Measuring persistence in aggregate output: ARMA models, fractionally integrated ARMA models and nonparametric procedures

Econometric issues in the estimation of persistence in macroeconomic time series are considered. In particular, the relative merits of estimates based on ARMA models, ARFIMA models and nonparametric procedures are investigated. It is shown that ARFIMA models are inappropriate for the purpose of estimating persistence. Furthermore, some of the criticism leveled in the literature against the use of ARMA models for estimating long run properties is put into perspective. Methodological issues arising in the estimation of ARMA models that are relevant to estimation of persistence are discussed. It is shown how overparameterization of an ARMA model may lead to severely downward biased estimates of persistence. The theoretical results are employed to explain some of the findings in Campbell & Mankiw (1987a) and Christiano & Eichenbaum (1990). The methodological aspects of the paper are also relevant for the problem of estimating the value of a spectral density at any given frequency. An empirical study confirms persistence estimates reported in Campbell & Mankiw (1987a), and shows that ARMA models as well as nonparametric procedures give very similar estimates of persistence if properly applied. First version received: May 1996/final version received: March 1998     

Fractional integration and business cycle features

We show in this article that fractionally integrated univariate models for GDP lead to a better replication of the main business cycle characteristics. We firstly show that the business cycle features are clearly affected by the degree of integration as well as by the other short run (AR, MA, etc.) components of the series. Then, we model the real GDP in the UK and the US by means of fractionally ARIMA (ARFIMA) model, and show that the time series can be specified in terms of this type of model with orders of integration higher than one but smaller than two. Comparing the ARFIMA specifications with those based on ARIMA models, we show via simulations that the former better describe the business cycles features of the data.Jel classification: C12, C15, C22The authors want to thank two anonymous referees for wise remarks. We have also benefited from questions and comments of the attendances at the econometric seminar of the Humboldt Universität zu Berlin and the ESEM2001 congress in Lausanne. Remaining errors and omissions are ours. All correspondence to: Luis A. Gil-Alana.First version received: February 2002/Final version received: December 2002     

An empirical note about additive outliers and nonstationarity in Latin-American inflation series

This note shows the empirical dangers of the presence of large additive outliers when testing for unit roots using standard unit root statistics. Using recent proposed procedures applied to four Latin-American inflation series, I show that the unit root hypothesis cannot be rejected.Jel classification: C2, C3, C5I want to thank Pierre Perron for useful comments on a preliminary version of this paper. Helpful comments from an anonymous referee, and Yiagadeesen Samy are appreciated. I thank the Editor Baldev Raj for useful comments about the final structure of this paper. Finally, I also thank André Lucas for helpful suggestions concerning the use of his nice computer program Robust Inference Plus Estimation (RIPE).First revision received: August 2001/Final revision received: December 2002     

Model selection for nonlinear time series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.First version received: September 2002/Final version received : October 2003I would like to thank Cees Diks, Cars Hommes and an anonymous referee for useful comments that significantly improved the paper.     

A system approach for measuring the euro area NAIRU

This paper addresses the issue of measuring the NAIRU for the euro area and assessing the robustness and precision of the obtained estimates. The empirical framework adopted is based on systems combining an Okun-type relationship between cyclical unemployment and the output gap with a Phillips curve and stochastic laws of motion for the NAIRU and potential output. Such systems have been estimated using Kalman-filter techniques. The results obtained point to an estimate of the area-wide NAIRU that is robust to changes in the underlying models. This robustness is shown to hold both in terms of the mean – i.e., the shape of the resulting NAIRU – and the variance of the process. The latter is derived through bootstrap exercises using the models alone or pooled together. The evidence found suggests that the increase in the aggregate NAIRU that took place in the early part of the sample period has come to a halt and may be about to be reversed.Jel classification: C11, C15, E31, E32The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the Institutions they belong to. The authors are grateful to Per Jansson for providing parts of the econometric RATS code and to Gonzalo Camba-Mendez and Frank Smets of the ECB for useful comments. Comments and recommendations by two anonimous referees are also gratefully acnowledged. All the remaining errors are the authors responsibility. All correspondence to Ricardo Mestre.First version received: January 2002/Final version received December 2002     

The accuracy of interest rate forecasts in the Asia-Pacific region: opportunities for portfolio management

We analysed interest rate forecasts from Australia, China, Hong Kong, India, Indonesia, Malaysia, New Zealand, Singapore, South Korea, Taiwan and Thailand. We assessed 532 forecast time series with a total of 85,264 individual interest rate forecasts. To do so, we carried out a comparison to naïve forecasts and investigated the forecast time series for topically orientated trend adjustments. In addition, we deployed the sign accuracy test and the unbiasedness test. The results are very sobering in part: 95.9% of all forecast time series are characterized by the phenomenon of topically orientated trend adjustments, and 99.4% of all forecast time series proved to be biased. Only a small proportion of the forecast time series (3.6%) reflected the future interest rate trend significantly more precisely than a naïve forecast. However, at the same time some of the results of the study are surprisingly positive. The sign accuracy test revealed that 48.3% of all forecast time series predict the interest rate trend significantly better than a random walk forecast.     

计量经济学方法之时间序列分析

本文介绍了一元时间序列分析中常用的AR、MA、ARMA和ARIMA等经典模型,分析了这几个经典模型的理论要点以及单位根检验的方法和程序,总结了时间序列分析在预测等方面的优势及其在复杂科学管理中的应用,并以我国一月期国债回购利率和上证180月收益率为分析对象,介绍了一元线性回归分析的基本步骤。     

Testing J-curve hypothesis and analysing the effect of exchange rate volatility on the balance of trade in India

This study estimates the balance of trade model similar to Rose (1991) to test the J-curve hypothesis and analyse the effect of conditional exchange rate volatility on the balance of trade in India. The model is estimated on quarterly data from 1975:02 to 1996:03 and the exchange rate is measured alternatively in terms of the trade and export weighted real effective exchange rate. The model variables are tied together in a long run equilibrium relationship. The study does not find any evidence for the presence of the J-curve effect in the balance of trade. The study finds the presence of weak ARCH but strong GARCH effects in the exchange rate series. But this exchange rate volatility does not play any significant role in affecting the balance of trade in India.Jel classification: F31, F32, F40, F41I am grateful to Dr. Glenn Otto of the University of New South Wales, Sydney, Australia for his valuable comments and incisive suggestions which helped to improve the paper substantially. I am also gratefull to an anonymous Referee and Editor, Baldev Raj, of the Journal for giving very useful suggestions. However, I am solely responsible for any error and omission that may remain in the paper. The views expressed in the article are my personal views and not of the institution Iam associated with.First version received: October 2000/Final version received: October 2002     

Retesting symmetry and homogeneity in a cointegrated demand system with bootstrapping: The case of meat demand in Greece

A small Almost Ideal Demand System is estimated for Greek meat consumption using the Johansen procedure in conjunction with parametric bootstrapping and Bartlett corrections. Asymptotic Wald and likelihood ratio tests broadly support the predicted number of cointegrating relationships but reject symmetry and homogeneity. Bootstrapping and Bartlett corrections give support to symmetry and homogeneity but give less support for the predicted number of cointegrating relationships.Jel classification: C32 D12First version received: September 2001/Final version received: March 2003     

Testing for changing shapes of income distribution: Italian evidence in the 1990s from kernel density estimates

By using nonparametric methods, this paper estimates the distribution of both household and size-adjusted real income in Italy between 1987–1998. Because of data sparseness in the distribution, an adaptive bandwidth is used, while to account for sample design a weighting variable is incorporated in the estimation procedure. The time invariance and the presence of modes in the distributions are tested by means of a nonparametric test and a bootstrap test, respectively. The empirical results suggest that the Italian income distribution significantly changed over time. During the eighties the density shifted rightwards, positively affecting the well being of a large fraction of Italian households. The 1993 recession altered the shape of income distribution increasing inequality and polarisation, and the following period of slow recovery did not show significant changes in the shape of distribution in terms of relative income with a consequent permanence of inequality. The polarisation of the distribution is more noticeable for size-adjusted income rather than whole household income, reflecting the influence of family size on income shape.Jel classification: C14, D31, I30The authors gratefully acknowledge financial support from the Italian Ministry of the Universities and Scientific Research (MIUR). We would like to thank two anonymous referees, Nicholas Longford, Aman Ullah and participants of the International workshop on Income Distribution and Welfare, Milan, May 2002 for their useful comments and suggestions. Obviously we are the solely responsible of any further error and omission.First version received: January 2002/Final version received: January 2003     

Performance of periodic time series models in forecasting

The paper provides a comparison of alternative univariate time series models that are advocated for the analysis of seasonal data. Consumption and income series from (West-) Germany, United Kingdom, Japan and Sweden are investigated. The performance of competing models in forecasting is used to assess the adequacy of a specific model. To account for nonstationarity first and annual differences of the series are investigated. In addition, time series models assuming periodic integration are evaluated. To describe the stationary dynamics (standard) time invariant parametrizations are compared with periodic time series models conditioning the data generating process on the season. Periodic models improve the in-sample fit considerably but in most cases under study this model class involves a loss in ex-ante forecasting relative to nonperiodic models. Inference on unit-roots indicates that the nonstationary characteristics of consumption and income data may differ. For German and Swedish data forecasting exercises yield a unique recommendation of unit roots in consumption and income data which is an important (initial) result for multivariate analysis. Time series models assuming periodic integration are parsimonious to specify but often involve correlated one-step-ahead forecast errors. First version received: April 1996/final version received: January 1998     

Rational expectations and fixed-event forecasts: An application to UK inflation

This paper tests a version of the rational expectations hypothesis using ‘fixed-event’ inflation forecasts for the UK. Fixed-event forecasts consist of a panel of forecasts for a set of outturns of a series at varying horizons prior to each outturn. The forecasts are the prediction of fund managers surveyed by Merrill Lynch. Fixed-event forecasts allow tests for whether expectations are unbiased in a similar fashion to the rest of the literature. But they also permit the conduct of particular tests of forecast efficiency - whether the forecasts make best use of available information - that are not possible with rolling-event data. We find evidence of a positive bias in inflation expectations. Evidence for inefficiency is much less clear cut.First version received: June 2002/ Final version received: November 2003We would like two anonymous referees and an editor for comments that have significantly improved the paper. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of England.     

Forecasting exchange rates in transition economies: A comparison of multivariate time series models

This article compares the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian vector error correction (BVEC) models in forecasting the exchange rates for five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Polish Zloty, Slovak Koruna and Slovenian Tolar) against the Euro and the US dollar. Among the specifications composing this battery of multivariate time series models, those with the smallest prediction error still fail to reject the test of equality of forecasting accuracy against the random walk model in short-term predictions, with the exception of the Slovenian Tolar/Euro exchange rate.First version received: October 2002/Final version received: September 2003The authors are grateful to two anonymous referees and the participants in the workshop Monetary and Exchange Rate Strategies Related to the Current European Unions Enlargement Processes, held in Leuven in September 2000, for very helpful comments.     

Taxation and Labor Markets

We exploit the common features of models such as union, search and efficiency wage models to develop a framework that can be used to analyze the effects of any revenue-neutral tax reform on employment. In particular, we show that taxes paid by workers are not equivalent to taxes paid by firms when taxes are non linear. Moreover, we show that the positive impact of tax progressivity on employment is attributable only to a limited set of hypotheses. Received May 2, 2001; revised version received November 27, 2001 Published online: December 5, 2002     

Policy matters. The long run effects of aggregate demand and mark-up shocks on the Italian unemployment rate

This paper estimates a VAR including labor productivity, real wage and unemployment rate, to identify the dynamic effects of technology, demand, and mark-up shocks, respectively, on the Italian labor market. Identification is achieved by imposing recursive restrictions on the matrix of long run multipliers. Our results show that both mark up and aggregate demand shocks permanently reduce the unemployment rate. Finally, technology shocks do not significantly affect the unemployment rate in the long run. These findings convey important policy implications: expansionary aggregate demand and deregulation policies reducing the mark up permanently decrease the Italian unemployment rate.Jel classification: C32, E32, J29This paper has been produced as part of a CEPR Research Network on New Approaches to the Study of Economic Fluctuations. We would like to thank Marcello DAmato, Mario Forni, Marco Lippi and Antonio Ribba for useful comments. We are also grateful to Bernd Sussmuth for pointing out to us several significant improvements to the paper.First version received: November 2001/Final version received: October 2002     

Quantile estimation of frontier production function

The purpose of the paper is to provide new information on the performance of frontier estimation methods, using data from Italian hotel industry. Quantile regression is also suggested as solution to frontier production function estimation. It is shown that, while the choice of estimation methods among conventional techniques significantly affects the economic analysis, quantile regression provides valuable new information by estimating the whole spectrum of production functions corresponding to different efficiency levels. In addition, the method makes available a coherent framework to analyze the performance of the conventional techiniques. Jel classification: C14, C16, D24We would like to thank the Co-Editor, the Associate Editor and an anonymous referee for comments and suggestions. The research was supported by the University Research Council and the National Research Council. The usual disclaimer applies.The estimates were computed using the Roger Koenker and StatLibS-Plus routine of quantile regression and the Tim Coelli and CEPA Web site FRONTIER 4.1 Program. The data set is provided by the Ho.Re.Ca. survey conducted by ISTAT in 1992.First version received: June 2001/Final version received: December 2002     

Financial development and economic growth in Australia: An empirical analysis

The paper empirically examines the dynamic relationship between financial development and economic growth in Australia in terms of bank-based and market-based financial structure. A time-series approach using the VAR Model is used to provide evidence for the dynamic relationship. The paper provides empirical evidence on the causal impact of the financial market on the economic growth of the Australian economy. The results suggest that financial intermediaries and financial markets have different impacts on economic growth given their diverse roles in the domestic economy. In particular there is evidence of causality from economic growth to the development of the financial intermediaries. On the other hand, development in the financial markets causes economic growth but there is no evidence of any causality from economic growth to financial markets. The sensitivity test using different interest rates does not change the results.I Jel classification: O16, G18, G28I We would like to thank Tilak Abeysinghe and Rajagurn Gunasekaran for their helpful comments on the first draft. Also, we would like to thank the Editor, Prof. Baldev Raj, and two anonymous referees for their helpful comments.First version received: October 2001/Final version received: October 2002     

Pricing-to-market tests in instrumental regressions: Case of the transportation equipment industry

Pricing-to-market (PTM) theory suggests that exporting monopolistic firms adjust their destination-specific mark-ups in the face of exchange rate shocks. A large proportion of the existing evidence for PTM comes from Wald tests applied to OLS- and IV-estimated parameters of single-equation models. Such tests can seriously over-reject in the presence of endogeneity and weak instruments so that some of the available results supporting PTM could be spurious. In this paper we revisit the PTM evidence for Japanese and German exporting firms in the transportation equipment industry. Using the model of Marston (1990), we apply exogeneity and LR-LIML-based tests for which the error probability is controlled irrespective of the quality of the available instruments. Our results show right-hand-side endogeneity in almost all of the examined PTM equations. In addition, we find that statistical decisions often differ depending on whether they are based on the traditional Wald test or on our proposed test.The authors would like to thank Philippe Barla, Jean-Thomas Bernard, Christos Constantatos, Larry Schembri, seminar participants at the Bank of Canada, and two anonymous referees for useful comments and suggestions. Thanks also to Richard Marston for providing data. Finally, a special thanks to Marjorie Santos for excellent research assistance. All remaining errors are our own and should not be attributed to the Bank of Canada.First version received: May 2002/Final version received: December 2002     

Forecasting industrial production and the early detection of turning points

In this paper we propose a simple model to forecast industrial production in Italy up to 6 months ahead. We show that the forecasts produced using the model outperform some popular forecasts as well as those stemming from an ARIMA model used as a benchmark and those from some single equation alternative models. We show how the use of these forecasts can improve the estimate of a cyclical indicator and the early detection of turning points for the manufacturing sector. This is of paramount importance for short-term economic analysis.The first draft of this paper was mostly prepared while Claudio Lupi was working as a Research Director at ISAE. The present version of the paper is a revision of a preliminary draft that was circulated under the same title as ISAE working paper 20/01. The authors would like to thank two anonymous referees, audiences at ISAE, Dublin (22nd International Symposium on Forecasting), and Ente Einaudi (econometrics seminars) for comments. Fruitful discussions and suggestions from Gianluca Cubadda, Sergio de Nardis, John FitzGerald, Antonio García-Ferrer, Franco Peracchi, and Tommaso Proietti are gratefully acknowledged. None of them is responsible for any remaining error. The opinions expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of ISAE or its staff.First revision received: Ocotber 2002/Final revision received: May 2003     

Random dynamical systems: a review

Summary. This paper provides a review of some results on the stability of random dynamical systems and indicates a number of applications to stochastic growth models, linear and non-linear time series models, statistical estimation of invariant distributions, and random iterations of quadratic maps.Received: 16 August 2002, Revised: 9 January, 2003, JEL Classification Numbers: C1, C6, D8, D9. Correspondence to: Mukul MajumdarThanks are due to A. Goswami and B.V. Rao for their detailed comments on an earlier version.