microstructure noise realized variance and optimal sampling a recent and extensive literature has pioneered the summing of squared observed intra daily returns realized variance to estimate the daily integrated variance of financial asset prices a traditional object of economic interest we show that in the presence of market microstructure noise realized variance does not identify the daily integrated variance of the frictionless equilibrium price however we demonstrate that the noise induced bias at very high sampling frequencies can be appropriately traded off with the variance reduction obtained by high frequency sampling and derive a mean squared error mse optimal sampling theory for the purpose of integrated variance estimation we show how our theory naturally leads to an identification procedure which allows us to recover the moments of the unobserved noise this procedure may be useful in other applications finally using the profits obtained by option traders on the basis of alternative variance forecasts as our economic metric we find that explicit optimization of realized variance s finite sample mse properties results in accurate forecasts and considerable economic gains copyright 2008 wiley blackwell

cooperative and noncooperative r d in duopoly with spillovers contrary to the usual assumption made in most oligopoly models relations among firms are seldom of a wholly cooperative or noncooperative type in many situations they compete in some fields while they cooperate in others an important example is the case of cooperative research efforts bringing fierce competitors together two types of agreement are observed first r d cooperation can take place at the so called precompetitive stage companies share basic information and efforts in the r d stage but remain rivals in the market place 1 a second type of agreement involves an extended collusion between partners creating common policies at the product level the usual justifications of this extension are the difficulties of protecting intellectual property the idea is then to allow partners who have achieved inventions together to also control together the processes and products which embody the results of their collaboration in order to recuperate jointly their r d investments 2 what could be expected from these types of agreement is a reduction in r d expenditures because of less wasteful duplication and a reduction of total production because of more reprinted from the american economic review 78 5 1133 1137 1988 center for operations research econometrics 1348 louvain la neuve belgium we are grateful to jean

nonmonetary effects of the financial crisis in propagation of the great depression this paper examines the effects of the financial crisis of the 1930s onthe path of aggregate output during that period our approach is complementary to that of friedman and schwartz who emphasized the monetary impact of the bank failures we focus on non monetary primarily credit related aspects of the financial sector output link and consider the problems of debtors as well as those of the banking system we argue that the financial disruptions of 1930 33 reduced the efficiency of the credit allocation process and that the resulting higher cost and reduced availability of credit acted to depress aggregate demand evidence suggests that effects of this type can help explain the unusual length and depth of the great depression this abstract was borrowed from another version of this item

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

learning and time varying macroeconomic volatility abstract this paper presents a dsge model in which agents learning about the economy can endogenously generate time varying macroeconomic volatility economic agents use simple models to form expectations and need to learn the relevant parameters their gain coefficient is endogenous and is adjusted according to past forecast errors the model is estimated using likelihood based bayesian methods the endogenous gain is jointly estimated with the structural parameters of the system the estimation results show that private agents appear to have often switched to constant gain learning with a high constant gain during most of the 1970s and until the early 1980s while reverting to a decreasing gain later on as a result the model can generate a pattern of volatility which is increasing in the 1970s and falling in the second half of the sample with a decline that can roughly match the magnitude of the so called great moderation in the 1984 2007 period the paper also documents how a failure to incorporate learning into the estimation may lead econometricians to spuriously find time varying volatility in the exogenous shocks even when these have constant variance by construction

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

estimation of an asymmetric stochastic volatility model for asset returns a stochastic volatility model may be estimated by a quasi maximum likelihood procedure by transforming to a linear state space form the method is extended to handle correlation between the two disturbances in the model and applied to data on stock returns

the quantitative importance of news shocks in estimated dsge models we estimate a dynamic stochastic general equilibrium dsge model with several frictions and both unanticipated and news shocks using quarterly u s data from 1954 to 2004 and bayesian methods we find that unanticipated shocks dominate news shocks in accounting for the unconditional variance of output consumption and investment growth interest rate and the relative price of investment the unanticipated shock to the marginal efficiency of investment is the dominant shock accounting for over 45 of the variance in output growth news shocks account for less than 15 of the variance in output growth within the set of news shocks nontechnology sources of news dominate technology news with wage markup news shocks accounting for about 60 of the variance share of both hours and inflation we find that in the estimated dsge model i the presence of endogenous countercyclical price and wage markups due to nominal frictions substantially diminishes the importance of news shocks relative to a model without these frictions and ii while there is little change in the estimated contributions of technology news when we restrict wealth effects on labor supply the contributions of nontechnology news shocks are relatively more sensitive

macroeconomic volatility and external imbalances abstract does macroeconomic volatility uncertainty affects accumulation of net foreign assets in oecd economies over the period 1970 2012 changes in country specific aggregate volatility are after controlling for a wide array of factors significantly positively associated with net foreign asset position a standard open economy model with time varying macroeconomic uncertainty can quantitatively account for this relationship the key mechanism is precautionary motive more uncertainty induces residents to save more and higher savings are in part channeled into foreign assets data and theory suggest that volatility is an important determinant of the medium long run evolution of external imbalances in developed countries

declining volatility in the u s automobile industry dramatic changes in the volatility of output occurred in the u s auto industry in the early 1980s namely output volatility declined the covariance of inventory investment and sales grew more negative and adjustments to production schedules which in earlier decades stemmed primarily from plants hiring and laying off workers were more often accomplished with changes in average hours per worker after the mid 1980s using a linear quadratic inventory model with intensive and extensive labor adjustments we show how all of these changes could have stemmed from one underlying factor a decline in the persistence of motor vehicle sales jel g31 l25 l62 m11

testing for indeterminacy an application to u s monetary policy reply this paper considers a prototypical new keynesian model in which the equilibrium is undetermined if monetary policy is passive the likelihood based estimation of dynamic equilibrium models is extended to allow for indeterminacies and sunspot fluctuations we construct posterior weights for the determinacy and indeterminacy region of the parameter space and estimates for the propagation of fundamental and sunspot shocks according to the estimated model u s monetary policy post 1982 is consistent with determinacy whereas the pre volcker policy is not we find that before 1979 indeterminacy substantially altered the propagation of shocks

unique equilibrium in a model of self fulfilling currency attacks even though self fulfilling currency attacks lead to multiple equilibria when fundamentals are common knowledge we demonstrate the uniqueness of equilibrium when speculators face a small amount of noise in their signals about the fundamentals this unique equilibrium depends not only on the fundamentals but also on financial variables such as the quantity of hot money in circulation and the costs of speculative trading in contrast to multiple equilibrium models our model allows analysis of policy proposals directed at curtailing currency attacks

stochastic volatility and dsge models abstract this paper argues that a specification of stochastic volatility commonly used in dsge models may not be appropriate because the level of a process with this specification does not have any moments we suggest three ways to overcome the problem

the stochastic volatility in mean model empirical evidence from international stock markets in this paper we present an exact maximum likelihood treatment for the estimation of a stochastic volatility in mean svm model based on monte carlo simulation methods the svm model incorporates the unobserved volatility as an explanatory variable in the mean equation the same extension is developed elsewhere for autoregressive conditional heteroscedastic arch models known as the arch in mean arch m model the estimation of arch models is relatively easy compared with that of the stochastic volatility sv model however efficient monte carlo simulation methods for sv models have been developed to overcome some of these problems the details of modifications required for estimating the volatility in mean effect are presented in this paper together with a monte carlo study to investigate the finite sample properties of the svm estimators taking these developments of estimation methods into account we regard sv and svm models as practical alternatives to their arch counterparts and therefore it is of interest to study and compare the two classes of volatility models we present an empirical study of the intertemporal relationship between stock index returns and their volatility for the united kingdom the united states and japan this phenomenon has been discussed in the financial economic literature but has proved hard to find empirically we provide evidence of a negative but weak relationship between returns and contemporaneous volatility which is indirect evidence of a positive relation between the expected components of the return and the volatility process copyright 2002 john wiley sons ltd

information capacity and innovation adoption researchers of innovation adoption and diffusion often have tested the hypothesis that firms with greater capacities to gather and evaluate information should adopt sooner however the data generally do not support this hypothesis a theoretical model of innovation adoption under uncertainty is developed to show that greater information capacity implies not only faster learning which tends to reduce the expected delay until adoption but also a more stringent adoption criterion which tends to increase the expected delay the resulting ambiguity provides an explanation for the lack of empirical support for this hypothesis

strategic timing of adoption of new technologies under uncertainty abstract in this paper we introduce experience effects into a duopoly game of timing of adoption of new technologies which exhibit exogenous technological progress departing from the existing literature with this model we obtain continuous and downward sloping reaction functions we find that a higher level of uncertainty increases the extent of dispersion between the equilibrium timings of adoption furthermore we find that the equilibrium timings are even more dispersed when the leader takes the follower s reaction into account when firm roles are made endogenous we find that if there is an incentive to lead follow the equilibrium timings are more less dispersed finally we show that it is possible for collusive adoption to improve welfare

least squares inference on integrated volatility and the relationship between efficient prices and noise the expected value of sums of squared intraday returns realized variance gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for joint inference on integrated variance noise moments and price noise relations in the iid noise case we derive the asymptotic variance of the and noise variance estimators and show that they are consistent the joint estimation approach is particularly attractive as it reveals important characteristics of the noise process which can be related to liquidity and market efficiency the analysis of dependence between the price and noise processes provides an often missing link to market microstructure theory we find substantial differences in the noise characteristics of trade and quote data arising from the effect of distinct market microstructure frictions this article has supplementary material online

measuring uncertainty and its impact on the economy we propose a new framework for measuring uncertainty and its effects on the economy based on a large var model with errors whose stochastic volatility is driven by two common unobservable factors representing aggregate macroeconomic and financial uncertainty the uncertainty measures can also influence the levels of the variables so that contrary to most existing measures ours reflect changes in both the conditional mean and volatility of the variables and their impact on the economy can be assessed within the same framework moreover identification of the uncertainty shocks is simplified with respect to standard var based analysis in line with the favar approach and with heteroskedasticity based identification finally the model which is also applicable in other contexts is estimated with a new bayesian algorithm which is computationally efficient and allows for jointly modeling many variables while previous var models with stochastic volatility could only handle a handful of variables empirically we apply the method to estimate uncertainty and its effects using us data finding that there is indeed substantial commonality in uncertainty sizable effects of uncertainty on key macroeconomic and financial variables with responses in line with economic theory

uncertainty competition and the adoption of new technology faced with the decision of whether or not to adopt a new technology whose economic value cannot be gauged with certainty the manager of the firm may elect to decrease the uncertainty by sequentially gathering information at a unit cost of c 0 updating his prior beliefs in a bayesian manner uncertainty regarding the actions of a competitor however cannot be reduced our model allows a manager to account for potential competition either substitute or complementary by inclusion of strategic considerations modelled in a game theoretic setting we show that the firm s best response mapping satisfies a dynamic programming recursion even when the one period reward function is unbounded providing management with a familiar tool to solve its problem best response behavior is characterized by a monotone sequence of pairs of threshold numbers which give rise to a cone shaped continuation region the continuation region is shown to shift up down with increases in the expected level of substitute complementary competition making the firm less more likely to adopt the innovation finally the existence of a nash equilibrium in cone shaped strategies is established

strategic intrafirm innovation adoption and diffusion 1 introduction this paper addresses two empirical observations that are common in the extensive literature on innovation diffusion first a firm usually adopts an innovation over time not instantaneously that is there are intrafirm diffusions mansfield 1968 nasbeth and ray 1974 romeo 1975 stoneman 1981 1983 second the time path of an intrafirm diffusion has a predictable shape diffusion curves plot the extent of adoption against time and are generally s shaped that is they are initially convex reach an inflection point and then are concave thereafter often they are also skewed in that they are initially convex for less than half of the length of the diffusion this skewing can be so severe that the diffusion curve is essentially concave davies 1979 stoneman 1983 given the voluminous literature on innovation diffusion it is surprising that intrafirm diffusions have not received more attention with few exceptions noted below the theoretical literature assumes adoption is a discrete choice variable and so occurs instantaneously moreover empirical studies typically assume adoption occurs at the date of first use of the innovation by the firm to the extent intrafirm diffusions occur these studies clearly overestimate the speed at which the innovation is put into use and thus the speed at which its benefits accrue to the firm and society intrafirm diffusions are especially common in the case of capital embodied new process innovations because adoption involves adjustment costs as well as acquisition costs in a seminal study mansfield 1968 found that the time interval between 10 and 90 usage of diesel locomotives ranged from three to more than 14 years for firms in the u s railroad industry more recent examples abound most readers have undoubtedly experienced at least once the adoption of new computer equipment in their workplace from my own experience not all users are upgraded to the new equipment within a day a week or even a month hence in this paper i analyze the intrafirm diffusion of a new process innovation in a differential game model of an oligopoly the model s predictions are consistent with the empirical regularities noted above first an intrafirm diffusion occurs in equilibrium because the marginal cost of adoption is increasing in the rate of adoption it is not optimal to adopt instantaneously just as it is not optimal to adjust to the desired level of a stock instantaneously when adjustment costs are increasing at the margin second the equilibrium intrafirm diffusion curve is either s shaped or concave moreover this diffusion curve is more likely to be sshaped the more competitive the industry the larger the marginal cost of adoption or the preinnovation unit cost of production or the smaller the demand the analysis also shows a firm s diffusion is longer and so the extent of its adoption at any date is lower the more competitive the industry the larger the marginal cost of adoption or the pre innovation unit cost of production or the smaller the demand that is a diffusion is longer the smaller the incentive to adopt whether due to lower flow profit or higher adoption flow cost one surprising result is that an increase in the unit cost reduction from the innovation has an ambiguous effect on the intrafirm diffusion the reason is that there are two conflicting effects first as is obvious a larger cost reduction allows each firm to earn a larger flow profit at every date from the same rate of adoption however a more subtle effect is that it also allows the firm to earn the same flow of profit with a slower rate of adoption and so lower adoption costs that is the firms also have an incentive to spread out the diffusion over a longer period of time to save on adoption costs these results are important for two reasons first they show that diffusion curves are more likely to have an s shape for longer diffusions

adoption and diffusion of an innovation of uncertain profitability the argument has frequently been made that the pattern of diffusion associated with most new innovations will typically have certain characteristics a diffusion curve for an innovation is usually defined as the proportion of its potential users who have already adopted as a function of time measured from the first adoption many empirical studies by both economists and other social scientists have shown that diffusion curves nearly always have two distinct characteristics i they are s shaped the proportion adopted is an increasing function of time which is initially convex but eventually becomes concave and ii they tend to be right hand skewed the inflection point occurs at a time corresponding to a proportion adopted which is less than one half so that the function is concave over the greatest amount of time in fact this skewing is occasionally severe enough to make the diffusion curve appear concave everywhere the focus of most empirical studies of innovation diffusion has centered on identification of either the major determinants of the speed of diffusion or the characteristics of firms which determine how long they delay adoption the seminal contributions are griliches 6 study of hybrid corn and mansfield s 121 study of 12 industrial innovations these studies and most of the similar ones following conclude that diffusion is faster for innovations with higher profitability and that large firms tend to be the earliest adopters some studies e g mansfield 121 herregat 71 have attempted to ascertain

leverage effects and stochastic volatility in spot oil returns a bayesian approach with var and cvar applications abstract crude oil markets have been quite volatile and risky in the past few decades due to the large fluctuations of oil prices we contribute to the current debate by testing for the existence of the leverage effect when considering daily spot returns in the wti and brent crude oil markets and by studying the direct impact of the leverage effect on measures of risk such as var and cvar more specifically we model spot crude oil returns using stochastic volatility sv models with various distributions of the errors we find that the introduction of the leverage effect in the traditional sv model with normally distributed errors is capable of adequately estimating risk for speculative oil suppliers in both the wti and brent markets our results also show that financial regulators model choice both on the supply and on the demand side would not be affected by the introduction of leverage focusing instead on firm s internal risk management our results show that the introduction of leverage would be useful for firms who are on the demand side for oil who use var for risk management and who are particularly worried about the magnitude of the losses exceeding var while wanting to minimize the opportunity cost of capital using the same logic firms who are on the supply side would be better off not considering the leverage effect

bubbles and capital flow volatility causes and risk management emerging market economies are fertile ground for the development of real estate and other financial bubbles despite these economies significant growth potential their corporate and government sectors do not generate the financial instruments to provide residents with adequate stores of value capital often flows out of these economies seeking these stores of value in the developed world bubbles are beneficial because they provide domestic stores of value and thereby reduce capital outflows while increasing investment but they come at a cost as they expose the country to bubble crashes and capital flow reversals we show that domestic financial underdevelopment not only facilitates the emergence of bubbles but also leads agents to undervalue the aggregate risk embodied in financial bubbles in this context even rational bubbles can be welfare reducing we study a set of aggregate risk management policies to alleviate the bubble risk we show that prudential banking regulation sterilization of capital inflows and structural policies aimed at developing public debt markets and property rights all have a high payoff in this environment

strategic timing of adoption of new technologies under uncertainty a note abstract this note clarifies the circumstances under which ex ante identical firms will choose different dates for the adoption of new technology in particular conditions under which diffusion will arise in both open loop and closed loop games are identified furthermore it is shown that the rents of nonidentical firms are not equalized even if pre emptive adoption is possible finally an example is given in which the reduction of the uncertainty associated with the implementation of new technology leads to a postponement of the adoption by the late adopter

regulation and preemptive technology adoption two rival firms must decide if and when to adopt a new technology knowing how adoption costs decline over time and how profit flows vary with adoption patterns in many cases price and entry regulations beneficially slow technology adoption by making preemption strategies less attractive in some cases these regulations can so discourage a firm from preemption as to change the order in which firms adopt new technologies speeding one firm s adoption date and slowing the other s in the context of a particular scenario for cable and telephone companies adoption of new fiber optic technologies the case for lifting the cross ownership ban depends on the extent to which telephone companies are able to implement a superior technology reregulation of cable companies strengthens this case

pricing european currency options a comparison of the modified black scholes model and a random variance model we use the modified black scholes model and a random variance option pricing model to study prices of european currency options traded in geneva the options which cannot be exercised early include calls and puts on the dollar swiss franc exchange rate in the empirical analysis we examine the model fit and the biases with respect to the strike price time to maturity and volatility there is some evidence of mispricing and there are small gains available by trading with the random variance model

innovation adoption and diffusion when there are competing innovations abstract firms face a choice between two innovations without knowing which of the two is better each firm has a prior that one of the innovations is better which is updated by bayes rule as trials with the innovations are made a simple decision rule indicating which innovation should be tried given any posterior is derived and used to define an expected diffusion curve for the better innovation this curve has the commonly observed ogive shape even in the absence of any external demonstration effect when the distribution of firm priors belongs to a general class

the stochastic volatility in mean model with time varying parameters an application to inflation modeling this article generalizes the popular stochastic volatility in mean model to allow for time varying parameters in the conditional mean the estimation of this extension is nontrival since the volatility appears in both the conditional mean and the conditional variance and its coefficient in the former is time varying we develop an efficient markov chain monte carlo algorithm based on band and sparse matrix algorithms instead of the kalman filter to estimate this more general variant the methodology is illustrated with an application that involves u s u k and germany inflation the estimation results show substantial time variation in the coefficient associated with the volatility highlighting the empirical relevance of the proposed extension moreover in a pseudo out of sample forecasting exercise the proposed variant also forecasts better than various standard benchmarks

the impact of the volatility of monetary policy shocks this paper studies the impact of the volatility of monetary policy using a structural vector auroregression svar model enriched along two dimensions first it allows for time varying variance of monetary policy shocks via a stochastic volatility specification second it allows a dynamic interaction between the level of the endogenous variables in the var and the time varying volatility the analysis establishes that the nominal interest rate output growth and inflation fall in reaction to an increase in the volatility of monetary policy the analysis also develops a dynamic stochastic general equilibrium model enriched with stochastic volatility to monetary policy that generates similar responses and provides a theoretical underpinning of these findings

irreversible investment and r d spillovers in a dynamic duopoly investments in new production processes usually involve a significant amount of rd an increase in uncertainty delaying the equilibrium calls for higher subsidization rates third numerical simulations show that the spillover reduces the difference between the leader s and the follower s maximum value functions accordingly our model can help generate realistic market betas

a non linear filtering approach to stochastic volatility models with an application to daily stock returns this paper develops a new model for the analysis of stochastic volatility sv models since volatility is a latent variable in sv models it is difficult to evaluate the exact likelihood in this paper a non linear filter which yields the exact likelihood of sv models is employed solving a series of integrals in this filter by piecewise linear approximations with randomly chosen nodes produces the likelihood which is maximized to obtain estimates of the sv parameters a smoothing algorithm for volatility estimation is also constructed monte carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates we illustrate our model by analysing daily stock returns on the tokyo stock exchange since the method can be applied to more general models the sv model is extended so that several characteristics of daily stock returns are allowed and this more general model is also estimated copyright 1999 john wiley sons ltd

innovation adoption and welfare under uncertainty the incentives of firms to adopt a new process need not coincide with maximum expected consumer surplus or social welfare if there is uncertainty before the process is adopted and if the only loss from failure is a fixed cost in some cases no firm will adopt an innovation likely to fail although expected welfare is maximized if one adopts in other cases both firms will adopt an innovation likely to succeed although expected welfare is maximized if one firm adopts this occurs because rivalry between firms leads them to adopt together when total expected profits are higher if one firm adopts copyright 1992 by blackwell publishing ltd

doubts and variability a robust perspective on exotic consumption series in order for consumption based asset pricing models to reconcile data on returns with that on consumption researchers have resorted to augmenting the consumption series in exotic ways when an agent s consumption series is subject to changes in volatility we show that concerns for model misspecication can induce fears of both disasters and long run risk we appeal to this pessimistic view to explain why introducing stochastic volatility in the presence of model uncertainty helps generate a more plausible unconditional market price of risk and time variation in the conditional market price of risk our analysis is based on a parameterization derived from bayesian estimation of our stochastic volatility model using us consumption data

reputations in the adoption of a new technology abstract this paper studies the effects of uncertainty on the timing of adoption of a new technology in a duopoly firms are uncertain of the innovative capabilities of their rivals and about the profitability of adoption these features lead to a richer and in some respects more plausible theory of adoption in which rents from delayed adoption are always realized and returns are not equalized across adoption times

investment adjustment costs an empirical assessment we evaluate empirical evidence for costs that penalize changes in investment using us industry data in aggregate models such investment adjustment costs have been introduced to help account for a variety of business cycle and asset market phenomena so far no attempt has been made to estimate these costs directly at a disaggregated level we consider an industry model with investment adjustment costs and estimate its parameters using generalized methods of moments the ndings indicate small costs associated with changing the ow of investment at the industry level the weighted average of the industry elasticities with respect to the shadow price of capital which depends inversely on the adjustment cost parameter is more than seven times larger than the largest estimate based on aggregate data we examine potential sources which may account for the large industry aggregate dierence overall our results suggest

estimation methods for stochastic volatility models a survey abstract although stochastic volatility sv models have an intuitive appeal their empirical application has been limited mainly due to difficulties involved in their estimation the main problem is that the likelihood function is hard to evaluate however recently several new estimation methods have been introduced and the literature on sv models has grown substantially in this article we review this literature we describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view we complete the survey with an application of the most important procedures to the s p 500 stock price index

stock prices and volume the authors undertake a comprehensive investigation of price and volume co movement using daily new york stock exchange data from 1928 to 1987 they adjust the data to take into account well known calendar effects and long run trends to describe the process they use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume four empirical regularities are found 1 positive correlation between conditional volatility and volume 2 large price movements are followed by high volume 3 conditioning on lagged volume substantially attenuates the leverage effect and 4 after conditioning on lagged volume there is a positive risk return relation article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

vintage capital investment and growth abstract we study the dynamics of growth and investment in a continuous time model with vintage capital vintage capital models may be characterized by non exponential rates of depreciation and technical change and can incorporate gestation lags as well as learning by using we investigate the effect of such features on the dynamics of investment and growth and show how they can contribute to explaining the volatile nature of investment time series

productivity growth transparency and monetary policy abstract this study examines whether central bank transparency about views of future productivity growth contributes to stabilizing macroeconomic fluctuations in a standard new keynesian model the central bank and private agents make their subjective estimates on the persistence of productivity growth in this situation if private agents believe that the central bank s projections include forecast errors on future productivity growth these beliefs can destabilize private agents own expectations because the central bank s forecast errors may lead to policy mistakes in the future consequently central bank transparency does not necessarily stabilize the variations of the output gap and inflation rate the central bank should respond strongly to the inflation rate if the impact of transparency is uncertain

the time varying volatility of macroeconomic fluctuations we investigate the sources of the important shifts in the volatility of us mac roeconomic variables in the postwar period to this end we propose the esti mation of dsge models allowing for time variation in the volatility of the structural innovations we apply our estimation strategy to a large scale model of the business cycle and find that shocks specific to the equilibrium condition of investment account for most of the sharp decline in volatility of the last two decades jel c51 e32

a maximum likelihood approach for non gaussian stochastic volatility models a maximum likelihood approach for the analysis of stochastic volatility models is developed the method uses a recursive numerical integration procedure that directly calculates the marginal likelihood only conventional integration techniques are used making this approach both flexible and simple experimentation shows that the method matches the performance of the best estimation tools currently in use new stochastic volatility models are introduced and estimated the model that best fits recent stock index data is characterized by a highly non gaussian stochastic volatility innovation distribution this model dominates a model that includes an autoregressive conditional heteroscedastic effect in the stochastic volatility process and a model that includes a stochastic volatility effect in the conditional mean

capital accumulation under technological progress and learning a vintage capital approach abstract in standard capital accumulation models all capital goods are equally productive and produce goods of the same quality however due to technological progress in reality it holds most of the time that newer capital goods are either more productive process innovation or produce goods of better quality product innovation implications of process innovation for the firm s investment policies are investigated while the output price development is subject to a business cycle and a given generation of capital goods gets more productive over time due to learning the problem is turned into an optimal control model that distinguishes the vintages of capital goods and where unlike most of the recent contributions it is possible to keep on investing in older technologies it is shown that i learning is one of the reasons why a firm may invest in old technologies even when apparently superior technologies are available ii investments in machines of a given age increase more over time under faster technological progress iii under faster technological progress investments are more vulnerable to output price developments and iv on average machines are older during recessions in deciding whether to invest in newer or older capital goods also the lower productivity due to aging versus differences in cost of discounting and acquisition have to be taken into account

modelling the dynamics of bitcoin and litecoin garch versus stochastic volatility models abstractwe examine and compare a large number of generalized autoregressive conditional heteroskedastic garch and stochastic volatility sv models using series of bitcoin and litecoin price retu

arch models properties estimation and testing abstract the aim of this survey paper is to provide an account of some of the important developments in the autoregressive conditional heteroskedasticity arch model since its inception in a seminal paper by engle 1982 this model takes account of many observed properties of asset prices and therefore various interpretations can be attributed to it we start with the basic arch models and discuss their different interpretations arch models have been generalized in different directions to accommodate more and more features of the real world we provide a comprehensive treatment of many of the extensions of the original arch model next we discuss estimation and testing for arch models and note that these models lead to some interesting and unique problems there have been numerous applications and we mention some of these as we present different models the paper includes a glossary of the acronyms for the models we describe

how do oil price shocks affect the output volatility of the u s energy mining industry the roles of structural oil price shocks abstract this paper focuses on how explicit structural shocks that characterize the endogenous character of international oil price change affect the output volatility of the u s crude oil and natural gas mining industries to this end we employ a modified structural vector autoregressive model svar to decompose real oil price changes into four components u s supply shocks non u s supply shocks aggregate demand shocks and oil specific demand shocks mainly driven by precautionary demand the results indicate that output volatility of the u s crude oil and natural gas mining industry has significantly negative responses to u s supply shocks aggregate demand shocks and oil specific demand shocks while lacks significant response to non u s supply shocks variance decomposition and historical decomposition confirm that u s supply shocks occupy most explaining variations in output volatility among the four structural oil shocks moreover the oil specific demand shocks explain more variation than that of aggregate demand shocks for the crude oil mining industry but the opposite is true for the natural gas mining industry

long run risks in the term structure of interest rates estimation summary this paper estimates a model in which persistent fluctuations in expected consumption growth expected inflation and their time varying volatility determine asset price variation the model features epstein zin recursive preferences which determine the market price of macro risk factors analysis of the us nominal term structure data from 1953 to 2006 shows that agents dislike high uncertainty and demand compensation for volatility risks also the time variation of the term premium is driven by the compensation for inflation volatility risk which is distinct from consumption volatility risk the central role of inflation volatility risk in explaining the time varying term premium is consistent with other empirical evidence including survey data in contrast the existing long run risks literature emphasizes consumption volatility risk and ignores inflation specific time varying volatility the estimation results of this paper suggest that inflation specific volatility risk is essential for fitting the time series of the us nominal term structure data copyright 2012 john wiley sons ltd

anticipation effects of technological progress on capital accumulation a vintage capital approach abstract due to embodied technological progress new generations of capital goods are more productive therefore in order to study the effects of technological progress a model must be analyzed in which different generations of capital goods can be distinguished we determine in what way the firm adjusts current investments to predictions of technological progress in the presence of market power we show that a negative anticipation effect occurs i e current investments in recent generations of capital goods decline when faster technological progress will take place in the future because then it becomes more attractive to wait for new generations of capital goods in case that only investments in new machines are possible actually a whole wave of anticipation phases arises

stock returns and volatility an empirical study of the uk stock market abstract attempts to quantify the relationship between stock returns and volatility have produced conflicting conclusions in recent u s studies our paper examines this issue in the u k context for the first time using daily weekly fortnightly and monthly returns on the financial times all share index from january 1965 to december 1989 volatility estimates are obtained from monthly sample variances and arch models expected returns are shown to have had a positive though not statistically significant relationship with expected volatility the relationship between the unexpected components of the returns and volatility series is less clear we find evidence for a negative relationship but only when volatility expectations are represented by standard deviations

inflation uncertainty and labour market conditions in the us recent inflation dynamics in the united states us questioned the role of driving forces of inflation in the long run although the us recorded one of the longest economic recovery periods and the

international and domestic collateral constraints in a model of emerging market crises abstract we build a model of emerging markets crises which features two types of collateral constraints firms in a domestic economy have limited borrowing capacity from international investors they also have limited borrowing capacity with respect to each other we study how the presence and changes in these collateral constraints affect financial and real variables a binding international constraint in the aggregate leads to a sharp rise in interest rates and fire sales of domestic assets while limited domestic collateral can lead to wasted international collateral these two collateral constraints can interact in important ways the first is disintermediation a fire sale of domestic assets causes banks to fail in their function of reallocating resources across the economy leading to wasted international collateral the second is a dynamic effect we show that firms in an economy with limited domestic collateral and a binding international collateral constraint will not adequately precaution against adverse shocks increasing the severity of these shocks

money demand heterogeneity and the great moderation abstract a forward looking model of the demand for money based on heterogeneous and sluggish portfolio adjustment can simultaneously account for the low short run and high long run semi elasticities reported in the literature the parameter estimates from the model for the short run and long run interest semi elasticities are 1 04 and 13 16 respectively a simulated version of the model suggests that the great moderation can be partially attributed to financial innovations in the late 1970s when moving toward a more flexible portfolio the model can account for almost one third of the observed decline in the volatilities of output consumption and investment

a new approach to identifying the real effects of uncertainty shocks this article introduces the use of the sign restrictions methodology to identify uncertainty shocks we apply our methodology to a class of vector autoregression models with stochastic volatility t

option values under stochastic volatility theory and empirical estimates abstract this paper numerically solves the call option valuation problem given a fairly general continuous stochastic process for return volatility statistical estimators for volatility process parameters are derived and parameter estimates are calculated for several individual stocks and indices the resulting estimated option values do not differ dramatically from black scholes values in most cases although there is some evidence that for longer maturity index options black scholes overvalues out of the money calls in relation to in the money calls

the diffusion of new technology and the market for an innovation this article shows that the diffusion of a capital embodied process innovation results from a pattern of decreasing incremental benefits and adoption costs for later adoptions strategic behavior is inessential to this finding we develop a method for comparing diffusion rates for different market structures in the capital equipment market we consider cases with market power on the seller s side of the market and on the buyers side of the market a case with no market power and the welfare optimal case we find that a joint venture adopts an innovation more slowly than other market regimes to protect existing capital investments and that the adoption rate is slower than is socially optimal a monopoly supplier on the other hand adopts at a rate faster than is socially optimal this result is usually also the case when there is no market power finally we show that the monopoly supplier accelerates adoptions faster than in the case where there is no market power but retards later adoptions market power thus makes a difference in diffusion rates and on which side of the market that power lies makes a considerable difference

second mover advantages in the strategic adoption of new technology under uncertainty abstract this paper introduces technological uncertainty into a timing game of new technology adoption it is shown that the timing neither necessarily involves first mover advantages in precommitment equilibria reinganum review of economic studies xlviii 1981 395 405 nor rent equalization due to the threat of preemption fudenberg and tirole review of economic studies lii 1985 383 401 rather there may be second mover advantages because of informational spillovers furthermore the model predicts that the equilibrium payoffs will typically be discontinuous and non monotonic in the probability that the new technology is profitable a welfare analysis reveals several market failures and suggests that policy intervention should adequately depend on the nature of uncertainty and the rate of technological progress

optimal timing of technology adoption abstract in a dynamic programming framework this paper investigates the optimal timing of technology adoption by a competitive firm when technology choice is irreversible and the firm faces a stochastic innovation process with uncertainties about both the speed of the arrival and the degree of improvement of new technologies a numerical example illustrates how the optimal timing decision is affected by changes in parameter values reflecting market conditions the firm s initial technological attributes and the characteristics of the stochastic innovation process some of these effects turn out to be in sharp contrast to common intuition contrasting the optimal decision rule derived here with the rule obtained under the net present value shows that the former implies a slower pace of adoption than implied by the latter the optimal decision rule is generalized for the case of multiple technology switches and it is shown that for all the switching decisions except the last one the optimal rule satisfies the net present value criterion

developing real option game models by mixing concepts from both game theoretic analysis and real options theory an investment decision in a competitive market can be seen as a game between firms as firms implicitly take into account other firms reactions to their own investment actions we review two decades of real option game models suggesting which critical problems have been solved by considering game theory and which significant problems have not been yet adequately addressed we provide some insights on the plausible empirical applications or shortfalls in applications to date and suggest some promising avenues for future research

the decline in u s output volatility explanations for the decline in u s output volatility since the mid 1980s include better policy good luck and technological change our multiple break estimates suggest that reductions in volatility since the mid 1980s extend not only to manufacturing inventories but also to sales this finding along with a concentration of the reduction in the volatility of inventories in materials and supplies and the lack of a significant break in the inventory sales covariance imply that new inventory technology cannot account for most of the decline in output volatility

were there regime switches in u s monetary policy working paper 2004 14 june 2004 abstract a multivariate model identifying monetary policy and allowing for simultaneity and regime switching in coefficients and variances is confronted with u s data since 1959 the best fit is with a model that allows time variation in structural disturbance variances only among models that also allow for changes in equation coefficients the best fit is for a model that allows coefficients to change only in the monetary policy rule that model allows switching among three main regimes and one rarely and briefly occurring regime the three main regimes correspond roughly to periods when most observers believe that monetary policy actually differed and the differences in policy behavior are substantively interesting though statistically ill determined the estimates imply monetary targeting was central in the early 80s but was also important sporadically in the 70s the changes in regime were essential neither to the rise in inflation in the 70s nor to its decline in the 80s jel classification e52 e47 c53 key words counterfactuals lucas critique policy rule monetary targeting simultaneity volatility model comparison i the debate over monetary policy change in an influential paper clarida gali and gertler 2000 cgg presented evidence that us monetary policy changed between the 1970 s and the 1980 s indeed that in the 70 s it was drastically worse they found that the policy rule apparently followed in the 70 s was one that when embedded in most stochastic general equilibrium models would imply non uniqueness of the equilibrium and hence vulnerability of the economy to sunspot fluctuations of arbitrarily large size their estimated policy rule for the later period on the other hand eliminated this indeterminacy these results are a possible explanation of the volatile and rising inflation of the 70 s and of its subsequent decline the cgg analysis has two important weaknesses one is that it fails to account for stochastic volatility us macroeconomic variables and particularly the federal funds rate have gone through periods of tranquility and of agitation with forecast error variances varying greatly from period to period ignoring such variation does not lead to inconsistent estimates of model parameters when the forecasting equations themselves are constant but it strongly biases toward a finding of changed parameters tests of the stability of the forecasting equations the other weakness is that the cgg analysis rests on powerful and implausible identifying assumptions they require that we accept that the response of the monetary authority to expected future inflation and output does not depend on the recent history of inflation money growth or output it is hard to understand why this should be so especially in the 70 s when monetarism was a prominent theme in policy debates congress was requiring reports from the fed of projected time paths of monetary aggregates and financial markets were reacting sensitively to weekly money supply numbers the requirement for existence and uniqueness of equilibrium in dynamic models is that the monetary policy rule show a more than unit response of interest rates to the sum of the logs of all nominal variables that appear on the right hand side of the reaction function if we force a particular measure of expected future inflation to proxy for all the nominal variables that actually appear independently in the reaction function we are bound to get distorted conclusions on the one hand because expected future inflation will be a noisy measure of the full set of nominal influences on policy we might get downward bias in our estimates from the usual errorsin variables effect on the other hand to the extent that expected future inflation like most expected future values shows less variation than current nominal variables we could find a mistaken scaling up of coefficients

realized volatility forecasting in the presence of time varying noise observed high frequency financial prices can be considered as having two components a true price and a market microstructure noise perturbation it is an empirical regularity coherent with classical market microstructure theories of price determination that the second moment of market microstructure noise is time varying we study the optimal from a finite sample forecast mean squared error mse standpoint frequency selection for realized variance in linear variance forecasting models with time varying market microstructure noise we show that the resulting sampling frequencies are generally considerably lower than those that would be optimally chosen when time variation in the second moment of the noise is unaccounted for these optimal lower frequencies have the potential to translate into considerable out of sample mse gains when forecasting using high frequency variance estimates we recommend treating the relevant frequency as a parameter and evaluating it jointly with the parameters of the f

on the diffusion of new technology a game theoretic approach this paper is an attempt at a rigorous albeit not exceedingly general analysis of the diffusion of new technology in particular consider an industry composed of two firms each using the current best practice technology the firms are assumed to be operating at nash equilibrium output levels generating a market price given demand and profit allocations when a cost reducing innovation is announced each firm must determine when if ever to adopt it based in part upon the discounted cost of implementing the new technology and in part upon the behavior of the rival firm if either firm adopts before the other it can expect to make substantial profits at the expense of the other firm on the other hand the discounted sum of purchase price and adjustment costs may decline with the lengthening of the adjustment period as various quasi fixed factors become more easily variable therefore although waiting costs the firm more in terms of foregone profits it may save money on the cost of purchasing the new technology thus the firm must weigh the costs and benefits of delaying adoption as well as take account of its rival s strategic behavior

preemption and rent equalization in the adoption of new technology we study the adoption of a new technology to illustrate the effects of preemption in games of timing we show that the threat of preemption equalizes rents in a duopoly but that this result does not extend to the general oligopoly game if the gain to preemption is sufficiently small then the optimal symmetric outcome which involves late adoption is an equilibrium this contrasts with reinganum s result that in precommitment equilibria there must be diffusion we develop a new and richer formalism for modeling games of timing which permits a continuoustime representation of the limit of discrete time mixed strategy equilibria

liquidity shortages and banking crises we show in this article that bank failures can be contagious unlike earlier work where contagion stems from depositor panics or contractual links between banks we argue that bank failures can shrink the common pool of liquidity creating or exacerbating aggregate liquidity shortages this could lead to a contagion of failures and a total meltdown of the system given the costs of a meltdown there is a possible role for government intervention unfortunately liquidity and solvency problems interact and can cause each other making it hard to determine the cause of a crisis we propose a robust sequence of intervention banks are often found at the center of systemic financial crises the causes of these crises have long been debated do they stem from depositor panics or do they arise because bank balance sheets are exposed to common factors if it is the latter then is there any sense in which bank failures can be contagious can anything be done to prevent these crises or stop them from propagating once they begin our purpose in this paper is to reexamine whether bank failures can start and propagate systemic crises even if we assume that depositors do not panic that is even if depositors actions are coordinated and they do not run simply because they fear others will run our focus is not because we think that panics are empirically unimportant the jury is still out on that instead we show that contagion can stem from an underlying real general equilibrium problem rather than just from lack of coordination among depositors from a policy perspective attempts to reassure investors through confidence building measures will not work if panic and lack of coordination are not the reasons for a crisis we begin in this paper with a model of a bank that we developed in diamond and rajan 2001 assets in this model are illiquid they cannot be borrowed against or sold for the full value of resources they will generate in their best use because the human capital necessary to generate that full value cannot

long run implications of investment specific technological change an attempt is made to disentangle its effects from the more traditional hicksneutral form of technological progress the balanced growth path for the model is characterized and calibrated to u s national income and product account nipa data the quantitative analysis suggests that investment specific technological change accounts for the major part of growth jel e13 030 041 047

timing of technology adoption and product market competition abstract this paper examines how product market competition affects firms timing of adopting a new technology as well as whether the market provides sufficient adoption incentives it demonstrates that adoption dates differ not only among symmetric firms but also among markets with different market features more specifically technology adoption can occur earlier in a market with cournot competition than in a market with bertrand competition it can also occur earlier in a market in which goods are not too close substitutes therefore this paper shows that competition toughness does not always reinforce adoption incentives when goods are sufficiently differentiated adoption occurs later than is socially optimal

multiplant firms and innovation adoption and diffusion 1 introductionone empirical regularity associated with the adoption of new technology is that large firms tend to adopt sooner than small firms e g see davies 1979 mansfield 1968 mansfield et al 1982 stoneman 1983 1995 or hoppe 2002 the usual explanation of course is that large firms expect a greater return from adoption than small firms however large firms do not always adopt first as can be seen from the diffusion of several new processes in the u s steel industry the basic oxygen furnace and continuous casting adams and mueller 1982 and thin slab casting ghemawat 1993 1995 this article develops a new theoretical model of innovation adoption and diffusion that explains why large firms tend to adopt first but admits conditions under which small firms adopt first the analysis focuses on the adoption of an innovation of uncertain profitability when a firm s size is measured by the number of plants it operates as is well known one reason for operating multiple plants is production costs that are increasing at the margin another reason is the existence of economies of multiplant operations cost savings that result solely from the operation of multiple plants theoretical and empirical support for these economies is mixed theoretically the operation of multiple plants can allow savings in nonproduction costs such as transportation distribution and inventory it can also allow economies of massed reserves cost savings associated with retaining proportionately fewer spare parts backup machines and repair persons in reserve information sharing between plants can reduce production and adoption costs however multiplant operation can also result in greater information costs van zandt and radner 2001 show that because information processing takes time computational constraints limit the amount of information that can be used in reaching a decision this informational crowding out effect can result in decreasing returns to size or diseconomies of multiplant operation in a seminal wide ranging study scherer et al 1975 find little empirical evidence in support of multiplant economies moreover when these economies do exist they involve savings in nonproduction costs more recently in their comparative study of the performance of light water nuclear reactor power plants in the united states and france lester and mccabe 1993 do find empirical support for production cost savings due to information sharing about learning by doing between plants in his study of the adoption of thin slab casting in the steel industry ghemawat 1995 1997 finds that nucor achieved cost savings due to information sharing between plants regarding both construction and production costs however he attributes these multiplant economies to specific aspects of nucor s organizational structure and observes that other steel firms with different organizational structures did not achieve these same cost savings given these conflicting results the analysis in this article assumes that if there are multiplant economies they take the form of savings in nonproduction costs in this case a large firm need not have a greater incentive to adopt first its increase in profit from the adoption of a success in all its plants is certainly greater however the existence of nonproduction cost economies can reduce the incentive of a large firm to adopt first suppose there are two firms a large firm with two plants and a small firm with one plant also suppose that when the innovation is first installed in a plant the adopter must shut down that plant for a finite amount of time in order to learn if the innovation is a success or not this shut down time can be considered as an experimental period during which the firm trains workers produces and tests prototypes attempts to overcome any problems associated with the use of the new technology or makes any necessary changes in its existing organization

on the fit of new keynesian models this article provides new tools for the evaluation of dynamic stochastic general equilibrium dsge models and applies them to a large scale new keynesian model we approximate the dsge model by a vector autoregression and then systematically relax the implied cross equation restrictions and document how the model fit changes we also compare the dsge model s impulse responses to structural shocks with those obtained after relaxing its restrictions we find that the degree of misspecification in this large scale dsge model is no longer so large as to prevent its use in day to day policy analysis yet is not small enough to be ignored

the thrift crisis mortgage credit intermediation and housing activity this paper evaluates the influence of periodic disruptions in the thrift industry on mortgage credit intermediation and housing activity results of the analysis indicate that disruptions in the thrift industry during the early 1980s imposed real costs on the economy by reducing the amount of mortgage credit intermediation estimation findings indicate a sizable mortgage interest rate premium stemming from the loss in thrift intermediation services during the early 1980s those higher mortgage rates served to dampen housing demand in turn exacerbating the cyclical decline in contrast empirical findings for the post recession period of the 1980s indicates a severing of the link between mortgage interest rates and thrift provision of mortgage credit copyright 1995 by ohio state university press

strategic investment in technological innovations abstract the aim of this paper is to determine the optimal timing of technology investment of a single firm in a duopoly framework as time passes different technologies are invented which after sometime become available for the firm to adopt the question here is not only when a firm should invest but also which technology should be adopted for different scenarios the optimal technology investment decision is determined outcomes range from pre emption equilibria to equilibria with second mover advantages

combining var and dsge forecast densities a popular macroeconomic forecasting strategy utilizes many models to hedge against instabilities of unknown timing see among others stock and watson 2004 clark and mccracken 2010 and jore et al 2010 existing studies of this forecasting strategy exclude dynamic stochastic general equilibrium dsge models despite the widespread use of these models by monetary policymakers in this paper we use the linear opinion pool to combine inflation forecast densities from many vector autoregressions vars and a policymaking dsge model the dsge receives a substantial weight in the pool at short horizons provided the var components exclude structural breaks in this case the inflation forecast densities exhibit calibration failure allowing for structural breaks in the vars reduces the weight on the dsge considerably but produces well calibrated forecast densities for inflation

a dynamic game of r and d patent protection and competitive behavior a theory of dynamic optimal resource allocation to r and d in an n firm industry is developed using differential games this technique represents a synthesis of the analytic methods previously applied to the problem static game theory and optimal control the use of particular functional forms allows the computation and detailed discussion of the nash equilibrium in investment rules this paper addresses the problem of resource allocation to research and development among the important issues that a firm engaging in r and d must evaluate are uncertainty regarding the feasibility and profitability of a particular innovation the possibility of a protracted development period the possibility that a rival firm may innovate first capturing either a patent or a significant share of the new market the possibility that a rival firm may imitate the innovation and appropriate some of the profits in the new market in what follows we will develop a theory of optimal resource allocation to research and development which incorporates the aspects of r and d enumerated above we will use a dynamic game theoretic analysis determining the nash equilibrium strategies for n identical firms the availability of perfect patent protection is shown to accelerate development of the innovation and the effect of increasing rivalry is addressed the impact of increasing rivalry on nash equilibrium investment in r and d depends upon the degree of appropriability of rewards if patent protection is perfect then increasing the number of nash rivals results in increased r and d effort however when imitation is rewarded the opposite may be true finally some notions of competitive and perfectly competitive equilibrium are examined in the context of the model developed below

reputational spillovers innovation licensing and entry abstract adoption of a new product by a multiproduct finn may affect all its sales by altering its reputation as an innovator if adopting a success has a halo effect that enhances the adopter s reputation then an inventor s licensing profit exceeds monopoly profit from the new product if adopting a failure has a black eye effect that damages the adopter s reputation then an inventor s licensing profit is maximized by a fixed fee not an auction when both effects are present an inventor licenses new products that are likely to succeed but enters with those that are likely to fail