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     

On the regime-switching and asymmetric dynamics of economic growth in the OECD countries

This study estimates the SETAR and STAR models and examines the regime-switching and asymmetric dynamics of economic growth for a comprehensive set of 10 OECD countries. The SETAR models of both Tsay and Hansen consistently reject the null hypothesis of linearity against the alternative hypothesis of threshold nonlinearity for all the sample countries. The STAR model reinforces the evidence and rejects the null hypothesis of linearity against STAR nonlinearity for all the sample countries, except Italy. The sequential F tests for the nested nulls suggest LSTAR nonlinearity for Austria, Japan, Korea, Mexico, Netherlands and New Zealand, and ESTAR nonlinearity for Finland, Germany and Norway. The forecast evaluations suggest that the SETAR models of Tsay and Hansen perform better, as compared to the AR, ARMA and STAR models. The forecasting performance of the STAR model is approximately similar to the forecasting performance of the linear AR and ARMA rivals. The persistence of lower regimes (with negative-growth or moderate-expansions) necessitates the need for the adoption of expansionary economic policies. While the longer durations of upper regimes (with positive-growth or fast-expansions) support the sustainability of the expansionary economic policies, the adequate precautions need to be taken for the inflationary implications of these policies.     

Early warning signals using AVaRs of infinitely divisible GARCH models — evidence from stock index markets

Classical time series models have failed to properly assess the risks that are associated with large adverse stock price behaviour. This article contributes to autoregressive moving average model–GARCH (ARMA–GARCH) models with standard infinitely divisible innovations and assesses the performance of these models by comparing them with other time series models that have normal innovation. We discuss the limitations of value at risk (VaR) and aim to develop early warning signal models using average value at risk (AVaRs) based on the ARMA–GARCH model with standard infinitely divisible innovations. Empirical results for the daily Dow Jones Industrial Average Index, the England Financial Times Stock Exchange 100 Index and the Japan Nikkei 225 Index reveal that estimating AVaRs for the ARMA–GARCH model with standard infinitely divisible innovations offers an improvement over prevailing models for evaluating stock market risk exposure during periods of distress in financial markets and provides a suitable early warning signal in both extreme events and highly volatile markets.     

Persistence profiles and business cycle fluctuations in a disaggregated model of U.K. output growth

This paper builds on recent work dealing with the measurement of the long-run response of output to different types of shocks at a multisectoral level. The paper re-examines the issues that surround the identification of shocks to particular sectors in a multisectoral model, and proposes “persistence profiles” of shocks as a method of carrying out impulse response analysis in multivariate systems. It is shown that, unlike the impulse response analysis familiar in the literature, the proposed “persistence profiles” are robust to the alternative parameterization of the underlying moving average representation. The analysis is applied to a simple multisectoral model of U.K. output growths, disaggregated by eight industrial sectors.     

Rent extraction by capitalists

Rent extraction by capitalists is present if the capital income share exceeds the capital output elasticity. Based on a sample of 111 countries during the period 1970–2010, panel model estimates show that: (i) the average capital income share significantly exceeds the average capital output elasticity; (ii) the difference between the average capital income share and the average capital output elasticity has increased over time; (iii) in democracies the average capital income share is not significantly different from the average capital output elasticity. The findings suggest that there exists more rent extraction by capitalists in autocracies and anocracies than in democracies.     

Cointegration,common features,and persistence in U.S. farm output

This paper determines the persistence of shocks to U.S. farm output at the sectoral and sub-sectoral level using a disaggregated vector autoregression framework. The persistence is measured under models that impose short-run common feature and long-run cointegration restrictions. The sub-sectoral outputs are found to have a relatively high degree of comovement in the short-run and a relatively low degree of comovement in the long-run. The common feature and cointegration restrictions are found to improve the precision of persistence and cross-persistence estimates. Subsectoral persistence shows considerable variation; persistence in Poultry & Eggs sub-sector is nearly three times the persistence in the Fruits & Nuts sub-sector. Two sub-sectors that share long-run common trends, Food Grains and Feed, Hay & Forage, also have significant cross-persistence, implying technological spillovers.     

Interpreting fluctuations in output growth in China

Unlike in OECD countries, fluctuations in output growth in China are not straightforward in their interpretation. On the one hand, they reflect the business cycle, which results from shocks to aggregate demand. On the other hand, they also reflect the structural transformations that have accompanied China’s transition to a market economy. Demand shocks can be identified by virtue of the persistence of their impact. This paper decomposes the variance in provincial, regional, and national output growth according to its persistence characteristics. The results suggest that during the reform period, only a minority of output growth variance can be attributed to demand shocks and business cycle fluctuations. It is also found that there is substantial heterogeneity in the persistence characteristics of output growth across provinces. Implications of the findings for macroeconomic policy are discussed.     

UNEMPLOYMENT PERSISTENCE AND THE NAIRU: A BAYESIAN APPROACH

This paper estimates the United States and euro area NAIRU in a Bayesian framework. We set out a simple structural model explaining unemployment by demand and supply factors, which are treated as unobserved variables that have observable effects on measured unemployment, output and inflation. The model allows for unemployment persistence and a time-varying core inflation rate. The results show that although cyclical shocks are very persistent, most of the increase in European unemployment is driven by structural factors. The degree of persistence is lower in the United States but demand shocks seem to be more important in explaining variation in unemployment.     

The dynamics of inflation: a study of a large number of countries

Over the last twenty years the statistical properties of inflation persistence has been the subject of intense investigation and debate without reaching a unanimous conclusion yet. In this article we attempt to shed further light to this debate using a battery of econometric techniques in order to provide robust evidence on the degree of inflation persistence and whether this has changed during the period in which several countries have followed inflation-targeting regimes or new monetary regimes. We consider the inflation rates of thirty developed and emerging economies using quarterly data for the period 1958 to 2007 which include alternative monetary policy regimes. The coefficient of the inflation parameter is estimated by Ordinary Least Squares (OLS), Autoregressive Moving Average (ARMA) and Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. Furthermore, the grid-bootstrap Median Unbiased (MUB) estimator approach developed by Hansen (1999) is used to estimate the finite sample OLS estimates coupled with the 95% symmetric confidence interval. We also examine parameter stability of persistence coefficients by estimating a model with time-varying parameters.     

Is there a trade-off between procyclicality and revisions in EC trend TFP estimations?

Potential output constitutes a central measure to determine compliance of the member states with the EU fiscal rules. The EU uses a production function approach to estimate potential output. In a Kalman filter model together with a Bayesian approach TFP is decomposed into a trend and a cycle. The aim of this paper is to examine the relationship between two widely discussed issues of the EC estimate of potential output, procyclicality and the extent of revisions. Procyclicality of the TFP trend depends on the prior assumptions for the residual variance of the TFP cycle equation. Exploiting this, simulations over increasing values of the priors of the residual variance of the TFP cycle equation are run for eight EU countries, leading to decreasing procyclicality of TFP trend estimates. Procyclicality of the estimated TFP trend reduces the standard error of revisions for half of the countries considered, while it implies an increase for the other countries or has no effect. Thus there is a trade-off between procyclicality of the TFP trend and the revision error, but it is not so clear cut. The standard errors of revisions of real-time estimates of the TFP trend as a criterion of model selection could improve forecasts additionally to the marginal likelihood value employed by the EC.     

An empirical study of outbound tourism demand in the UK

A general to specific methodology is used to construct UK demand for outbound tourism models to twelve destinations. A tourism destination preference index is introduced to take into account social, cultural and psychological influences on tourists' decisions concerning their overseas holiday destinations. The tests support the existence of a cointegration relationship for each of 11 UK overseas holiday destinations. The corresponding error correction models are estimated. The empirical results show that the long-run income elasticities for all destinations range from 1.70 to 3.90 with an average of 2.367. The lowest and highest short-run income elasticities are 1.05 and 3.78 respectively, with an average of 2.216. The estimates of the income elasticities imply that overseas holidays are highly income elastic while the own-price elasticities suggest that the demand for UK outbound tourism is relatively own-price inelastic. In terms of the significance of substitution prices in the regression equations, Ireland is the favourite substitute destination for UK outbound tourists. Ex post forecasts over a period of six years are generated from the ECM models and the results compared with those of a naive model, an AR(1) model, an ARMA(p,q) model, and a VAR model. The forecasting performance criteria show that the ECM model has the best overall forecasting performance for UK outbound tourism.     

Estimates of output gaps in four Southeast Asian countries

The output gaps derived for four countries using a generalized Hamilton model are compared with conventional output gap estimates. Further research is needed to explain why the output gap identifies crisis episodes as slowdowns instead of recessions in some countries.     

Unit Root Analyses of the Causality Between Japanese Money and Income

Unit root techniques and cointegration analysis have develop ed considerably in the last ten years. At the same time, the nonstationary test for Granger causality has been developed. We shed some new light on Japanese money supply and income causality by using nonstationary techniques. We specify univariate ARMA models of money, income, GNP deflator and rate of interest, initially by using the Dickey and Fuller (DF) or the augmented DF (ADF) tests. Two diagnostic tests are applied to each selected ARMA regression. One is the residual DF test, and the other is the moving average (MA) unit root test of residuals . After selecting the ARMA model, some causality tests are applied to the error correction model (ECM) of a vector autoregression (VAR) one of which is ordinary least squares (OLS) and another is the maximum likelihood (ML) method. The former requires only the standard F -test on the deleted variables in the ECM. The latter requires the Johansen's ML method in estimating cointegration. Causality is found to go from income to money supply but not the other way. Appendices include a simple implementation of the MA unit root test, a pedagogical proof of the Granger causality tests developed by Toda and Phillips (1993) and an interpretation of the test proposed by Toda and Yamamoto (1995).
JEL Classification Numbers: C32, E50     

The persistence of unemployment in the USA and Europe in terms of fractionally ARIMA models

This article examines the persistence of unemployment in the USA and four European countries by means of fractionally integrated ARMA (ARFIMA) models. In doing so, a type of flexibility in modelling low-frequency dynamics not achieved by non-fractionally ARIMA models can be provided. The results indicate that the unemployment series are much more persistent in some countries such as the UK and France, than in others including Germany or the USA.     

INVENTORY ACCOUNTING AND PROFIT EVALUATION

In an inventory model with exogenous sales, FIFO and LIFO criteria are formalized and compared with national account estimates for intermediate and finished good products. The model is simulated by utilizing manufacturing input and output prices for Italy (1970–88). LIFO and national account estimates of inventory are usually close and also imply reliable measures of output level and changes which can be shown by solving the quantity model. Conversely, FIFO exhibits larger profits and leads in real terms to unsatisfactory estimates of output changes.     

Public and private capital productivity in Russia: a non-parametric investigation

The productivity of public capital has been very popular research topic for US and other OECD countries, while studies using data from transitional countries are almost non-existent. In this paper, we analyze the productivity of public and private capital in Russia with parametric and non-parametric regression methods utilizing a unique regional level panel data from 2003 to 2007. More specifically, we assess public capital’s spillover effects, i.e., the productivity of public capital on private output, as well as the productivity of different capital ownership types on total output. We find that public capital has a clear positive effect on private output. However, our estimates and test statistics show that parametric methods are not able to grasp vast non-linearities and heterogeneity present among Russian regions, while the non-parametric approach can capture these important features of the data better. Furthermore, we find that multicollinearity is an important methodological problem which should be accounted for in analysis concerning capital data. Our results also suggest that the impact of public capital in Russia is heterogeneous in the sense that for some regions its contribution to private output is insignificant or even negative while it has a considerable positive role for most regions. Concerning the capital elasticities of total output, we find that public capital is less productive than private capital and roughly as productive as joint private-public capital.     

The Multi-Sectoral Thirlwall’s Law: evidence from 14 developed European countries using product-level data

The paper reports estimates of import and export functions for five technological sectors in 14 developed European countries. These functions have never before been estimated for developed countries adopting a technological classification of sectors. The paper compares estimates of income elasticities found using vector error-correction models employing aggregate deflators, with estimates found using cross-product panels employing product-specific quality-adjusted price indexes recently calculated by Feenstra and Romalis. The results indicate that the income elasticities of imports and exports are higher for medium- and high-tech manufactures, which suggests the importance of moving from the production of simple goods to the production of goods with high technological content. The estimates also suggest that the Multi-Sectoral Thirlwall’s Law holds for the countries analysed, while comparing the estimates revealed that cross-product panels with quality-adjusted prices generate considerably more robust results. The investigation reveals that using a more recent time period generates estimates of income elasticities of demand for primary products and resource-based manufactures that tend to be higher than the estimates found by studies that have used longer time periods, while the opposite holds for low-, medium-, and high-tech manufactures.     

Decomposing the persistence of real exchange rates

We propose a new methodology for decomposing the persistence of deviations from purchasing power parity (PPP). By directly comparing the impulse response function (IRF) of a vector autoregressive (VAR) model, where the real exchange rate is Granger caused by a set of candidate variables, with the IRF of the equivalent ARMA model for the real exchange rate, we capture the effects of the Granger-causing variables on the half-life of deviations from PPP. Our empirical results for a set of 20 industrial countries suggest that on average around 50% of the persistence of real exchange rates can be attributed to nominal interest rate differentials, inflation differentials and relative business cycle position with the numenaire country. Finally, we provide confidence intervals for the contributions of the aforementioned variables to the persistence of deviations from PPP by means of Monte Carlo simulations.     

Nonlinear Exchange Rate Adjustment in the Enlarged Eurozone: Evidence and Implications for Candidate Countries

This paper sheds light on the importance of the validity of PPP hypothesis for the accessing process of the candidate countries towards EMU. The evidence of nonlinear adjustment in real exchange rates suggests the estimation of a nonlinear SETAR model. While linear half‐life estimates are biased upward (five years on average), SETAR half‐life estimates imply a faster reverting process (1.5 years on average). Moreover, we found that TPI‐based real exchange rates are more appropriate than CPI‐based real exchange rates in testing for PPP hypothesis. For the cluster of EMU countries and for the pre‐EMU period, our nonlinear model confirms stationarity for the majority of the TPI‐based real exchange rates with half‐life estimates less than a year.     

Cointegration,dynamic structure,and the validity of purchasing power parity in African countries

The purpose of this paper is to test the validity of the purchasing power parity (PPP) in Africa in the context of a multivariate error-correction model. This approach allows for the consideration of long-run elasticities as well as the dynamics of the short-run adjustment of exchange rates to changes in domestic and foreign prices. Monthly data for fourteen African countries are used, and the period examined is 1973:4 through 2007:7 (i.e., 412 observations). Results from long-run cointegration analysis, short-run error correction models, persistence profile analysis and variance decomposition all confirm the validity of PPP in these moderate-to-high inflation countries, where estimates of half-life deviations from PPP are found to be outside the range suggested by Rogoff (1996).