address this question because computer speeds were not great enough however modern supercomputers make it possible to reopen this issue in this paper we will examine two well known stochastic control models the macrae model and the abel model although no general conclusions can be drawn the results from the macrae model and the abel model indicate that in certain cases active learning may be superior to passive learning and certainty equivalence in the almost all cases we have analyzed so far active learning is superior to passive learning which in turn is superior to certainty equivalence

how effective is potential competition abstract i examine robustness of perfect contestability a small sunk cost s causes large deviations from the results if the response lag l is even smaller there is an essential discontinuity at s 0 l i also examine what happens if incumbant not entrant exists after l

adaptive control in the presence of time varying parameters in the previous chapters two strands of literature have been brought together the first strand is the research on time varying parameters following a return to normality model viz harvey and phillips 1982 and swamy and tinsley 1980 1 the second strand is the work on adaptive control in the tradition of tse and bar shalom 1973 and kendrick 1981 as indicated in chapter 2 given a time horizon of t periods the goal was to find the values of control variables for period 0 period 1 and so on until period t 1 which minimized the objective functional or cost to go in an adaptive control framework for each period in the time horizon say period t several trial or search values of the controls were tried 2 the optimal cost to go associated with each search control was then calculated following kendrick 1981 ch 10 the computations performed at time t were organized in three steps first the nominal value for the parameters for period t through t was computed using their estimates for time t 1 and their expected law of motion the first search control was also selected then the search for the optimal control was carried out this step included a use the search control and the nominal value for the parameters to get the projected states and covariances in period t 1 b get the nominal path for the states and controls for the period t 1 through t by solving the certainty equivalence ce problem with the projected states as the initial condition c compute the riccati matrices for periods t 1 t d update and project the covariances from period t 1 given t i e the covariance seen at point a above to t 1 e calculate the approximate cost to go for the period t through t f choose a new search control and repeat a f until all search points are evaluated g select the control which yields the minimum cost after the selected control was applied to the system and the process moved one step forward in time the estimates of the states and parameters were updated

intertemporal market division a case of alternating monopoly abstract in this paper we report on an equilibrium with market dominance that exists in a simple two firm model that features neither entry barriers nor sophisticated punishment strategies this equilibrium induces an intertemporal market division in which the two firms alternate as monopolists despite the fact that the model also sustains a cournot duopoly even when initially both firms are active in the market the alternating monopoly reveals itself rather quickly moreover it pareto dominates the cournot equilibrium as it is close to the cartel outcome several examples of what well may be such alternating monopolies are presented

why inflation rose and fell policy makers beliefs and u s postwar stabilization policy this paper provides an explanation for the run up of u s inflation in the 1960s and 1970s and the sharp disinflation in the early 1980s which standard macroeconomic models have difficulties in addressing i present a model in which rational policymakers learn about the behavior of the economy in real time and set stabilization policy optimally conditional on their current beliefs the steady state associated with the self confirming equilibrium of the model is characterized by low inflation however prolonged episodes of high inflation ending with rapid disinflations can occur when policymakers underestimate both the natural rate of unemployment and the persistence of inflation in the phillips curve i estimate the model using likelihood methods the estimation results show that the model accounts remarkably well for the evolution of policymakers beliefs stabilization policy and the postwar behavior of inflation and unemployment in the united states

learning by doing and the value of optimal experimentation abstract recent research on learning by doing has provided the limit properties of beliefs and actions for a class of learning problems in which experimentation is an important aspect of optimal decision making however under these conditions the optimal policy cannot be derived analytically because bayesian learning about unknown parameters introduces a nonlinearity in the dynamic optimization problem this paper utilizes numerical methods to characterize the optimal policy function for a learning by doing problem that is general enough for practical economic applications the optimal policy is found to incorporate a substantial degree of experimentation under a wide range of initial beliefs about the unknown parameters dynamic simulations indicate that optimal experimentation dramatically improves the speed of learning and the stream of future payoffs furthermore these simulations reveal that a policy which separates control and estimation and does not incorporate experimentation frequently induces a long lasting bias in the control and target variables while these sequences tend to converge steadily under the optimal policy they frequently exhibit non stationary behavior when estimation and control are treated separately

fixed costs sunk costs entry barriers and sustainability of monopoly this paper shows that i fixed costs of sufficient magnitude assure the existence of a vector of sustainable prices for the products of a natural monopolist prices making him invulnerable against entry ii nevertheless fixed costs do not constitute barriers to entry that is they need not have undesirable welfare consequences iii indeed in market forms that we call perfectly contestable large fixed costs are completely compatible with many desirable attributes of competitive equilibrium iv sunk costs do however constitute barriers to entry and v finally the profit and welfare consequences of entry barriers are described formally in this paper it is shown that i fixed costs of sufficient magnitude assure the existence of a vector of sustainable prices a set of product prices that make a natural monopolist invulnerable against successful entry ii nevertheless costs that are truly fixed do not constitute barriers to entry that is they do not have the welfare consequences normally attributed to barriers to entry iii indeed there are markets of a form which we call perfectly contestable markets and whose properties may be approximated in practice in which large fixed costs are completely compatible with many if not most of the desirable attributes of competitive equilibrium iv sunk costs do however constitute barriers to entry and v finally the resource allocation problems that stem from fixed costs are formally identical with those that accompany public goods both their sources and their character are the same thus the rationale for public supply of public goods may be no different from that pertaining to nationalization of natural monopolies

potential competition actual competition and economic welfare though the origins of anti trust legislation at least in the united states undoubtedly lie in late nineteenth century populist sentiments its current intellectual foundations rest on modern welfare economics these intellectual foundations provide more than just rhetoric as courts have increasingly relied on the testimony of economists to interpret and reinterpret the inevitably vague language of the legislation the reliance on modern welfare economics is somewhat paradoxical for the assumptions underlying the fundamental theorem of welfare economics are peculiarly ill suited to deal with competition in the central area to which anti trust is applied the industrial sectors of modern economies these sectors are characterized by important non convexities which admittedly present inherent problems for competition the competition that does take place is as likely to take the form of product and r d competition rather than price competition product competition plays no role in the conventional welfare paradigm which assumes a complete set of commodities and it is not that arrow and debreu simply forgot to include technical change in their formulations the natural assumptions underlying the analysis of the production marketing and utilization of knowledge are basically inconsistent with those underlying the arrow debreu model invited paper european economic association meetings copenhagen august 1987 financtal support from the national science foundation and the hoover institution is gratefully acknowledged the presence of non convexittes in production is central in explaining why only a ftnite subset of the set of possible commodities is in fact produced techmcal change is characterized by non convexities in its production radner and stiglitz 1984 if technology exhibits say constant returns to scale at a fixed technology when inputs devoted to r d are included it exhibits non convexities the value or information may increuse with the scale of production while conventional theory focuses on markets for homogeneous commodities each piece of new knowledge must be dinerent from previously produced knowledge knowledge has many of the properties of public goods it being both dificult and undesirable to exclude markets for knowledge are at best imperfect and as we have argued

the role of model uncertainty and learning in the u s postwar policy response to oil prices abstract this paper studies optimal monetary policy in a framework that explicitly accounts for policymakers uncertainty about the channels of transmission of oil prices into the economy more specifically using postwar us data i examine the evolution of the policy recommendations originating from an optimal linear regulator problem that encompasses model uncertainty and learning as proposed by cogley and sargent 2005b in this environment i find that one of the underlying models dominates the robust interest rate response to oil prices and i show that this result is due to the instability of this specification in the sample period under analysis