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on Econometrics |
| By: | Claudio Morana (University of Piemonte Orientale, Faculty of Economics,Via Perrone 18, 28100, Novara, Italy,) |
| Abstract: | In this paper we study the zero frequency spectral properties of fractionally cointegrated long memory processes and introduce a new frequency domain principal components estimator of the cointegration space and the factor loading matrix for the long memory factors. We find that for fractionally differenced (fractionally) cointegrated processes the squared multiple coherence at the zero frequency is equal to one, the spectral density matrix at the zero frequency is singular, and the factor loading and cointegrating matrices can be obtained from the eigenvectors of the spectral matrix at the zero frequency, associated with the positive and zero roots, respectively. A Monte Carlo simulation reveals that the proposed principal components estimator has already good properties with relatively small sample sizes. |
| Keywords: | Fractional cointegration, long memory, frequency domain analysis. |
| JEL: | C22 |
| Date: | 2004–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040321&r=ecm |
| By: | Gonzalo Camba-Mendez (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt/Main, Germany.); George Kapetanios (Department of Economics, Queen Mary, University of London, Mile End Rd, London E1 4NS,) |
| Abstract: | The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix whose rank is known. |
| Keywords: | Tests of Ran; Spectral Density Matrix. |
| JEL: | C12 C32 C52 |
| Date: | 2004–04 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040349&r=ecm |
| By: | Bauer, Dietmar (arsenal research, Vienna, Austria); Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | We investigate autoregressive approximations of multiple frequency I(1) processes. The underlying data generating process is assumed to allow for an infinite order autoregressive representation where the coefficients of the Wold representation of the suitably filtered process satisfy mild summability constraints. An important special case of this process class are MFI(1) VARMA processes. The main results link the approximation properties of autoregressions for the nonstationary multiple frequency I(1) process to the corresponding properties of a related stationary process, which are well known. First, uniform error bounds on the estimators of the autoregressive coefficients are derived. Second, the asymptotic properties of order estimators obtained with information criteria are shown to be closely related to those for the associated stationary process obtained by suitable filtering. For multiple frequency I(1) VARMA processes we establish divergence of order estimators based on the BIC criterion at a rate proportional to the logarithm of the sample size. |
| Keywords: | Unit roots, Multiple frequency I(1) process, Nonrational transfer function, Cointegration, VARMA process, Information criteria |
| JEL: | C13 C32 |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:174&r=ecm |
| By: | Claudio Morana (University of Piemonte Orientale, Faculty of Economics, Via Perrone 18, I-28100, Novara, Italy) |
| Abstract: | In the paper we propose a new methodological approach to core inflation estimation,based on a frequency domain principal components estimator, suited to estimate systems of fractionally cointegrated processes. The proposed core inflation measure is the scaled common persistent factor in inflation and excess nominal money growth and bears the interpretation of monetary inflation. The proposed measure is characterised by all the properties that an “ideal” core inflation process should show, providing also a superior forecasting performance relative to other available measures. |
| Keywords: | Long memory; Common factors; Fractional cointegration; Markov switching; Core inflation; Euro area. |
| JEL: | C22 E31 E52 |
| Date: | 2004–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040305&r=ecm |
| By: | Daniel Dias (Banco de Portugal, Research Department.); Carlos Robalo Marques (Corresponding author: Banco de Portugal, Research Department.) |
| Abstract: | This paper elaborates on the alternative measure of persistence recently suggested in Marques (2004), which is based on the idea of mean reversion. A formal distinction between the “unconditional probability of a given process not crossing its mean in period t” and its estimator, is made clear and the relationship between this new measure and the widely used “sum of the autoregressive coefficients”, as alternative measures of persistence, is investigated. Using the law of large numbers and the central limit theorem, properties for the estimator of the new measure of persistence are established, which allow tests of hypotheses to be performed, under very general conditions. Finally, some Monte Carlo experiments are conducted in order to compare the finite sample properties of the estimator for the “unconditional probability of a given process not crossing its mean in period t” and the OLS estimator for the “sum of the autoregressive coefficients”. |
| Keywords: | Inflation persistence; mean reversion; non-parametric estimator. |
| JEL: | E31 C22 E52 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050450&r=ecm |
| By: | Kunst, Robert M. (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and Department of Economics, University of Vienna) |
| Abstract: | The occurrence of decision problems with changing roles of null and alternative hypotheses has increased interest in extending the classical hypothesis testing setup. Particularly, confirmation analysis has been in the focus of some recent contributions in econometrics. We emphasize that confirmation analysis is grounded in classical testing and should be contrasted with the Bayesian approach. Differences across the three approaches – traditional classical testing, Bayes testing, joint confirmation – are highlighted for a popular testing problem. A decision is searched for the existence of a unit root in a time-series process on the basis of two tests. One of them has the existence of a unit root as its null hypothesis and its non-existence as its alternative, while the roles of null and alternative are reversed for the other hypothesis test. |
| Keywords: | Confirmation analysis, Decision contours, Unit roots |
| JEL: | C11 C12 C22 C44 |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:177&r=ecm |
| By: | Andreas Beyer (European Central Bank); Roger E. A. Farmer (UCLA, Dept. of Economics, 8283 Bunche Hall, Box 951477, Los Angeles, CA 90095-1477, USA); Jérôme Henry (European Central Bank, Postfach 16 03 19, D-60066, Frankfurt am Main, Germany); Massimiliano Marcellino (IEP-Bocconi University, IGIER and CEPR) |
| Abstract: | New-Keynesian models are characterized by the presence of expectations as explanatory variables. To use these models for policy evaluation, the econometrician must estimate the parameters of expectation terms. Standard estimation methods have several drawbacks, including possible lack of identification of the parameters, misspecifi- cation of the model due to omitted variables or parameter instability, and the common use of inefficient estimation methods. Several authors have raised concerns over the validity of commonly used instruments to achieve identification. In this paper we analyze the practical relevance of these problems and we propose remedies to weak identifi- cation based on recent developments in factor analysis for information extraction from large data sets. Using these techniques, we evaluate the robustness of recent findings on the importance of forward looking components in the equations of the New-Keynesian model. |
| Keywords: | New-Keynesian Phillips curve; forward looking output equation; Taylor rule; rational expectations; factor analysis; determinacy of equilibrium. |
| JEL: | E5 E52 E58 |
| Date: | 2005–08 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050510&r=ecm |
| By: | Maarten Dossche (National Bank of Belgium, Boulevard de Berlaimont 14, 1000 Brussels, Belgium); Gerdie Everaert (SHERPPA, Ghent University, Hoveniersberg 24, 9000 Ghent, Belgium) |
| Abstract: | Time series estimates of inflation persistence incur an upward bias if shifts in the inflation target of the central bank remain unaccounted for. Using a structural time series approach we measure different sorts of inflation persistence allowing for an unobserved time-varying inflation target. Unobserved components are identified using Kalman filtering and smoothing techniques. Posterior densities of the model parameters and the unobserved components are obtained in a Bayesian framework based on importance sampling. We find that inflation persistence, expressed by the half-life of a shock, can range from 1 quarter in case of a cost-push shock to several years for a shock to long-run inflation expectations or the output gap. |
| Keywords: | Inflation persistence; inflation target; Kalman filter; Bayesian analysis. |
| JEL: | C11 C13 C22 C32 E31 |
| Date: | 2005–06 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050495&r=ecm |
| By: | Marco Del Negro (Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree St NE, Atlanta GA 30309-4470, USA); Frank Schorfheide (Department of Economics, 3718 Locust Walk, University of Pennsylvania, Philadelphia, PA 19104-6297, USA) |
| Abstract: | This paper proposes a novel method for conducting policy analysis with potentially misspecified dynamic stochastic general equilibrium (DSGE) models and applies it to a New Keynesian DSGE model along the lines of Christiano, Eichenbaum, and Evans (JPE 2005) and Smets and Wouters (JEEA 2003). Specifically, we are studying the effects of coefficient changes in interest-rate feedback rules on the volatility of output growth, inflation, and nominal rates. The paper illustrates the sensitivity of the results to assumptions on the policy invariance of model misspecifications. |
| Keywords: | Bayesian Analysis; DSGE Models; Model Misspecification. |
| JEL: | C32 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050475&r=ecm |
| By: | Christian Dreger; Hans-Eggert Reimers |
| Abstract: | In this paper the seasonal unit root test of Hylleberg et al. (1990) is generalized to cover a heterogenous panel. Test statistics are proposed and critical values are obtained by simulation. The new test is applied for unemployment behaviour in industrialized countries. |
| Date: | 2004–06 |
| URL: | http://d.repec.org/n?u=RePEc:iwh:dispap:191&r=ecm |
| By: | Paul McNelis (Department of Economics, Georgetown University,Washington, DC 20057); Peter McAdam (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt/Main, Germany.) |
| Abstract: | This paper applies linear and neural network-based “thick” models for forecasting inflation based on Phillips–curve formulations in the USA, Japan and the euro area. Thick models represent “trimmed mean” forecasts from several neural network models. They outperform the best performing linear models for “real-time” and “bootstrap” forecasts for service indices for the euro area, and do well, sometimes better, for the more general consumer and producer price indices across a variety of countries. |
| Keywords: | Neural Networks; Thick Models; Phillips curves; real-time forecasting; bootstrap. |
| JEL: | C12 E31 |
| Date: | 2004–04 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040352&r=ecm |
| By: | Anindya Banerjee (Corresponding author: Department of Economics, European University Institute, Via della Piazzuola, 43, 50133 Firenze, Italy); Massimiliano Marcellino (IEP-Bocconi University, IGIER, and CEPR,Via Salasco, 5, 20136, Milano, Italy); Igor Masten (Faculty of Economics, University of Ljubljana, Kardeljeva ploscad 17, 1000, Ljubljana, Slovenia) |
| Abstract: | The accession of ten countries into the European Union makes the forecasting of their key macroeconomic indicators an exercise of some importance. Because of the transition period, only short spans of reliable time series are available, suggesting the adoption of simple time series models as forecasting tools. However, despite this constraint on the span of data, a large number of macroeconomic variables (for a given time span) are available, making the class of dynamic factor models a reasonable alternative forecasting tool. The relative performance of these two forecasting approaches is compared by using data for five new Member States. The role of Euro-area information for forecasting and the usefulness of robustifying techniques such as intercept corrections are also evaluated. We find that factor models work well in general, although with marked differences across countries. Robustifying techniques are useful in a few cases, while Euro-area information is virtually irrelevant. |
| Keywords: | Factor models; forecasts; time series models; new Member States. |
| JEL: | C53 C32 E37 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050482&r=ecm |
| By: | Nicholai Benalal (European Central Bank, Directorate General Economics); Juan Luis Diaz del Hoyo (European Central Bank, Directorate General Economics); Bettina Landau (European Central Bank, Directorate General Economics); Moreno Roma (European Central Bank, Directorate General Economics); Frauke Skudelny (European Central Bank, Directorate General Economics) |
| Abstract: | In this paper we investigate whether the forecast of the HICP components (indirect approach) improves upon the forecast of overall HICP (direct approach) and whether the aggregation of country forecasts improves upon the forecast of the euro-area as a whole, considering the four largest euro area countries. The direct approach provides clearly better results than the indirect approach for 12 and 18 steps ahead for the overall HICP, while for shorter horizons the results are mixed. For the euro area HICP excluding unprocessed food and energy (HICPX), the indirect forecast outperforms the direct whereas the differences are only marginal for the countries. The aggregation of country forecasts does not seem to improve upon the forecast of the euro area HICP and HICPX. This result has however to be taken with caution as differences appear to be rather small and due to the limited country coverage. |
| Keywords: | Forecasting short-term inflation, HICP sub-components/aggregation, Bayesian VARs, Model Selection |
| JEL: | C11 C32 C53 E31 E37 |
| Date: | 2004–07 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040374&r=ecm |
| By: | Michael Dueker |
| Abstract: | A pair of simple modifications to the Kalman filter recursions makes possible the filtering of models in which one or more state variables is truncated normal. Such recursions are broadly applicable to macroeconometric models that have one or more probit-type equation, such as vector autoregressions and estimated dynamic stochastic general equilibrium models. |
| Keywords: | Macroeconomics - Econometric models |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2005-057&r=ecm |
| By: | Giovanni Lombardo (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany); Alan Sutherland (School of Economics and Finance, University of St Andrews, St Andrews, KY16 9AL, United Kingdom) |
| Abstract: | This paper shows how to compute a second-order accurate solution of a non-linear rational expectation model using algorithms developed for the solution of linear rational expectation models. The result is a state-space representation for the realized values of the variables of the model. This state-space representation can easily be used to compute impulse responses as well as conditional and unconditional forecasts. |
| Keywords: | Second order approximation; Solution method for rational expectation models. |
| JEL: | C63 E0 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20050487&r=ecm |
| By: | Gonzalo Camba-Méndez (Corresponding author. European Central Bank, Kaiserstrasse 29, D-60311, Frankfurt am Main, Germany.); George Kapetanios (Department of Economics, Queen Mary, University of London, Mile End Road, London E1 4N, United Kingdom.) |
| Abstract: | Standard measures of prices are often contaminated by transitory shocks. This has prompted economists to suggest the use of measures of underlying inflation to formulate monetary policy and assist in forecasting observed inflation. Recent work has concentrated on modelling large datasets using factor models. In this paper we estimate factors from datasets of disaggregated price indices for European countries. We then assess the forecasting ability of these factor estimates against other measures of underlying inflation built from more traditional methods. The power to forecast headline inflation over horizons of 12 to 18 months is adopted as a valid criterion to assess forecasting. Empirical results for the five largest euro area countries as well as for the euro area are presented. |
| Keywords: | Core Inflation; Dynamic Factor Models; Forecasting. |
| JEL: | E31 C13 C32 |
| Date: | 2004–11 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040402&r=ecm |
| By: | Frank Smets (European Central Bank, CEPR and University of Ghent.); Raf Wouters (National Bank of Belgium.) |
| Abstract: | In monetary policy strategies geared towards maintaining price stability conditional and unconditional forecasts of inflation and output play an important role. This paper illustrates how modern sticky-price dynamic stochastic general equilibrium models, estimated using Bayesian techniques, can become an additional useful tool in the forecasting kit of central banks. First, we show that the forecasting performance of such models compares well with a-theoretical vector autoregressions. Moreover, we illustrate how the posterior distribution of the model can be used to calculate the complete distribution of the forecast, as well as various inflation risk measures that have been proposed in the literature. Finally, the structural nature of the model allows computing forecasts conditional on a policy path. It also allows examining the structural sources of the forecast errors and their implications for monetary policy. Using those tools, we analyse macroeconomic developments in the euro area since the start of EMU. |
| Keywords: | Forecasting; DSGE models; monetary policy; euro area. |
| JEL: | E4 E5 |
| Date: | 2004–09 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20040389&r=ecm |
| By: | Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | This paper re-assesses the panel (unit root test) evidence for PPP on four monthly data sets. We discuss and illustrate that commonly-used first generation panel unit root tests are inappropriate for PPP analysis since they are constructed for cross-sectionally uncorrelated panels. Given that real exchange rate panel data sets are – almost by construction – highly cross-sectionally correlated, so called second generation panel unit root methods that allow for and model cross-sectional dependence should be applied. Using inappropriate first generation tests, quite strong evidence for PPP is found. However, this evidence vanishes entirely when resorting to an appropriate method (e.g. the one developed in Bai and Ng, 2004a) for nonstationary cross-sectionally correlated panels. We strongly believe that our findings are relevant beyond the data sets investigated here for illustration. |
| Keywords: | PPP, Real exchange rate index, Unit root, Panel, Cross-sectional dependence, Factor model |
| JEL: | C23 F30 F31 |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:176&r=ecm |