Nonlinearities and Fractional Integration in the US Unemployment Rate*

This paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach introduces fractional integration and nonlinearities simultaneously into the same framework, using a Lagrange multiplier procedure with a standard null‐limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some nonlinear functions of labour‐demand variables such as real oil prices and real interest rates. We also find evidence of a long‐memory component. Our results are consistent with a hysteresis model with path dependency rather than a non‐accelerating inflation rate of unemployment (NAIRU) model with an underlying unemployment equilibrium rate, thereby giving support to more activist stabilization policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policy‐making.     

Multiple shifts and fractional integration in the US and UK unemployment rates

This paper analyses the long-run behaviour of the US and UK unemployment rates by testing for possibly fractional orders of integration and multiple shifts using a sample of over 100 annual observations. The results show that the orders of integration are higher than zero in both series, which implies long memory. If we assume that the underlying disturbances are white noise, the values are higher than 0.5, i.e., nonstationary. However, if the disturbances are autocorrelated, the orders of integration are in the interval (0, 0.5), implying stationarity and mean-reverting behaviour. Moreover, when multiple shifts are taken into account, unemployment is more persistent in the US than in the UK, implying the need for stronger policy action in the former to bring unemployment back to its original level.     

PHILLIPS CURVES AND UNEMPLOYMENT DYNAMICS: A CRITIQUE AND A HOLISTIC PERSPECTIVE

Abstract.  The conventional wisdom that inflation and unemployment are unrelated in the long run implies the compartmentalization of macroeconomics. While one branch of the literature models inflation dynamics and estimates the unemployment rate compatible with inflation stability, another one determines the real economic factors that drive the natural rate of unemployment. In the context of the new Phillips curve, we show that frictional growth, i.e. the interplay between lags and growth, generates an inflation–unemployment trade-off in the long run. We thus argue that a holistic framework, such as the chain reaction theory (CRT), should be used to jointly explain the evolution of inflation and unemployment. A further attraction of the CRT approach is that it provides a synthesis of the traditional structural macroeconometric models and the (structural) vector autoregressions.     

Understanding the Fisher equation

It is argued that univariate long memory estimates based on ex post data tend to underestimate the persistence of ex ante variables (and, hence, that of the ex post variables themselves) because of the presence of unanticipated shocks whose short‐run volatility masks the degree of long‐range dependence in the data. Empirical estimates of long‐range dependence in the Fisher equation are shown to manifest this problem and lead to an apparent imbalance in the memory characteristics of the variables in the Fisher equation. Evidence in support of this typical underestimation is provided by results obtained with inflation forecast survey data and by direct calculation of the finite sample biases. To address the problem of bias, the paper introduces a bivariate exact Whittle (BEW) estimator that explicitly allows for the presence of short memory noise in the data. The new procedure enhances the empirical capacity to separate low‐frequency behaviour from high‐frequency fluctuations, and it produces estimates of long‐range dependence that are much less biased when there is noise contaminated data. Empirical estimates from the BEW method suggest that the three Fisher variables are integrated of the same order, with memory parameter in the range (0.75, 1). Since the integration orders are balanced, the ex ante real rate has the same degree of persistence as expected inflation, thereby furnishing evidence against the existence of a (fractional) cointegrating relation among the Fisher variables and, correspondingly, showing little support for a long‐run form of Fisher hypothesis. Copyright © 2004 John Wiley & Sons, Ltd.     

Risk dependence and cointegration between pharmaceutical stock markets: The case of China and the USA

This paper analyses risk-integration and the degree of dependence between the Values-at-Risk (VaRs) estimates for the two major pharmaceutical stock markets in the world: USA and China. To do this, we study the dependence and fractional cointegration properties among risks. Using daily returns for an eleven-year period, we estimated the VaRs obtained for pharmaceutical market portfolios in China (Shanghai) and the USA (NYSE) using the market model and considering both long and short trading positions. We conclude that the Shanghai pharmaceutical market is riskier than NYSE, although is predictable and losses in both markets exhibit tail dependence between VaR estimates. Particularly, there is lower tail VaR dependence for long position and upper tail dependence for short positions, both being small and fairly constant. On the other hand, we have not found fractional cointegration between risks, suggesting that China’s pharmaceutical sector is not integrated into the global pharmaceutical market.     

Unemployment or credit: Which one holds the potential? Results for a small open economy with a low degree of financialization

This paper investigates the relative importance of unemployment versus credit in determining the potential level of real activity for a small open economy with a low degree of financialization. We use a multivariate unobserved component model (MUC) to derive the potential output and the associated output gap for the Lithuanian economy. The model is estimated via Bayesian methods and the time paths of unobserved variables are extracted via the Kalman filter. The inclusion of unemployment in the MUC model substantially improves the estimates of the output gap in real time. Adding information about credit further emphasizes the overheating of the economy in the pre-crisis period, both in real time and ex post. Including credit preserves the conclusions regarding turning points. We uncover a strong negative correlation between the model-implied unemployment gap (without accounting for credit) and real credit growth. Data revisions do not appear to be the primary source of revisions of output gap estimates.     

A Note On Long Memory Time Series

This note presents the fractional integrated processes which are the main models used to describe long memory phenomena.¹ Section 1 briefly defines the concept of fractional integration, shows the fundamental properties and provides a short summary of the estimation methods. Section 2 consists of a survey of their extensions in order to model long-term cycles.     

Loss given default models incorporating macroeconomic variables for credit cards

Based on UK data for major retail credit cards, we build several models of Loss Given Default based on account level data, including Tobit, a decision tree model, a Beta and fractional logit transformation. We find that Ordinary Least Squares models with macroeconomic variables perform best for forecasting Loss Given Default at the account and portfolio levels on independent hold-out data sets. The inclusion of macroeconomic conditions in the model is important, since it provides a means to model Loss Given Default in downturn conditions, as required by Basel II, and enables stress testing. We find that bank interest rates and the unemployment level significantly affect LGD.     

A fractional cointegration var analysis of exchange rate dynamics

In their seminal work, Baillie and Bollerslev (1994) carried out an analysis of deviations from the cointegrating relationship of seven important exchange rates. They suggested that the exchange rate series possess long memory and therefore such processes could be well described as fractionally integrated processes. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons. In this work we analyze the cointegrating structure of five exchange rates to the US dollar, namely the British pound, the Euro, the Swedish Krona, the Canadian Dollar and the Swiss Franc. The series possess long memory and we show that they can be modeled through fractional integration. In fact, standard cointegration is rejected with the more traditional Johansen CVAR methodology. By using the recently introduced Fractionally Cointegrated VAR by Johansen and Nielsen (2012) we provide a cointegrating relationship taking into account fractional integration.     

Executive Summary

Our assessment of the outlook for the UK economy over the next two years has become slightly more cautious in the wake of the additional fiscal tightening announced in the November Budget. Although we had anticipated tax and public spending measures of the right magnitude in 1994/95, the Budget was more severe in 1995/96 and beyond than we had expected. We have scaled back our estimates of growth for 1995 and 1996 accordingly. On a more positive note, we expect the outlook for inflation to be better than we indicated last October. The mid-1990s are' likely to see a period of sustained low inflation which has not been seen since the 1960s. The government's target measure - RPI excluding mortgage interest - is not expected to test the 4 per cent target ceiling though it is stuck in the 3-3.5 per cent range for most of the forecast period. Despite expecting slower growth, we are now more optimistic about unemployment, which we expect to fall below 2.4 million in 1997. We now believe that increased labour market flexibility should allow the economy to grow on a lower real wage and productivity growth path, at least while unemployment remains so high. However, whether this improved performance would allow the UK to sustain an unemployment of below 2 million without a serious resurgence of inflation is still open to question.     

A MORE FLEXIBLE LABOUR MARKET?

The firm downward trend in unemployment has been one of the most surprising aspects of the UK recovery to date. Unemployment has fallen at a much earlier stage of recovery than it did in the 1980s, despite the fact that measured growth has been fairly modest to date. More favourable demographic trends have contributed to this decline, as has early retirement and an expansion of higher education. It is also possible that growth is being understated. However, the decline in unemployment has also led to the suggestion that the UK labour market has become more flexible. In this Forecast Release, we examine this claim. We identify a number of ways in which both the demand for and the supply of labour have become more flexible. But in one crucial respect - real wage flexibility - the evidence is less persuasive. That should not prevent unemployment falling in the short term. But it could limit the extent to which a substantial further fall in unemployment could he sustained without inflation re-emerging.     

Testing Granger Causality in the presence of threshold effects

This paper proposes a Granger Causality test allowing for threshold effects. The proposed test can be conducted on the basis of the threshold autoregressive distributed lag model or the augmented logistic smooth transition autoregressive model. The proposed test is applied to the U.S. civilian unemployment rate, and it is shown that real investment, real GDP and real interest rate are helpful for improving the in-sample fit of unemployment.     

Does ethics improve stock market resilience in times of instability?

This paper compares the resilience of ethical (Islamic and socially responsible) indexes among five developed (US, UK, Japan, Canada, Australia) and three emerging markets (Brazil, India, South Africa) during the period following the 2008 subprime crisis. It relies on a multivariate CAPM-EGARCH model that accounts for sudden changes in volatility through the application of an iterated cumulative sums of squares (ICSS) algorithm on daily data over the sample period 2008–2014 to model time-varying volatility and ensure reliable estimates. The study confirms the lower systemic risk associated with Islamic indexes during the bearish period and reports that SRI, despite being more subject to systemic risk, offered higher alphas in highly integrated markets, while Islamic indexes performed better in less integrated ones. The evidence also reveals a very limited increase in the models’ predictability power from the integration of sudden changes in volatility into the EGARCH models during the full sample period. This limit is more marked during the bearish sub-period. Our findings have important implications for international investment and portfolio diversification perspectives in times of financial downturn.     

Wages,work intensity and unemployment in Japan,UK and USA

This paper focuses on the impact of excess labour supply on wage inflation in Japan, the US and the UK. Excess labour supply is not simply measured as officially registered unemployed persons but includes a measure of excess supply within the firm, i.e. work intensity. The empirical analysis confirms the importance of broadening the unemployment definition. Interesting differences arise in the cross-country comparison. Our key conclusions are that work intensity is an important factor in determining wage inflation, and that results based on recorded unemployment rates alone seriously underestimate the flexibility of real wages.     

Unemployment Experiences of Young Men: on the Road to Stable Employment?*

This study examines the unemployment experiences of young men in the United Kingdom over the period 1982.IV–1998.I. The empirical results show that repeated unemployment is a dominant feature of the UK labour market and that individual heterogeneity affects mainly the incidence of unemployment and only to a much lesser extent the duration of unemployment. We estimate that about 73% of the young unemployed find stable employment before the age of 35. The remaining 27%, concentrated among the lower‐skilled, keep returning into unemployment, suggesting structural employment instability. These findings imply that a labour market programme targeted at increasing the employability of the young unemployed would yield long‐term benefits by not only getting them out of unemployment but also keeping them out of unemployment.     

Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance

We examine the sensitivity of estimates of the MPH model with respect to assumptions on the censoring mechanism in the context of an economic model of optimal unemployment insurance. We assume a parametric model for the duration of interest and leave the distribution of censoring unrestricted, allowing it to be correlated with observed and unobserved characteristics. We provide a practical characterization of the identified set with moment inequalities and suggest methods for estimating this set. We apply this approach to estimate the elasticity of unemployment exit rate with respect to unemployment benefit. Finally, we investigate welfare consequences of our estimates.     

Further Evidence on the Statistical Properties of Real GNP*

The well‐known lack of power of unit‐root tests has often been attributed to the short length of macroeconomic variables and also to data‐generating processes (DGPs) departing from the I(1)–I(0) models. This paper shows that by using long spans of annual real gross national product (GNP) and GNP per capita (133 years), high power can be achieved, leading to the rejection of both the unit‐root and the trend‐stationary hypothesis. More flexible representations are then considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that both FI and SB formulations are in general preferred to the autoregressive integrated moving average (ARIMA) [I(1) or I(0)] formulations. As a novelty in this literature, new techniques are applied to discriminate between FI and SB. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non‐stationary, highly persistent but mean‐reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.     

UK term structure decompositions at the zero lower bound

This paper employs a zero lower bound (ZLB) consistent shadow‐rate model to decompose UK nominal yields into expectation and term premium components. Compared to a standard affine term structure model, it performs relatively better in a ZLB setting by capturing the stylized facts of the yield curve. The ZLB model is then exploited to estimate inflation expectations and risk premiums. This entails jointly pricing and decomposing nominal and real UK yields. We find evidence that medium‐ and long‐term inflation expectations are contained within narrower bounds since the early 1990s, suggesting monetary policy credibility improved after the introduction of inflation targeting.     

A Semiparametric Analysis of the Term Structure of the US Interest Rates*

The short end of the US$ term structure of interest rates is analysed allowing for the possibility of fractional integration and cointegration. This approach permits mean‐reverting dynamics for the data and the existence of a common long run stochastic trend to be maintained simultaneously. We estimate the model for the period 1963–2006 and find it compatible with this structure. The restriction that the data are I(1) and the errors are I(0) is rejected, mainly because the latter still display long memory. This result is consistent with a model of monetary policy in which the Central Bank operates affecting contracts with short term maturity, and the impulses are transmitted to contracts with longer maturities and then to the final goals. However, the transmission of the impulses along the term structure cannot be modelled using the Expectations Hypothesis.     

Estimating time variation in measurement error from data revisions: an application to backcasting and forecasting in dynamic models

Over time, economic statistics are refined. This implies that data measuring recent economic events are typically less reliable than older data. Such time variation in measurement error affects optimal forecasts. Measurement error, and its time variation, are of course unobserved. Our contribution is to show how estimates of these can be recovered from the variance of revisions to data using a behavioural model of the statistics agency. We illustrate the gains in forecasting performance from exploiting these estimates using a real‐time dataset on UK aggregate expenditure data. Copyright © 2009 John Wiley & Sons, Ltd.