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The paper considers optimal monetary stabilization policy in a forward-looking model, when the central bank recognizes that private-sector expectations need not be precisely model-consistent, and wishes to choose a policy that will be as good as possible in the case of any beliefs that are close enough to model-consistency. It is found that commitment continues to be important for optimal policy, that the optimal long-run inflation target is unaffected by the degree of potential distortion of beliefs, and that optimal policy is even more history-dependent than if rational expectations are assumed. JEL Classification: E52, E58, E42
Using a unique data set of regional inflation rates we are examining the extent and dynamics of inflation dispersion in major EMU countries before and after the introduction of the euro. For both periods, we find strong evidence in favor of mean reversion (ß-convergence) in inflation rates. However, half-lives to convergence are considerable and seem to have increased after 1999. The results indicate that the convergence process is nonlinear in the sense that its speed becomes smaller the further convergence has proceeded. An examination of the dynamics of overall inflation dispersion (ó-convergence) shows that there has been a decline in dispersion in the first half of the 1990s. For the second half of the 1990s, no further decline can be observed. At the end of the sample period, dispersion has even increased. The existence of large persistence in European inflation rates is confirmed when distribution dynamics methodology is applied. At the end of the paper we present evidence for the sustainability of the ECB's inflation target of an EMU-wide average inflation rate of less than but close to 2%. Klassifikation: E31, E52, E58
In this paper, we examine the cost of insurance against model uncertainty for the Euro area considering four alternative reference models, all of which are used for policy-analysis at the ECB.We find that maximal insurance across this model range in terms of aMinimax policy comes at moderate costs in terms of lower expected performance. We extract priors that would rationalize the Minimax policy from a Bayesian perspective. These priors indicate that full insurance is strongly oriented towards the model with highest baseline losses. Furthermore, this policy is not as tolerant towards small perturbations of policy parameters as the Bayesian policy rule. We propose to strike a compromise and use preferences for policy design that allow for intermediate degrees of ambiguity-aversion.These preferences allow the specification of priors but also give extra weight to the worst uncertain outcomes in a given context. JEL Klassifikation: E52, E58, E61
This study offers a historical review of the monetary policy reform of October 6, 1979, and discusses the influences behind it and its significance. We lay out the record from the start of 1979 through the spring of 1980, relying almost exclusively upon contemporaneous sources, including the recently released transcripts of Federal Open Market Committee (FOMC) meetings during 1979. We then present and discuss in detail the reasons for the FOMC's adoption of the reform and the communications challenge presented to the Committee during this period. Further, we examine whether the essential characteristics of the reform were consistent with monetarism, new, neo, or old-fashioned Keynesianism, nominal income targeting, and inflation targeting. The record suggests that the reform was adopted when the FOMC became convinced that its earlier gradualist strategy using finely tuned interest rate moves had proved inadequate for fighting inflation and reversing inflation expectations. The new plan had to break dramatically with established practice, allow for the possibility of substantial increases in short-term interest rates, yet be politically acceptable, and convince financial markets participants that it would be effective. The new operating procedures were also adopted for the pragmatic reason that they would likely succeed. JEL Klassifikation: E52, E58, E61, E65.
In this paper, we examine the cost of insurance against model uncertainty for the Euro area considering four alternative reference models, all of which are used for policy-analysis at the ECB.We find that maximal insurance across this model range in terms of aMinimax policy comes at moderate costs in terms of lower expected performance. We extract priors that would rationalize the Minimax policy from a Bayesian perspective. These priors indicate that full insurance is strongly oriented towards the model with highest baseline losses. Furthermore, this policy is not as tolerant towards small perturbations of policy parameters as the Bayesian policy rule. We propose to strike a compromise and use preferences for policy design that allow for intermediate degrees of ambiguity-aversion.These preferences allow the specification of priors but also give extra weight to the worst uncertain outcomes in a given context. JEL Klassifikation: E52, E58, E61.
This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex-ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex-post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. We demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment e.ectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogo. (1989). From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved. JEL Klassifikation: G22, E21, D11, D91.
Using data from the Consumer Expenditure Survey we first document that the recent increase in income inequality in the US has not been accompanied by a corresponding rise in consumption inequality. Much of this divergence is due to different trends in within-group inequality, which has increased significantly for income but little for consumption. We then develop a simple framework that allows us to analytically characterize how within-group income inequality affects consumption inequality in a world in which agents can trade a full set of contingent consumption claims, subject to endogenous constraints emanating from the limited enforcement of intertemporal contracts (as in Kehoe and Levine, 1993). Finally, we quantitatively evaluate, in the context of a calibrated general equilibrium production economy, whether this set-up, or alternatively a standard incomplete markets model (as in Ayiagari 1994), can account for the documented stylized consumption inequality facts from the US data. JEL Klassifikation: E21, D91, D63, D31, G22
This paper studies an overlapping generations model with stochastic production and incomplete markets to assess whether the introduction of an unfunded social security system leads to a Pareto improvement. When returns to capital and wages are imperfectly correlated a system that endows retired households with claims to labor income enhances the sharing of aggregate risk between generations. Our quantitative analysis shows that, abstracting from the capital crowding-out effect, the introduction of social security represents a Pareto improving reform, even when the economy is dynamically effcient. However, the severity of the crowding-out effect in general equilibrium tends to overturn these gains. Klassifikation: E62, H55, H31, D91, D58 . April 2005.
This paper makes an attempt to present the economics of credit securitization in a non-technical way, starting from the description and the analysis of a typical securitization transaction. The paper sketches a theoretical explanation for why tranching, or nonproportional risk sharing, which is at the heart of securitization transactions, may allow commercial banks to maximize their shareholder value. However, the analysis makes also clear that the conditions under which credit securitization enhances welfare, are fairly restrictive, and require not only an active role of the banking supervisiory authorities, but also a price tag on the implicit insurance currently provided by the lender of last resort. Klassifikation: D82, G21, D74. February 16, 2005.
We evaluate the importance of the precautionary saving motive by relying on a direct question about precautionary wealth from the 1995 and 1998 waves of the Survey of Consumer Finances. In this survey, a new question has been designed to elicit the amount of desired precautionary wealth. This allows us to assess the amount of precautionary accumulation and to overcome many of the problems of previous works on this topic. We find that a precautionary saving motive exists and affects virtually every type of household. However, precautionary savings account for only 8 percent of total wealth holdings. Even though this motive does not give rise to large amounts of wealth, particularly for young and middle-age households, it is particularly important for two groups: older households and business owners. Overall, we provide strong evidence that we need to take the precautionary saving motive into account when modeling saving behavior. Klassifizierung: D91, E21, C21
The Basle securitisation framework explained: the regulatory treatment of asset securitisation
(2005)
The paper provides a comprehensive overview of the gradual evolution of the supervisory policy adopted by the Basle Committee for the regulatory treatment of asset securitisation. We carefully highlight the pathology of the new “securitisation framework” to facilitate a general understanding of what constitutes the current state of computing adequate capital requirements for securitised credit exposures. Although we incorporate a simplified sensitivity analysis of the varying levels of capital charges depending on the security design of asset securitisation transactions, we do not engage in a profound analysis of the benefits and drawbacks implicated in the new securitisation framework. JEL Klassifikation: E58, G21, G24, K23, L51. Forthcoming in Journal of Financial Regulation and Compliance, Vol. 13, No. 1 .
The theory of intertemporal consumption choice makes sharp predictions about the evolution of the entire distribution of household consumption, not just about its conditional mean. In the paper, we study the empirical transition matrix of consumption using a panel drawn from the Bank of Italy Survey of Household Income and Wealth. We estimate the parameters that minimize the distance between the empirical and the theoretical transition matrix of the consumption distribution. The transition matrix generated by our estimates matches remarkably well the empirical matrix, both in the aggregate and in samples stratified by education. Our estimates strongly reject the consumption insurance model and suggest that households smooth income shocks to a lesser extent than implied by the permanent income hypothesis. Klassifikation: D52, D91, I30
The effects of public policy programmes which aim at internalising spill-overs due to successful innovation are analysed in a sequential double-sided moral hazard double-sided adverse selection framework. The central focus lies in analysing their impact on contract design. We show that in our framework only ex post grants are a robust instrument for implementing the first-best situation, whereas the success of guarantee programmes, ex ante grants and some public-private partnerships depends strongly on the characteristics of the project: in certain cases they not only give no further incentives but even destroy contract mechanisms and so worsen the outcome.
Credit card debt puzzles
(2005)
Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve only the former puzzle (Laibson et al., 2003). Bertaut and Haliassos (2002) proposed an 'accountant-shopper' framework for the latter. The current paper builds, solves, and simulates a fully-specified accountant-shopper model, to show that this framework can actually generate both types of co-existence, as well as target credit card utilization rates consistent with Gross and Souleles (2002). The benchmark model is compared to setups without self-control problems, with alternative mechanisms, and with impatient but fully rational shoppers. Klassifikation: E210, G110
Financial markets embed expectations of central bank policy into asset prices. This paper compares two approaches that extract a probability density of market beliefs. The first is a simulatedmoments estimator for option volatilities described in Mizrach (2002); the second is a new approach developed by Haas, Mittnik and Paolella (2004a) for fat-tailed conditionally heteroskedastic time series. In an application to the 1992-93 European Exchange Rate Mechanism crises, that both the options and the underlying exchange rates provide useful information for policy makers. JEL Klassifikation: G12, G14, F31.
While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. This paper investigates two methods of combining them and their use in modeling and predicting financial risk. Based on 25 daily stock return series, the empirical results indicate that the new models offer a plausible description of the data. They are also shown to be competitive with, or superior to, use of the hyperbolic distribution, which has gained some popularity in asset-return modeling and, in fact, also nests the Gaussian and Laplace. Klassifikation: C16, C50 . March 2005.
Trusting the stock market
(2005)
We provide a new explanation to the limited stock market participation puzzle. In deciding whether to buy stocks, investors factor in the risk of being cheated. The perception of this risk is a function not only of the objective characteristics of the stock, but also of the subjective characteristics of the investor. Less trusting individuals are less likely to buy stock and, conditional on buying stock, they will buy less. The calibration of the model shows that this problem is sufficiently severe to account for the lack of participation of some of the richest investors in the United States as well as for differences in the rate of participation across countries. We also find evidence consistent with these propositions in Dutch and Italian micro data, as well as in cross country data. Klassifikation: D1, D8
The paper documents lack of awareness of financial assets in the 1995 and 1998 Bank of Italy Surveys of Household Income and Wealth. It then explores the determinants of awareness, and finds that the probability that survey respondents are aware of stocks, mutual funds and investment accounts is positively correlated with education, household resources, long-term bank relations and proxies for social interaction. Lack of financial awareness has important implications for understanding the stockholding puzzle and for estimating stock market participation costs. Klassifikation: E2, D8, G1
Default risk sharing between banks and markets : the contribution of collateralized debt obligations
(2005)
This paper contributes to the economics of financial institutions risk management by exploring how loan securitization a.ects their default risk, their systematic risk, and their stock prices. In a typical CDO transaction a bank retains through a first loss piece a very high proportion of the expected default losses, and transfers only the extreme losses to other market participants. The size of the first loss piece is largely driven by the average default probability of the securitized assets. If the bank sells loans in a true sale transaction, it may use the proceeds to to expand its loan business, thereby incurring more systematic risk. We find an increase of the banks' betas, but no significant stock price e.ect around the announcement of a CDO issue. Our results suggest a role for supervisory requirements in stabilizing the financial system, related to transparency of tranche allocation, and to regulatory treatment of senior tranches. JEL Klassifikation: D82, G21, D74 .
How do markets spread risk when events are unknown or unknowable and where not anticipated in an insurance contract? While the policyholder can "hold up" the insurer for extra contractual payments, the continuing gains from trade on a single contract are often too small to yield useful coverage. By acting as a repository of the reputations of the parties, we show the brokers provide a coordinating mechanism to leverage the collective hold up power of policyholders. This extends both the degree of implicit and explicit coverage. The role is reflected in the terms of broker engagement, specifically in the ownership by the broker of the renewal rights. Finally, we argue that brokers can be motivated to play this role when they receive commissions that are contingent on insurer profits. This last feature questions a recent, well publicized, attack on broker compensation by New York attorney general, Elliot Spitzer. Klassifikation: G22, G24, L14
From a macroeconomic perspective, the short-term interest rate is a policy instrument under the direct control of the central bank. From a finance perspective, long rates are risk-adjusted averages of expected future short rates. Thus, as illustrated by much recent research, a joint macro-finance modeling strategy will provide the most comprehensive understanding of the term structure of interest rates. We discuss various questions that arise in this research, and we also present a new examination of the relationship between two prominent dynamic, latent factor models in this literature: the Nelson-Siegel and affine no-arbitrage term structure models. JEL Klassifikation: G1, E4, E5.
Using unobservable conditional variance as measure, latent-variable approaches, such as GARCH and stochastic-volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing "observable" or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time-series models for realized volatility exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time-varying volatility of realized volatility leads to a substantial improvement of the model's fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting. Klassifikation: C22, C51, C52, C53
This paper computes the optimal progressivity of the income tax code in a dynamic general equilibrium model with household heterogeneity in which uninsurable labor productivity risk gives rise to a nontrivial income and wealth distribution. A progressive tax system serves as a partial substitute for missing insurance markets and enhances an equal distribution of economic welfare. These beneficial effects of a progressive tax system have to be traded off against the efficiency loss arising from distorting endogenous labor supply and capital accumulation decisions. Using a utilitarian steady state social welfare criterion we find that the optimal US income tax is well approximated by a flat tax rate of 17:2% and a fixed deduction of about $9,400. The steady state welfare gains from a fundamental tax reform towards this tax system are equivalent to 1:7% higher consumption in each state of the world. An explicit computation of the transition path induced by a reform of the current towards the optimal tax system indicates that a majority of the population currently alive (roughly 62%) would experience welfare gains, suggesting that such fundamental income tax reform is not only desirable, but may also be politically feasible. JEL Klassifikation: E62, H21, H24 .
This paper introduces a method for solving numerical dynamic stochastic optimization problems that avoids rootfinding operations. The idea is applicable to many microeconomic and macroeconomic problems, including life cycle, buffer-stock, and stochastic growth problems. Software is provided. Klassifikation: C6, D9, E2 . July 28, 2005.
We explore the macro/finance interface in the context of equity markets. In particular, using half a century of Livingston expected business conditions data we characterize directly the impact of expected business conditions on expected excess stock returns. Expected business conditions consistently affect expected excess returns in a statistically and economically significant counter-cyclical fashion: depressed expected business conditions are associated with high expected excess returns. Moreover, inclusion of expected business conditions in otherwise standard predictive return regressions substantially reduces the explanatory power of the conventional financial predictors, including the dividend yield, default premium, and term premium, while simultaneously increasing R2. Expected business conditions retain predictive power even after controlling for an important and recently introduced non-financial predictor, the generalized consumption/wealth ratio, which accords with the view that expected business conditions play a role in asset pricing different from and complementary to that of the consumption/wealth ratio. We argue that time-varying expected business conditions likely capture time-varying risk, while time-varying consumption/wealth may capture time-varying risk aversion. Klassifikation: G12
We provide a novel benefit of "Alternative Risk Transfer" (ART) products with parametric or index triggers. When a reinsurer has private information about his client's risk, outside reinsurers will price their reinsurance offer less aggressively. Outsiders are subject to adverse selection as only a high-risk insurer might find it optimal to change reinsurers. This creates a hold-up problem that allows the incumbent to extract an information rent. An information-insensitive ART product with a parametric or index trigger is not subject to adverse selection. It can therefore be used to compete against an informed reinsurer, thereby reducing the premium that a low-risk insurer has to pay for the indemnity contract. However, ART products exhibit an interesting fate in our model as they are useful, but not used in equilibrium because of basis-risk. Klassifikation: D82, G22
This paper characterizes the optimal inflation buffer consistent with a zero lower bound on nominal interest rates in a New Keynesian sticky-price model. It is shown that a purely forward-looking version of the model that abstracts from inflation inertia would significantly underestimate the inflation buffer. If the central bank follows the prescriptions of a welfare-theoretic objective, a larger buffer appears optimal than would be the case employing a traditional loss function. Taking also into account potential downward nominal rigidities in the price-setting behavior of firms appears not to impose significant further distortions on the economy. JEL Klassifikation: C63, E31, E52 .
Wider participation in stockholding is often presumed to reduce wealth inequality. We measure and decompose changes in US wealth inequality between 1989 and 2001, a period of considerable spread of equity culture. Inequality in equity wealth is found to be important for net wealth inequality, despite equity's limited share. Our findings show that reduced wealth inequality is not a necessary outcome of the spread of equity culture. We estimate contributions of stockholder characteristics to levels and inequality in equity holdings, and we distinguish changes in configuration of the stockholder pool from changes in the influence of given characteristics. Our estimates imply that both the 1989 and the 2001 stockholder pools would have produced higher equity holdings in 1998 than were actually observed for 1998 stockholders. This arises from differences both in optimal holdings and in financial attitudes and practices, suggesting a dilution effect of the boom followed by a cleansing effect of the downturn. Cumulative gains and losses in stockholding are shown to be significantly influenced by length of household investment horizon and portfolio breadth but, controlling for those, use of professional advice is either insignificant or counterproductive. JEL Classification: E21, G11
Using a set of regional inflation rates we examine the dynamics of inflation dispersion within the U.S.A., Japan and across U.S. and Canadian regions. We find that inflation rate dispersion is significant throughout the sample period in all three samples. Based on methods applied in the empirical growth literature, we provide evidence in favor of significant mean reversion (ß-convergence) in inflation rates in all considered samples. The evidence on ó-convergence is mixed, however. Observed declines in dispersion are usually associated with decreasing overall inflation levels which indicates a positive relationship between mean inflation and overall inflation rate dispersion. Our findings for the within-distribution dynamics of regional inflation rates show that dynamics are largest for Japanese prefectures, followed by U.S. metropolitan areas. For the combined U.S.-Canadian sample, we find a pattern of within-distribution dynamics that is comparable to that found for regions within the European Monetary Union (EMU). In line with findings in the so-called 'border literature' these results suggest that frictions across European markets are at least as large as they are, e.g., across North American markets. Klassifikation: E31, E52, E58
We selectively survey, unify and extend the literature on realized volatility of financial asset returns. Rather than focusing exclusively on characterizing the properties of realized volatility, we progress by examining economically interesting functions of realized volatility, namely realized betas for equity portfolios, relating them both to their underlying realized variance and covariance parts and to underlying macroeconomic fundamentals.
Volatility forecasting
(2005)
Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1.
What do academics have to offer market risk management practitioners in financial institutions? Current industry practice largely follows one of two extremely restrictive approaches: historical simulation or RiskMetrics. In contrast, we favor flexible methods based on recent developments in financial econometrics, which are likely to produce more accurate assessments of market risk. Clearly, the demands of real-world risk management in financial institutions - in particular, real-time risk tracking in very high-dimensional situations - impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for high-dimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities, hopefully stimulating the development of improved market risk management technologies that draw on the best of both worlds.
Market discipline for financial institutions can be imposed not only from the liability side, as has often been stressed in the literature on the use of subordinated debt, but also from the asset side. This will be particularly true if good lending opportunities are in short supply, so that banks have to compete for projects. In such a setting, borrowers may demand that banks commit to monitoring by requiring that they use some of their own capital in lending, thus creating an asset market-based incentive for banks to hold capital. Borrowers can also provide banks with incentives to monitor by allowing them to reap some of the benefits from the loans, which accrue only if the loans are in fact paid o.. Since borrowers do not fully internalize the cost of raising capital to the banks, the level of capital demanded by market participants may be above the one chosen by a regulator, even when capital is a relatively costly source of funds. This implies that capital requirements may not be binding, as recent evidence seems to indicate. JEL Classification: G21, G38
Some have argued that recent increases in credit risk transfer are desirable because they improve the diversification of risk. Others have suggested that they may be undesirable if they increase the risk of financial crises. Using a model with banking and insurance sectors, we show that credit risk transfer can be beneficial when banks face uniform demand for liquidity. However, when they face idiosyncratic liquidity risk and hedge this risk in an interbank market, credit risk transfer can be detrimental to welfare. It can lead to contagion between the two sectors and increase the risk of crises. Klassifikation: G21, G22
Under a conventional policy rule, a central bank adjusts its policy rate linearly according to the gap between inflation and its target, and the gap between output and its potential. Under "the opportunistic approach to disinflation" a central bank controls inflation aggressively when inflation is far from its target, but concentrates more on output stabilization when inflation is close to its target, allowing supply shocks and unforeseen fluctuations in aggregate demand to move inflation within a certain band. We use stochastic simulations of a small-scale rational expectations model to contrast the behavior of output and inflation under opportunistic and linear rules. Klassifikation: E31, E52, E58, E61. July, 2005.
We find that on average consumers chose the contract that ex post minimized their net costs. A substantial fraction of consumers (about 40%) still chose the ex post sub-optimal contract, with some incurring hundreds of dollars of avoidable interest costs. Nonetheless, the probability of choosing the sub-optimal contract declines with the dollar magnitude of the potential error, and consumers with larger errors were more likely to subsequently switch to the optimal contract. Thus most of the errors appear not to have been very costly, with the exception that a small minority of consumers persists in holding substantially sub-optimal contracts without switching. Klassifikation: G11, G21, E21, E51
Ignoring the existence of the zero lower bound on nominal interest rates one considerably understates the value of monetary commitment in New Keynesian models. A stochastic forward-looking model with lower bound, calibrated to the U.S. economy, suggests that low values for the natural rate of interest lead to sizeable output losses and deflation under discretionary monetary policy. The fall in output and deflation are much larger than in the case with policy commitment and do not show up at all if the model abstracts from the existence of the lower bound. The welfare losses of discretionary policy increase even further when inflation is partly determined by lagged inflation in the Phillips curve. These results emerge because private sector expectations and the discretionary policy response to these expectations reinforce each other and cause the lower bound to be reached much earlier than under commitment. JEL Klassifikation: E31, E52