An objective function for simulation based inference on exchange rate data

The assessment of models of financial market behaviour requires evaluation tools. When complexity hinders a direct estimation approach, e.g., for agent based microsimulation models, simulation based estimators might provide an alternative. In order to apply such techniques, an objective function is required, which should be based on robust statistics of the time series under consideration. Based on the identification of robust statistics of foreign exchange rate time series in previous research, an objective function is derived. This function takes into account stylized facts about the unconditional distribution of exchange rate returns and properties of the conditional distribution, in particular, autoregressive conditional heteroscedasticity and long memory. A bootstrap procedure is used to obtain an estimate of the variance-covariance matrix of the different moments included in the objective function, which is used as a base for the weighting matrix. Finally, the properties of the objective function are analyzed for two different agent based models of the foreign exchange market, a simple GARCH-model and a stochastic volatility model using the DM/US-$ exchange rate as a benchmark. It is also discussed how the results might be used for inference purposes. Research has been supported by the DFG grant WI 20024/2-1/2. We are indebted to two anonymous referees of this journal, Leigh Tesfatsion, Patrick Burns and other participants of the CEF’06 conference in Limassol for helpful comments on preliminary versions of this paper.     

Confidence Bands for Impulse Responses: Bonferroni vs. Wald

In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. If they are based on the joint asymptotic distribution possibly constructed with bootstrap methods in a frequentist framework, often individual confidence intervals are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint coverage probability lower than the desired one. If instead the Wald statistic is used and the joint bootstrap distribution of the impulse response coefficient estimators is taken into account and mapped into the band, it is shown that such a band is typically rather conservative. It is argued that, by using the Bonferroni method, a band can often be obtained which is smaller than the Wald band.     

Evaluating FOMC forecast ranges: an interval data approach

The Federal Open Market Committee (FOMC) of the U.S. Federal Reserve publishes the range of members’ forecasts for key macroeconomic variables, but not the distribution of forecasts within this range. To evaluate these projections, previous papers compare the midpoint of the range with the realized outcome. This paper proposes an alternative approach to forecast evaluation that takes account of the interval nature of projections. It is shown that using the conventional Mincer–Zarnowitz approach to evaluate FOMC forecasts misses important information contained in the width of the forecast interval. This additional information plays a minor role at short forecast horizons but turns out to be of sometimes crucial importance for longer-horizon forecasts. For 18-month-ahead forecasts, the variation of members’ projections contains information that is more relevant for explaining future inflation than information embodied in the midpoint. Likewise, when longer-range forecasts for real GDP growth and the unemployment rate are considered, the width of the forecast interval comprises information over and above the one given by the midpoint alone.     

Calculating joint confidence bands for impulse response functions using highest density regions

This paper proposes a new nonparametric method of constructing joint confidence bands for impulse response functions of vector autoregressive models. The estimation uncertainty is captured by means of bootstrapping, and the highest density region (HDR) approach is used to construct the bands. A Monte Carlo comparison of the HDR bands with existing alternatives shows that the former are competitive with the bootstrap-based Bonferroni and Wald confidence regions. The relative tightness of the HDR bands matched with their good coverage properties makes them attractive for applications. An application to corporate bond spreads for Germany highlights the potential for empirical work.     

Quasi-Monte Carlo methods in stochastic simulations: An application to policy simulations using a disequilibrium model of the West German economy 1960–1994

Different stochastic simulation methods are used in order to check the robustness of the outcome of policy simulations. The application of a macroeconometric disequilibrium model of the West German economy to a fiscal policy simulation is taken as an example. Due to nonlinearities arising from regime specific reactions inside the model, confidence intervals for the simulation results have to be obtained by means of stochastic simulations. The robustness of the results is assessed using different methodologies. In particular, different methods for the generation of uniform error terms and their conversion to normal variates are applied. These methods include standard approaches as well as quasi-Monte Carlo methods. First version received: May 1998/final version accepted: August 1999     

Causes and Effects of Financing Constraints at the Firm Level

This paper focuses on the empirical assessment of determinants and effects of financing constraints at the firm level. Using a standard model of credit rationing based on asymmetric information firm age and size are found to be factors which should influence the probability of financing constraints. Improving business conditions strengthen the degree of informational asymmetry. A unique panel of firm data for Germany, including direct information on financing constraints, is used for the econometric analysis. Firms' size and improving business conditions are found to have a significant effect. Furthermore, a significant impact on investment and R&D expenditures cannot be rejected.