testing for nonlinear dependence in daily foreign exchange rates the purpose of this article is to investigate whether daily changes in five major foreign exchange rates contain any nonlinearities although the data contain no linear correlation evidence indicates the presence of substantial nonlinearity in a multiplicative rather than additive form further examination reveals that a generalized autoregressive conditional heteroskedasticity model can explain a large part of the nonlinearities for all five exchange rates copyright 1989 by the university of chicago

exchange rate and price dynamics under adaptive and rational expectations an empirical analysis abstract while the concept of rational expectations has become a central tenant of open economy macroeconomic modeling frankel and froot 1990a using survey data find that exchange rate expectations are either extrapolative or regressive we estimate structural and semi structural open economy macroeconomic models with static adaptive and rational expectations to empirically investigate these questions the two major results of the paper are first that the restrictions imposed by static expectations are overwhelmingly rejected in favor of either adaptive or rational expectations and second that it is not possible to choose empirically between rational and adaptive expectations jel f31

methods for robust control robust control allows policymakers to formulate policies that guard against model misspecification the principal tools used to solve robust control problems are state space methods see hansen l p sargent t j 2008 robustness princeton university press giordani p soderlind p 2004 solution of macromodels with hansen sargent robust policies some extensions journal of economic dynamics and control 28 12 2367 2397 in this paper we show that the structural form methods developed by dennis 2007 optimal policy rules in rational expectations models new solution algorithms macroeconomic dynamics 11 1 31 55 to solve control problems with rational expectations can also be applied to robust control problems with the advantage that they bypass the task often onerous of having to express the reference model in state space form in addition we show how to implement two different timing assumptions with distinct implications for the robust policy and the economy we apply our methods to a new keynesian dynamic stochastic general equilibrium model and find that robustness has important effects on policy and the economy

the duration vector a continuous time extension to default free interest rate contingent claims abstract this paper presents a continuous time contingent claims framework for the traditional duration vector models of chambers et al journal of financial and quantitative analysis march 1988 89 104 prisman and shores journal of banking and finance 12 1988 493 504 and others by embedding these into the merton the bell journal of economics and management science 4 1973 141 183 stochastic interest rate option pricing model using this framework we analyze the interest rate risk characteristics of bond options and callable bonds we derive duration measures that are significantly different from the ones reported previously in the literature by garman journal of financial economics 14 1985 309 315 jamshidian and zhu advances in futures and options research 3 1988 63 95 and others the upper and lower bounds of the duration vectors of bond options and callable bonds are investigated an empirical technique based on the implied volatility methodology is suggested for the computation of the duration vectors of bond options and callable bonds

assessing nominal income rules for monetary policy with model and data uncertainty nominal income rules for monetary policy have long been debated but two issues are of particular recent interest first there are questions about the performance of such rules over a range of plausible empirical models especially models with and without explicit rational inflation expectations second there are questions about the performance of these rules in real time using the type of data that is actually available contemporaneously to policy makers rather than final revised data this paper determines optimal monetary policy rules in the presence of such model uncertainty and real time data uncertainty and finds only a limited role for nominal output growth

solution of macromodels with hansen sargent robust policies some extensions abstract we summarize some methods useful in formulating and solving hansen sargent robust control problems and suggest extensions to discretion and simple rules matlab octave and gauss software is provided we illustrate these extensions with applications to the term structure of interest rates the time inconsistency of optimal monetary policy the effects of expectations on the variances of inflation and output and on whether central banks should make their forecasts public

robust control with commitment a modification to hansen sargent i examine the hansen and sargent 2003 robust control of forward looking models journal of monetary economics 50 581 604 formulation of the robust stackelberg problem and show that their method of constructing the approximating equilibrium is generally invalid i then turn to the hansen and sargent 2007 robustness manuscript version dated march 22 2007 treatment which responding to the problems raised in this paper changes subtly but importantly how the robust stackelberg problem is formulated in the context of hansen and sargent 2007 robustness manuscript version dated march 22 2007 i prove first that their method for obtaining the approximating equilibrium is now equivalent to the one developed in this paper and second that the worst case specification errors are not subject to a time consistency problem in the context of the erceg et al 2000 optimal monetary policy with staggered wage and price contracts journal of monetary economics 46 281 313 sticky wage sticky price model i find that a robust central bank will fear primarily that the supply side of its approximating model is misspecified and that robustness affects importantly central bank promises about future policy

expectations in the german hyperinflation reconsidered abstract data on forward foreign exchange rates during the german hyperinflation after world war i provide direct observations of expected changes in the spot rate although levels of these forward rates seem to be efficient predictors of the spot rate the predicted changes in the spot rate are biased downward substantially and do not meet the specific conditions of rationality indeed the bias in the forward rate predictions is similar to bias in adaptive expectations of the spot rate the behavior of the forward rate can be rationalized as a gradual market adaptation to a new regime of volatile and escalating inflation reasonably represented by adaptive expectations the strict definition of rational expectations needs to be broadened to allow for the difficulty of distinguishing between permanent and transitory shocks

pricing stock and bond options when the default free rate is stochastic we derive formulas for the valuation of call options on stocks and bonds when the defaultfree rate is stochastic the formulas highlight the role of the correlation between the unanticipated returns on the underlying security and the changes in the short term rate in determining the options value our numerical analysis indicates that option prices predicted by the proposed formula differ from those predicted by the black and scholes formula when this correlation is relatively large and the short term rate s instantaneous variance is relatively large as well moreover the proposed formula predicts higher lower stock option prices than those predicted by the black and scholes formula for correlation values that are lower higher than some positive critical value

using survey data to test standard propositions regarding exchange rate expectations survey data provide a measure of exchange rate expectations superior to the forward rate in that no risk premium interferes we estimate extrapolative adaptive and regressive models of expectations static or random walk expectations and bandwagon expectations are rejected current appreciation generates the expectation of future depreciation because variables other than the contemporaneous spot rate receive weight in comparing expectations to the process governing the spot rate we find statistically significant bias no variable is as ubiquitous in international financial theory and yet as elusive empirically as investors expectations regarding exchange rates in the past expectations have been modeled in an ad hoc way often by using the forward exchange rate there is however a serious problem with using the forward discount as the measure of the expected change in the exchange rate in that the two may not be equal the gap that may separate the forward discount and expected depreciation is generally interpreted as a risk premium most of the large empirical literature testing the unbiasedness of the forward exchange rate for example has found it necessary either arbitrarily to assume away the existence of the risk premium if the aim

alternative financial policy rules in an open economy under rational and adaptive expectations the potential instability of a fixed monetary rule combined with automatic fixed stabilisers is a well established feature of closed economy is lm models with wealth effects and asset accumulation this paper examines the stability issue in a general open economy macromodel with alternative expectations mechanisms rational or adaptive in both the labour market and the foreign exchange market the fixed monetary rule is found to be stabilising only in special cases notably when post tax real interest rates are negative and the foreign exchange market is characterised by high capital mobility and rational expectations by contrast the alternative rule of fixing the rate of growth of nominal government debt is stable for a wide range of parameter values and alternative expectations schemes

new keynesian models and monetary policy a re examination of the stylized facts using an empirical new keynesian model with optimal discretionary monetary policy we estimate key parameters the central bank s preference parameters the degree of forwardlooking behavior in the determination of inflation and output and the variances of inflation and output shocks to match some broad characteristics of u s data the parameterization we obtain implies a small concern for output stability but a large preference for interest rate smoothing and a small degree of forward looking behavior in price setting but a large degree of forward looking in the determination of output our methodology also allows us to carefully examine the consequences of alternative parameterizations and to provide intuition for our results

imperfect credibility and robust monetary policy this paper studies the behavior of a central bank that seeks to conduct policy optimally while having imperfect credibility and harboring doubts about its model taking the smets wouters model as the central bank s approximating model the paper s main ndings are as follows first a central bank s credibility can have large consequences for how policy responds to shocks second central banks that have low credibility can bene t from a desire for robustness because this desire motivates the central bank to follow through on policy announcements that would otherwise not be time consistent third even relatively small departures from perfect credibility can produce important declines in policy performance finally as a technical contribution the paper develops a numerical procedure to solve the decision problem facing an imperfectly credible policymaker that seeks robustness

optimal fiscal policy with robust control abstract this paper analyzes how consumer uncertainty affects optimal fiscal policy in the lucas and stokey 1983 framework the consumers lacking confidence in their knowledge of the stochastic environment endogenously tilt their subjective probability model away from an approximating probability model the government though is confident that the approximating probability model characterizes the stochastic environment this confidence dichotomy reveals a range of possible objective functions for an altruistic government i assume that the government maximizes the consumers expected utility under the consumers own subjective probability model it is found that this government relies less heavily on labor taxes to absorb the fiscal shock than would be optimal if consumers were fully confident in their probability model this policy helps mitigate the direct welfare cost associated with consumer uncertainty i compare this policy to the one implemented by a government that maximizes the consumers expected utility under the approximating probability model

robust control of forward looking models abstract this paper shows how to formulate and compute robust ramsey aka stackelberg plans for linear models with forward looking private agents the leader and the followers share a common approximating model and both have preferences for robust decision rules because both doubt the model since their preferences differ the leader s and followers decision rules are fragile to different misspecifications of the approximating model we define a stackelberg equilibrium with robust decision makers in which the leader and follower have different worst case models despite sharing a common approximating model to compute a stackelberg equilibrium we formulate a bellman equation that is associated with an artificial single agent robust control problem the artificial bellman equation contains a description of implementability constraints that include euler equations that describe the worst case analysis of the followers as an example the paper analyzes a model of a monopoly facing a competitive fringe

optimal feedback rules in an open economy macromodel with rational expectations this paper outlines procedures for deriving optimal time invariant linear feedback rules in continuous time linear stochastic models under rational expectations it also examines the derivation of optimal simple rules of a similar type these procedures are applied to an open economy model under rational expectations and the consequences of uncertainty about stochastic disturbance structures for policy design are considered the results indicate some preference for price level or nominal income rules rather than a monetary rule for the open economy

pricing stock and bond options when the default free rate is stochastic a comment this paper corrects the bond option formula presented by r rabinovitch 1989 equation 10 with just one state variable driving the economy the formula should be the same as the ones presented by jamshidian 1989 and chaplin 1987

term structure evidence on interest rate smoothing and monetary policy inertia abstract numerous studies have used quarterly data to estimate monetary policy rules or reaction functions that appear to exhibit a very slow partial adjustment of the policy interest rate the conventional wisdom asserts that this gradual adjustment reflects a policy inertia or interest rate smoothing behavior by central banks however such quarterly monetary policy inertia would imply a large amount of forecastable variation in interest rates at horizons of more than 3 months which is contradicted by evidence from the term structure of interest rates the illusion of monetary policy inertia evident in the estimated policy rules likely reflects the persistent shocks that central banks face

an exact bond option formula this paper derives a closed form solution for european options on pure discount bonds assuming a mean reverting gaussian interest rate model as in vasicek 8 the formula is extended to european options on discount bond portfolios

how robustness can lower the cost of discretion model uncertainty has the potential to change importantly how monetary policy is conducted making it an issue that central banks cannot ignore using a standard new keynesian business cycle model this paper analyzes the behavior of a central bank that conducts policy under discretion while fearing that its model is misspecified the main results are as follows first policy performance can be improved if the discretionary central bank implements a robust policy this important result is obtained because the central bank s desire for robustness directs it to assertively stabilize inflation thereby mitigating the stabilization bias associated with discretionary policymaking second the central bank s fear of model misspecification leads it to forecast future outcomes under the belief that inflation in particular will be persistent and have large unconditional variance raising the probability of extreme outcomes private agents however anticipating the policy response make decisions under the belief that inflation will be more closely stabilized that is more tightly distributed than under rational expectations finally as a technical contribution the paper shows how to solve with robustness an important class of linear quadratic decision problems

expectations and exchange rate dynamics after a decade of floating abstract dornbusch s model of expectations and exchange rate dynamics has been a theoretical success and an empirical failure the premise underlying this paper is that the price and exchange rate dynamics inherent in his model cannot be captured by single equation methods to capture these dynamics we estimate dornbusch s model using constrained maximum likelihood methods which incorporate cross equation restrictions derived from the structural equations and assumption of rational expectations our central result is that the estimation of dornbusch s model is much more successful than single equation methods have led us to believe

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