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

stabilization theory and policy 50 years after the phillips curve this paper discusses the impact of a w h phillips seminal work in macroeconomic stabilization policy on subsequent developments in that field we begin by reviewing the various stabilization rules adopted by phillips and show how these relate to optimal stabilization rules that emerge from linear quadratic optimization problems most of the early st abilization literature was associated with backward looking variables the development of rational expectations in the 1960 s and 1970 s posed a challenge for stabilization policy this arose from the role of forward looking inflationary expectations in the phillips curve and the effect this had on the design of optimal stabilization rules through issues such as the lucas critique and the time consistency of policy we also briefly comment on a long standing debate pertaining to the merits of fixed policy rules versus discretionary or optimal policy the latter part of the paper discusses some of the more contemporary aspects of stabilization policy thereby serving to illustrate the durability of phillips contributions

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

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

an eoq model with imperfect quality items inspection errors shortage backordering and sales returns abstract in practice the items received in a lot may contain defective items and the screening process to eliminate the defective items may involve both a type i and a type ii error due to the defective items and the inspection errors shortages may sometimes occur in this paper we develop an economic order quantity model with imperfect quality items inspection errors shortage backordering and sales returns a closed form solution is obtained for the optimal order size the maximum shortage level and the optimal order reorder point if shortages are not allowed we adopt the order overlapping scheme proposed by maddah et al 2010 computers and industrial engineering 58 4 691 695 to develop an eoq model to prevent shortages during the screening process numerical examples show the impacts of the defective probability the inspection errors and the holding and backordering costs on the optimal solution

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

eoq with a correlated binomial supply abstract this paper considers a variant of the economic order quantity eoq model under random supply a binomial supply model is adopted where every item received is of imperfect quality with the same probability we study the realistic case where the qualities of items in an order are correlated and draw useful insights the most interesting of which is that correlation decreases the order size several practical correlation patterns are investigated and discussed we also show that several commonly used models in the literature can be represented by an equivalent correlated binomial supply model

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

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

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

a century of evolution from harris s basic lot size model survey and research agenda abstract determining the economic lot size has always represented one of the most important issues in production planning this problem has long attracted the attention of researchers and several models have been developed to meet requirements at minimum cost in this paper we explore and discuss the evolution of these models during one hundred years of history starting from the basic model developed by harris in 1913 up to today following harris s work a number of researchers have devised extensions that incorporate additional considerations the evolution of eoq theory strongly reflects the development of industrial systems over the past century here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the eoq problem finally a new research agenda is proposed and discussed

the short run volatility of money stock targeting abstract the altered allocations of money market volatility obtained by alternative monetary policy procedures are illustrated by stochastic simulations of a staff monthly model the results indicate the nature of the tradeoff between short run volatility in the money stock and in the funds rate that is available to money stock targeting procedures

buying greenhouse insurance the economic costs of carbon dioxide emission limits in recent years a growing concern that the increasing accumulation of greenhouse gases will lead to undesirable changes in global climate has resulted in a number of proposals both in the united states and internationally to set physical targets for reducing greenhouse gas emissions but what will these proposals cost based on the authors earlier ground breaking work buying greenhouse insurance outlines a way to think about greenhouse effect decisions under uncertainty it describes an insightful model for determining the economic costs of limiting carbon dioxide emissions produced by burning fossil fuels and provides a solid analytical base for rethinking public policy on the farreaching issue of global warming manne and richels present region by region estimates of the costs that would underlie an international agreement using a computer model known as global 2100 they analyze the economic impacts of limiting c02 emissions under alternative supply and conservation scenarios the results clearly indicate that a reduction in emissions is not the sole policy response to potential climate change following a summary of the greenhouse effect its likely causes and possible consequences manne and richels take up issues that concern the public at large they provide an overview of global 2100 look at how the u s energy sector is likely to evolve under businessas usual conditions and under carbon constraints and describe the concept of greenhouse insurance they consider possible global agreements including an estimate of benefits that might result from trading in an international market in emission rights they conclude with a technical description directed toward modeling specialists alan manne is professor of operations research at stanford university richard richels is director of the energy analysis and planning department at the electric power research institute

dynamic specifications in optimizing trend deviation macro models abstract as noted in surveys by goodfriend and king in b bernanke j rotemberg eds nber macroeconomics annual mit press cambridge ma 1997 pp 231 283 and walsh monetary theory and policy mit press cambridge ma and exemplified by models analyzed in taylor 1999 there is encouraging progress in developing optimizing trend deviation macro models that provide useful insights into the transmission and design of monetary policy several controversial features of a minimalist trend deviation model with optimizing households firms and bond traders are examined dynamic specifications are suggested to improve the data based realism while preserving the simplicity of the minimalist model

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

scientific progress and irreversibility an economic interpretation of the precautionary principle abstract we consider the problem of the optimal use of a good whose consumption can produce damages in the future scientific progress is made over time that provides information on the distribution of the intensity of damages we show that this progress induces earlier prevention effort only if prudence is larger than twice absolute risk aversion this paper thus identifies the class of quite restrictive but plausible conditions such that scientific uncertainties justify an immediate reduction of the consumption of a potentially toxic substance

optimal vendor investment for reducing defect rate in a vendor buyer integrated system with imperfect production process this paper investigates a single vendor single buyer integrated production inventory model with stochastic demand and imperfect production process it is assumed that there is an inspection activity on the part of the buyer with a fixed screening rate greater than the demand rate the vendor invests money in order to improve the production process quality and reduce the number of defectives the expected annual integrated total cost is derived under the n shipment policy and an iterative procedure is suggested to determine the optimal decisions the benefit of investment in reducing the defect rate is illustrated by way of numerical examples it is observed that the higher the defect rate the more beneficial the investment numerical studies further explore that an increased demand requires an increased investment to optimize the total cost

economic production quantity model for items with imperfect quality abstract the assumptions necessary to justify the use of economic production quantity epq eoq models are rarely met to provide mathematical models that more closely conform to actual inventories and respond to the factors that contribute to inventory costs the models must be extended or altered this paper hypothesizes a production inventory situation where items received or produced are not of perfect quality items of imperfect quality not necessarily defective could be used in another production inventory situation that is less restrictive process and acceptance control the electronics industry gives good examples of such situations this paper extends the traditional epq eoq model by accounting for imperfect quality items when using the epq eoq formulae this paper also considers the issue that poor quality items are sold as a single batch by the end of the 100 screening process a mathematical model is developed and numerical examples are provided to illustrate the solution procedure

economic order quantity for items with imperfect quality revisited abstract we rectify a flaw in an economic order quantity eoq model with unreliable supply characterized by a random fraction of imperfect quality items and a screening process developed by salameh and jaber 2000 economic production quantity model for items with imperfect quality international journal of production economics 64 1 3 59 64 this leads to simple expressions of the optimal order quantity and expected profit per unit time we then analyze the effect of screening speed and variability of the supply process on the order quantity and show that the order quantity in our model is larger than that of the classical eoq model when the variability of the yield rate is reasonably low in addition we extend the model by allowing for several batches of imperfect quality items to be consolidated and shipped in one lot this is likely to be useful when there are economies of scale in shipping of imperfect quality items finally we present numerical results to illustrate the application of the model and draw insights

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

on employer specific information and internal labor markets the human capital literature of which becker s 2 paper is the seminal work stresses the productivity enhancing effects of schooling and on the job training later work by spence 21 and others emphasizes the fact that it is difficult for employers to ascertain the productivity of potential employees and suggests that activities such as schooling may provide employers with signals as to workers productivities in the signalling literature it is assumed that information generated concerning an individual s abilities is general in that it is known to all potential employers yet the information that an employer gathers concerning his workers abilities is not likely to be completely transferable to other employers as a consequence as rosen 18 249 points out there are limitations on the ability of the price system to achieve efficient assignments if the price system is incomplete there is a role for entrepreneurial activity of assembling an optimal work force this paper analyzes the employment relations that arise when employers information concerning new workers abilities is incomplete until after a period of employment the acquisition of such employer specific information is shown to lead to what has been referred to in the literature as internal labor markets internal labor markets as identified by dunlop 5 32 are the complex of rules which determine the movement of workers among job classifications within administrative units these movements may be transfers promotions demotions or layoffs to the exterior labor markets doeringer and piore 3 emphasize skill specificity and on the job training as the key factors in the emergence of the internal labor market along similar lines williamson wachter and harris 22 point out that job idiosyncracy can result in employment relations with attributes like those of internal labor markets by way of contrast this paper emphasizes the role of employer specific information in generating internal labor markets the theory provides an explanation as to why employers dismiss current employees at the same time that new employees are hired evidence that dismissal rates are not insignificant is presented in section iv the theory also provides a new rationale for long term em

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

robust permanent income and pricing i suppose there exists an extremely powerful and if i may so speak malignant being whose whole endeavours are directed toward deceiving me rene descartes meditations ii 1

complex nonlinear dynamics and computational methods in the summer of 1997 berc rustem asked us whether we would be interested in editing a special issue of the journal of economic dynamics control on complex nonlinear dynamics and computational methods we were enthusiastic about the idea and soon started soliciting papers on these themes this issue contains 19 contributions by some experts in the eld and should provide the reader with an impression of the current s dechert 1996 goodwin 1990 hommes 1991 lorenz 1993 medio 1992 puu 1997 rosser 1991 and de vilder 1995 for more discussions concerning this controversy is the main source of economic uctuations to be found in exogenous random shocks to an inherently stable linear economic system or can nonlinear economic laws of motion explain a signi cant part of observed uctuations in output growth rates capital stocks inventories stock prices exchange rates and other economic or nancial variables this controversy dates back to the 1930s and the 1940s when frisch slutsky and tinbergen a o proposed their propagation mechanism subject to exterior random impulses as a way of modeling business cycles in contrast e g kaldor goodwin and hicks argued that the

economic ordering quantity models for items with imperfect quality abstract in this paper we first look at the issue of non shortages in models with proportional imperfect quality when the proportion of the imperfects is a random variable more specifically we revisit the papers of salameh and jaber int j prod econom 64 2000 59 and chan et al prod plann control 14 2003 588 and we point out that the sufficient conditions given in these papers to ensure that shortages will not occur may not really prevent their occurrence next considering the timing of withdrawing the imperfect quality items from stock we clarify a point not clearly stated in salameh and jaber int j prod econom 64 2000 59 and we extented this model to the case in which withdrawing takes place at the end of the planning horizon finally we establish that the objective of maximizing the mean average profit which was set in salameh and jaber int j prod econom 64 2000 59 is superfluous and the results given there can be obtained by ignoring the revenue issues assumed in the model and minimizing directly the mean average cost

economic order quantity model for items with imperfect quality with learning in inspection abstract the economic order quantity eoq model is the simplest and earliest inventory model in the literature its simple mathematics is attributed to its assumptions which are rarely met salameh and jaber 2000 economic production quantity model for items with imperfect quality int j prod econ 64 59 64 addressed one of these assumptions that items received or produced are not of perfect quality this paper extends salameh and jaber s work for the case where there is learning in inspection the model is realistic in that it considers situations of lost sales and backorders mathematical models are developed with numerical examples provided and results discussed for the cases of i partial transfer of learning ii total transfer of learning and iii no transfer of learning

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

climate change and optimal energy technology r d policy public policy response to global climate change presents a classic problem of decision making under uncertainty theoretical work has shown that explicitly accounting for uncertainty and learning in climate change can have a large impact on optimal policy especially technology policy however theory also shows that the specific impacts of uncertainty are ambiguous in this paper we provide a framework that combines economics and decision analysis to implement probabilistic data on energy technology research and development r d policy in response to global climate change we find that given a budget constraint the composition of the optimal r d portfolio is highly diversified and robust to risk in climate damages the overall optimal investment into technical change however does depend in a non monotonic way on the risk in climate damages finally we show that in order to properly value r d abatement must be included as a recourse decision

firm specific training layoffs and unreliable workers firm specific training layoffs and unreliable workers 1 introduction early work in implicit contract theory argues that a long term relationship between a worker and a firm evolves due to the risk sharing nature of the implicit contract between a risk averse worker and a risk neutral firm some authors have criticized this initial argument see for example haltiwanger 1983 feeling that a long term relationship between a worker and a firm and the terms of an implicit contract between the two in large parts is explained via hiring costs training costs and the like this is the approach taken in the early work of becker 1975 oi 1962 and the most recent work of jovanovic 1979a these latter explanations are also appealing because long term relations between a worker and a firm are typically characterized by quits that decline with tenure and wages that increase with tenure as discussed in mortensen 1988 explanations of these phenomena fall into two categories job search theories or job training theories job search theories stress that there is a match specific component to the productivity of any worker firm match that a good match will result in a long term relationship explains why wages are positively correlated with tenure to explain a rising wage profile within a given match requires that the firm and the worker learn about the quality of their match over time a good match will be a long term one and the wage will rise over time as the match is discovered to be a good one jovanovic 1979b and barron and loewenstein 1985 model such a learning process job training theories maintain that long term relationships with rising wages exist because of firm specific training that increases with tenure again see jovanovic 1979a as an example this paper integrates these two theories in this paper firm specific training evolves as an increasing function of a worker s tenure with a firm this is so because there is a positive probability that a worker is unreliable in that he will be searching for another employer the firm being unable to identify in advance which workers are unreliable will update its prior belief as to a worker s reliability as a function of the worker s tenure the total level of training at any point in time will be an increasing function of this updated belief thus learning about the quality of a match an aspect of the job search theories plays an important role in explaining the level of firm specific training this learning process can also play a role in determining optimal layoffs if an unreliable worker is more likely to receive an acceptable outside offer when the worker is laid off than when he is employed the firm can use layoffs to elicit information about the worker s reliabiliy based upon this fact layoffs may occur even when the worker s marginal product exceeds his value of leisure before discussing the model in detail one crucial assumption deserves comment unlike previous work such a salop and salop 1976 enforceable self revealing contracts are ruled out by assumption thus the firm here cannot commit itself to a wage contract promising low wages initially in exchange for high wages as job tenure increases which contract would attract only reliable workers this assumption is of course a polar extreme but as such is consistent with more recent work in contract theory which investigates the terms of self enforcing contracts see for example holmstrom 1983 the idea is to provide a comparison with contracts in an idealized economy with no enforcement problems this assumption is justified if the cost of writing a legally enforceable contract is prohibitive or if as suggested in charmichael 1984 reputational forces are insufficient to deter a firm from cheating although workers here are risk neutral the model could be amended to include risk averse agents

disaggregation and consolidation of imperfect quality shipments in an extended epq model abstract we consider a standard economic production quantity epq model due to manufacturing variability a fraction p of the produced inventory will have imperfect quality where p is a random variable with a known distribution we consider a 100 inspection policy and further assume that the inspection rate is larger than that of production thus all imperfect quality items will be detected by the end of the production cycle for such an augmented epq model we first derive the new optimal production quantity assuming that the imperfect quality items are salvaged once at the end of every production cycle then we extend this base model to allow for disaggregating the shipments of imperfect quality items during a single production run finally we consider aggregating or consolidating the shipments of imperfect items over multiple production runs under both scenarios we derive closed form expressions for both the economic production quantity and the batching policy and show that our desegregation consolidation schemes can lead to significant cost savings over the base model

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

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

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

the performance of forecast based monetary policy rules under model uncertainty we investigate the performance of forecast based monetary policy rules using five macroeconomic models that reflect a wide range of views on aggregate dynamics we identify the key characteristics of rules that are robust to model uncertainty such rules respond to the one year ahead inflation forecast and to the current output gap and incorporate a substantial degree of policy inertia in contrast rules with longer forecast horizons are less robust and are prone to generating indeterminacy in light of these results we identify a robust benchmark rule that performs very well in all five models over a wide range of policy preferences

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

managing disinflation under uncertainty in this paper we analyze disinflation policy when a central bank has imperfect information about private sector inflation expectations but learns about them from economic outcomes which are in part the result of the disinflation policy itself the form of uncertainty is manifested as uncertainty about the effect of past disinflation policy on the current output gap this differs from other studies on learning and control in a monetary policy context e g ellison 2006 svensson and williams 2007 that assume uncertainty about the effects of current policy actions on the economy we derive the central bank s optimal disinflation strategy under active learning dop and compare it with two limiting cases certainty equivalence policy cep or passive learning and a brainard style cautionary monetary policy cp it turns out that under the dop inflation stays between the levels implied by the cep and the cp a novel result e g unlike beck and wieland 2002 is that this holds irrespective of the initial level of inflation at high levels of inherited inflation the dop moves closer to the cep at low levels of inherited inflation the dop resembles the cp

an optimal policy for a single vendor single buyer integrated production inventory problem with process unreliability consideration abstract this article develops a model to determine an optimal integrated vendor buyer inventory policy for flawed items in a just in time manufacturing environment the objective is to minimize the total joint annual costs incurred by the vendor and the buyer the production process is assumed to deteriorate during processing and produces a certain number of defective items for practical purpose the article is concerned with the policy in which the delivery quantity to the buyer is identical at each replenishment the expected annual integrated total cost function is derived and a solution procedure is established to find out the optimal solution finally the solution technique is illustrated with a numerical example available in the literature

lot sizing with a markov production process and imperfect items scrapped abstract this paper considers an inventory system within the economic order quantity eoq model framework under random supply the production process can go out of control with a constant probability and start producing imperfect quality items such a system has been studied in the literature under the assumption that defective items are reworked instantaneously and returned to inventory in some situations imperfect quality items are not necessarily defective and are removed from the inventory to be used elsewhere this paper develops two models where imperfect items are removed from inventory the first model finds the expected cost and optimal lot size assuming that imperfect quality items are removed from inventory at no cost the second model assumes that batches of imperfect quality are consolidated and shipped together due to economies of scale in shipping analytical and numerical results are developed for both models revealing several managerial insights

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

an imperfect production process in a volume flexible inventory model abstract this paper hypothesizes an imperfect production inventory system where the items produced are a mixture of perfect and imperfect quality some of the imperfect quality items can be sold at a reduced selling price the unit production cost is taken to be a function of the finite production rate which is treated as a decision variable the mathematical expression for the expected profit function is derived and it is maximized subject to different constraints of the system using interior penalty function method for constrained optimization the algorithm of which is given the solution procedure is illustrated with the help of numerical examples the sensitivity of each variable to changes in the values of the parameters of the system is examined lastly various issues conforming the system are discussed

an integrated production inventory model with imperfect production processes and weibull distribution deterioration under inflation abstract this study develops an integrated production and inventory model from the perspectives of both the manufacturer and the retailer the model assumes a varying rate of deterioration partial backordering inflation imperfect production processes and multiple deliveries the elapsed time until the production process shift is assumed to be arbitrarily distributed the discounted cash flow and classical optimization technique are used to derive the optimal solution a numerical example including the sensitivity analysis is given to validate the results of the production inventory model the integrated decision results in lower optimal joint cost compared with an independent decision by the manufacturer and the retailer

an eoq model with backorders and rejection of defective supply batches abstract we consider a single echelon inventory installation under the classical eoq with backorders paradigm to study the effects of supply quality on cost performance previous research on imperfect supply quality has focused on variants of the proportional deterministic or random yield problem where supply batches are all accepted and then used after screening any defects in this paper we study an alternative setting where entire supply batches may be defective below quality standards and therefore rejected on arrival note that such supply flow disruptions are analogous to those considered within the economic order quantity with disruptions eoqd area of research we first present an exact model for the system expected cost and show its convexity optimal cost and respective values of the decision variables i e planned order quantity and backorders are then obtained in a closed form interestingly under perfect supply quality all expressions reduce to those of classical eoq analytical and computational results reveal the serious impact of inferior supply quality on system cost as well as the sensitivity of the system parameters

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

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

joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles abstract this study deals with an imperfect epq economic production quantity price dependent inventory model over two types of cycles in the first cycle the retailer sells only good product with actual price and in the second he sells the products with a discount price in the production run time the non conforming items are produced at a random rate and they are reworked after the regular production run time and the reworked items are almost perfect as good as original quality items the retailer starts the second cycle when a certain percent of good items are left to him after the completion of regular production the retailer continues simultaneously two cycles up to which both types of the products are available to him now our objective is to find out optimal ordering lot size and optimal price for which the profit of the integrated model is maximum also we check the best strategy of retailer for the time of starting second cycle a numerical example is provided to illustrate the behavior and application of the model

note on economic production quantity model for items with imperfect quality a practical approach abstract in this note we present a simple approach for determining the economic production quantity for an item with imperfect quality we compare the results based on the simple approach with the optimal method for determining the lot size and show that almost optimal results are obtained using the simple approach

fundamental irreversibilities in stock externalities abstract this paper concerns the irreversibility effect in stock externalities in an environment of uncertainty with learning taking place one may wish to under emit today to avoid potential environmental irreversibilities alternatively one may wish to under invest in pollution control capital avoiding investments in sunk capital that turn out to be wasted the paper develops theoretical results on the tension between these two effects and separates risk aversion from the irreversibility effect the paper also presents a simple example in climate change policy

regulation with anticipated learning about environmental damages a regulator anticipates learning about the relation between environmental stocks and economic damages for a model with linear quadratic abatement costs and environmental damages and a general learning process we show analytically that anticipated learning decreases the optimal level of abatement at a given information set if learning causes the regulator to eventually decide that damages are higher than previously thought learning eventually increases abatement learning also favors the use of taxes rather than quotas using a model that is calibrated to describe the problem of global warming we show numerically that anticipated learning causes a significant reduction in first period abatement and a small increase in the preference for taxes rather than quotas even if the regulator s initial priors about environmental damages are much too optimistic he is able to learn quickly enough to keep the expected stock trajectory near the optimal trajectory

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

climate policy under fat tailed risk an application of dice uncertainty plays a significant role in evaluating climate policy and fat tailed uncertainty may dominate policy advice should we make our utmost effort to prevent the arbitrarily large impacts of climate change under deep uncertainty in order to answer to this question we propose a new way of investigating the impact of fat tailed uncertainty on optimal climate policy the curvature of the optimal carbon tax against the uncertainty we find that the optimal carbon tax increases as the uncertainty about climate sensitivity increases but it does not accelerate as implied by weitzman s dismal theorem we find the same result in a wide variety of sensitivity analyses these results emphasize the importance of balancing the costs of climate change against its benefits also under deep uncertainty 2013 springer science business media dordrecht

uncertainty learning and heterogeneity in international environmental agreements this paper concerns the formation of international environmental agreements under uncertainty about environmental damage with different models of learning complete learning partial learning or no learning the results of the existing literature are generally pessimistic the possibility of either complete or partial learning generally reduces the level of global welfare that can be achieved from forming an iea relative to no learning that literature regards uncertainty as a parameter common to all countries so that countries are identical ex ante as well as ex post in this paper we extend the literature to the case where there is no correlation between damage costs across countries each country is uncertain about a particular parameter in our case the benefit cost ratio drawn from a common distribution but ex post each country s realized parameter value is independently drawn consequently while countries remain identical ex ante they may be heterogeneous ex post we show that this change reinforces the negative conclusions about the effects of partial learning on international environmental agreements but under certain conditions moderates the negative conclusions about the effects of complete learning

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

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

robustness and u s monetary policy experimentation we study how a concern for robustness modifies a policy maker s incentive to experiment a policy maker has a prior over two submodels of inflationunemployment dynamics one submodel implies an exploitable trade off the other does not bayes law gives the policy maker an incentive to experiment the policy maker fears that both submodels and his prior probability distribution over them are misspecified we compute decision rules that are robust to misspecifications of each submodel and of the prior distribution over submodels we compare robust rules to ones that cogley colacito and sargent 2007 computed assuming that the models and the prior distribution are correctly specified we explain how the policy maker s desires to protect against misspecifications of the submodels on the one hand and misspecifications of the prior over them on the other have different effects on the decision rule

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

mitigation of the lucas critique with stochastic control methods abstract lucas in brunner k meltzer a h eds the phillips curve and the labor markets supplementary series to the journal of monetary economics 1976 pp 19 46 pointed out that when optimization is performed on a deterministic macro model the resulting policy may not reflect the true optimal solution private agents may react to announced policies and consequently model parameters will start to drift the aim of this paper is to develop a methodology for deriving an optimal policy in the presence of rational expectations and parameter drift this drift is captured by a stochastic optimization framework with time varying parameters the resulting optimal policy is capable of tracking changes in the parameters due to policy changes a numerical example illustrates how the methodology provides a way to mitigate the effects of the lucas critique

optimally derived fixed rules and indicators abstract monetary targets have come to be regarded as inadequate for the conduct of short term monetary policy both among theoreticians and practitioners of policy in this paper two approaches are put forward analysed and evaluated for improving the performance of monetary targets according to the first approach simple rules for monetary targets are derived within an optimisation framework these rules related to ultimate targets are simple so that they can be announced and are flexible so that they are subject to revision when the economy drifts away from its course due to unexpected shocks the second approach is based on indicators and complements monetary targets with exchange rate targets through a simple feedback law for determining interest rate policy the advantage of this feedback law is that it provides the mechanism through which policy is to be revised in response to shocks if such a feedback law is announced private economic agents have the means of distinguishing discretionary and arbitrary changes of policy from those which are needed to bring the economy back to the announced and committed course this approach is used to analyse and extend the suggestions in the house of commons report on international monetary arrangements the common ground between the two approaches is an optimisation framework with respect to the parameters of either the fixed simple rules or the simple feedback laws this is discussed in section 1 the approach of deriving simple fixed rules is illustrated in a monetarist model in which there is a link between private sector expectations and the credible announcement of monetary targets the model is explained in section 2 and simple fixed rules are discussed in section 3 the performance of simple rules for monetary targets is evaluated in terms of a minimax strategy with model uncertainty between the monetarist model and a keynesian model without the assumption of announcement effects this is discussed in section 4 optimal feedback laws are derived and analysed in section 5 the parameter sensitivity of these feedback laws with respect to the model and the objective function as well as their behaviour under shocks is also examined

the climate change learning curve abstract the purpose of this paper is to confront economic models of climate change with the reality that limited information exists with which to form expectations about the evolution of the climate a key element in the tension between those who believe we should impose aggressive climate change mitigation policies and those who do not is the question of if we are merely in a long period of shock induced above average temperatures or if observed increases in temperature are a result of carbon emissions this paper characterizes learning dynamics resulting from the use of observations of temperature to update beliefs about two key characteristics of global climate the persistence of natural trends and the sensitivity of temperature to atmospheric carbon levels this paper shows that contrary to predictions in the literature that uncertainty may be resolved very quickly the time to learn the true processes may be in the order of thousands of years further this paper shows the effects of uncertainty on the likelihood that observations from the statistical record lead to important estimate and policy errors

economic order quantity for growing items abstract economic order production quantity eoq epq models have generally been presented for manufacturing products incorporating some important features of a specific category of products different eoq epq models have been proposed in literature this study proposes a new class of inventory models i e a model for a specific type of inventory items growing items poultry and livestock are good examples of growing inventory items we begin by proposing a general mathematical model which can be used for different types of growing items followed by a particular mathematical model for a specific type of poultry we calculate the optimal order quantity of the growing items at the start of a growing cycle the optimal length of the growing cycle and the optimal total profit numerical examples are provided for a type of poultry to illustrate the model a sensitivity analysis is presented to study the effect of the main parameters of the model in terms of its decision variables and objective function the results of the sensitivity analysis suggest that production costs are the most crucial parameter

economic order quantity models for imperfect items with buy and repair options abstract one of the celebrated extensions of the economic order production quantity eoq epq model is one that assumes a received shipment contains a fraction of imperfect non conforming quality items where these items detected by 100 screening are sold as a single batch at a discounted price this paper revisits this model salameh and jaber 2000 int j prod econ 64 1 59 64 and extends it by assuming that a shipment is coming from a distant supplier and therefore it is not feasible to replace the imperfect items with an additional order to the same supplier to address this restriction two models are presented the first assumes that imperfect items are sent to a repair shop who charges a cost plus a markup margin while the second model assumes that imperfect items are replaced by good ones from a local supplier at a higher cost the inventory environment assumed in this paper is relevant in todays globalised supply chains thus practical implications of the problem faced are discussed numerical results are also presented and discussed the results show that there exists a threshold value of the unit purchase cost of an emergency ordered item and a fraction of defectives to which it is decided to either buy or repair

global warming irreversibility and learning a number of economists have argued that the literature on the irreversibility effect implies that current abatement of greenhouse gas emissions should be greater when there is the possibility of obtaining better information in the future about the potential damages from global warming than when there is no possibility of obtaining better information in this paper we show that even the simplest model of global warming does not satisfy either of epstein s 1980 sufficient conditions so it is not possible to use epstein s analysis to tell whether the irreversibility effect applies to models of global warming we derive an alternative sufficient condition for the irreversibility effect to hold

eoq models for a coordinated two level international supply chain considering imperfect items and environmental impact abstract for a two level supply chain models are presented to determine the optimal production shipment policy for items with imperfect quality in three different scenarios a both the vendor and the buyer are in the same country b the vendor and the buyer are in different countries where the stochastic behavior of the exchange rate between the two countries is modeled using a mean reverting process and c environmental impact is incorporated in determining the optimal production shipment policy by taking into account the fixed and variable carbon emission costs the objective is to minimize the total expected cost per unit time for each scenario considering equal shipment size the total expected cost per unit time is derived and the solution procedure is proposed numerical examples are presented and the results are discussed

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

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

an economic order quantity model with defective items and shortages abstract the fundamental assumption of an economic order quantity eoq model is that 100 of items in an ordered lot are perfect this assumption is not always pertinent for production processes because of process deterioration or other factors this paper develops an eoq model for that each ordered lot contains some defective items and shortages backordered it is assumed that 100 of each lot are screened to separate good and defective items which are collection of imperfect quality and scrap items the effect of percentage defective on optimal solution is studied while numerical examples are provided for the developed model

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 and stock effects in environmental regulation the case of greenhouse gas emissions abstract this paper concerns the optimal regulation of greenhouse gases that lead to global climate change in particular we focus on uncertainty and learning which over time resolves uncertainty we present an empirical stochastic model of climate economy interactions and present results on the tension between postponing control until more is known vs acting now before irreversible climate change takes place uncertainty in our model is in the damage caused by global warming the results suggest that a temporary carbon tax may dominate a permanent one because a temporary tax may induce increased flexibility

cost benefit analysis under uncertainty a note on weitzman s dismal theorem abstract weitzman s 2009 famous dismal theorem argues that fat tails in the distribution of warming may pose problems for cost benefit analysis as it may imply that society might be willing to exchange today s consumption for future consumption at an infinite rate his analysis is based on the stochastic discount factor we show that in situations in which the stochastic discount factor is applicable it is optimal for society to devote only a finite amount of resources to protect against climate change for general assumptions on the investment returns cost benefit analysis must consider the joint distribution of the marginal utility of future consumption and marginal returns to investment in the different future states of nature we explore the range of situations under which challenges for applying cost benefit analysis under uncertainty remain

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

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

bayesian learning growth and pollution abstract environmental problems such as climate change have great uncertainties current expectations are that uncertainties about climate change will be resolved quickly we examine this hypothesis theoretically and computationally we consider bayesian learning about the relationship between greenhouse gas levels and global mean temperature changes a key uncertainty learning is non trivial because of a stochastic shock to the realized temperature we find theoretically the expected learning time which is related to the variance of the shock and the emissions policy implying a tradeoff between the benefits of controlling emissions and information we imbed the learning model into an optimal growth model with a climate sector and solve the resulting dynamic program we find computationally that learning takes on average over 90 yr far longer than currently believed

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

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