Unemployment Series Research Articles

On model based seasonal adjustment procedures

In this note the unobserved component approach underlying the software package SEATS is compared with the Beveridge-Nelson type of decomposition for seasonal time series. The main strength of the SEATS approach lies in the appealing model formulation and the careful specification and adjustment of the input series. However, there are some theoretical problems with orthogonal decompositions which may be avoided by using the Beveridge-Nelson approach. The German unemployment series is studied to illustrate the properties of the alternative methods practically.

Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment

This paper discusses identification, specification, estimation and forecasting for a general class of periodic unobserved components time series models with stochastic trend, seasonal and cycle components. Convenient state space formulations are introduced for exact maximum likelihood estimation, component estimation and forecasting. Identification issues are considered and a novel periodic version of the stochastic cycle component is presented. In the empirical illustration, the model is applied to postwar monthly US unemployment series and we discover a significantly periodic cycle. Furthermore, a comparison is made between the performance of the periodic unobserved components time series model and a periodic seasonal autoregressive integrated moving average model. Moreover, we introduce a new method to estimate the latter model.

Multiple unemployment equilibria and asymmetric dynamics—Norwegian evidence

A high degree of persistence in European unemployment rates is often termed unemployment hysteresis, which is equated with the presence of a unit root in unemployment series using linear models. However, the implications of this practice are difficult to reconcile with existing evidence on long run unemployment behaviour and the asymmetric response of unemployment to positive and negative shocks. This paper investigates whether the persistence and asymmetric response to positive and negative shocks may be due to the existence of multiple equilibria. Using Norwegian unemployment data, which share important characteristics with other European unemployment series, this paper characterises unemployment behaviour by applying a logistic smooth transition autoregressive (LSTAR) model. It appears that unemployment is a stationary variable that has switched between two stable equilibria during the period 1972–2003. The paper demonstrates that a large shock, or a sequence of small shocks, may cause a transition from one equilibrium level to another and that unemployment responds asymmetrically to large positive and negative shocks, but symmetrically to small shocks.

Unemployment variation over the business cycles: a comparison of forecasting models

AbstractAsymmetry has been well documented in the business cycle literature. The asymmetric business cycle suggests that major macroeconomic series, such as a country's unemployment rate, are non‐linear and, therefore, the use of linear models to explain their behaviour and forecast their future values may not be appropriate. Many researchers have focused on providing evidence for the non‐linearity in the unemployment series. Only recently have there been some developments in applying non‐linear models to estimate and forecast unemployment rates. A major concern of non‐linear modelling is the model specification problem; it is very hard to test all possible non‐linear specifications, and to select the most appropriate specification for a particular model. Artificial neural network (ANN) models provide a solution to the difficulty of forecasting unemployment over the asymmetric business cycle. ANN models are non‐linear, do not rely upon the classical regression assumptions, are capable of learning the structure of all kinds of patterns in a data set with a specified degree of accuracy, and can then use this structure to forecast future values of the data. In this paper, we apply two ANN models, a back‐propagation model and a generalized regression neural network model to estimate and forecast post‐war aggregate unemployment rates in the USA, Canada, UK, France and Japan. We compare the out‐of‐sample forecast results obtained by the ANN models with those obtained by several linear and non‐linear times series models currently used in the literature. It is shown that the artificial neural network models are able to forecast the unemployment series as well as, and in some cases better than, the other univariate econometrics time series models in our test. Copyright © 2004 John Wiley & Sons, Ltd.

Forecasting unemployment using an autoregression with censored latent effects parameters

Monthly observed unemployment typically displays explosive behavior in recessionary periods, while there seems to be stationary behavior in expansions. Allowing parameters in an autoregression to vary across regimes, and hence over time, can capture this feature. In this paper, we put forward a new autoregressive time series model with time-varying parameters, where this variation depends on a linear indicator variable. When the value of this variable exceeds a stochastic threshold level, the parameters change. We discuss representation, estimation and interpretation of the model. Also, we analyze its forecasting performance for unemployment series of three G-7 countries, and we compare it with various related models.

MODELING ASYMMETRIES AND MOVING EQUILIBRIA IN UNEMPLOYMENT RATES

The paper discusses a simple univariate nonlinear parametric time-series model for unemployment rates, focusing on the asymmetry observed in many OECD unemployment series. The model is based on a standard logistic smooth transition autoregressive model for the first difference of unemployment, but it also includes a lagged level term. This model allows for asymmetric behavior by permitting “local” nonstationarity in a globally stable model. Linearity tests are performed for a number of quarterly, seasonally unadjusted, unemployment series from OECD countries, and linearity is rejected for a number of them. For a number of series, nonlinearity found by testing can be modeled satisfactorily by use of our smooth transition autoregressive model. The properties of the estimated models, including persistence of the shocks according to them, are illustrated in various ways and discussed. Possible existence of moving equilibria in series not showing asymmetry is investigated and modeled with another smooth transition autoregressive model.

Measuring unemployment persistence in terms of I(d) statistical models

In the paper the unemployment rate series of nineteen countries are examined by means of fractionally integrated techniques. The results show that unemployment series are more persistent in some countries, such as Finland, Belgium or Spain, than in others, like the USA, Japan, Austria, Italy or Canada.

Extracting Economic Cycles using Modified Autoregressions

We review a family of modified autoregressive models in both discrete‐ and continuous‐time formulations. We present the case for these models by showing first how a standard discrete‐time autoregressive model with orders selected by criteria such as the Akaike information criterion can fail to identify the correct periods of cyclical variations in a simulated example. We then show how the modified models can overcome this failure, and further illustrate this success with a real example of an unemployment series. A new extension of the continuous‐time modified model to multivariate series is described. This is applied to a pair of series with mixed monthly, quarterly and annual sampling intervals. Common cyclical components of the two series are then extracted.

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.

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.

Decline and Fall: Unemployment among Britain’s Non-White Ethnic Communities 1960–1999

Summary The declining employment fortunes of Britain’s non-white communities, relative to whites, are explained. To achieve this comparison, some historical official sources of unemployment data are reviewed. The earliest known official time series on unemployment of non-whites dates back to 1960. This historical context is explored, especially the reluctance to make the early data more widely known. An unemployment series for non-white males and females from 1970 to 1999 is derived in two separate ways by splicing together official sources. These series are compared with unemployment of whites to demonstrate a relative increase in unemployment of non-whites.

Testing Theory and the Analysis of Time Series Data

Although the relationship between unemployment and crime has been a longstanding interest in criminology, there is little agreement about appropriate models for analyzing this relationship. David Greenberg's (this issue) discussion highlights two issues that raise questions about recent research on the unemployment–crime relationship. First, he extends the work of Hale and Sabbagh (1991) and argues that cointegration methods should be used instead of first-differenced regression models to analyze unemployment and crime time series data. Second, he argues that previous attempts to test his strain theory linking unemployment to the age distribution of crime rely on flawed hypotheses, inappropriate data, and faulty measurement. In this paper, I address both of Greenberg's claims. I begin with a discussion of the relative utility of cointegration analysis and of first-differenced regression models for the analysis of the unemployment–crime relationship, focusing on the link between theory and statistical model. I then discuss the possibility of ever testing and falsifying Greenberg's strain theory.

Quasi‐likelihood Estimation of Non‐invertible Moving Average Processes

Classical methods based on Gaussian likelihood or least‐squares cannot identify non‐invertible moving average processes, while recent non‐Gaussian results are based on full likelihood consideration. Since the error distribution is rarely known a quasi‐likelihood approach is desirable, but its consistency properties are yet unknown. In this paper we study the quasi‐likelihood associated with the Laplacian model, a convenient non‐Gaussian model that yields a modified L1 procedure. We show that consistency holds for all standard heavy tailed errors, but not for light tailed errors, showing that a quasi‐likelihood procedure cannot be applied blindly to estimate non‐invertible models. This is an interesting contrast to the standard results of the quasi‐likelihood in regression models, where consistency usually holds much more generally. Similar results hold for estimation of non‐causal non‐invertible ARMA processes. Various simulation studies are presented to validate the theory and to show the effect of the error distribution, and an analysis of the US unemployment series is given as an illustration.

Education and the natural rate of unemployment

We show how changes in the educational composition of the labour force affect both the level and the behaviour over time of aggregate unemployment series. We also demonstrate that if it had not been for such changes, the US unemployment series would look 'European' since the within-group unemployment series all have that same appearance. We derive a natural-rate model of unemployment for two education groups, providing microfoundations for inter-group differences in wages and unemployment, and evaluate its plausibility in light of microeconomic evidence.

Sacrifice Ratio in Europe: A Comparison of France, Germany, Italy and the U.K.

The aim of this paper is twofold. First, we try to assess to what extent the transmission mechanisms are different across Europe. We concentrate on Europe's four biggest economies: France, Germany, Italy and U.K. Second, we seek to evaluate whether the building of Europe (through the Single Market implementation and the run-up to EMU) has triggered a process of convergence among European countries. The econometric methodology takes its roots in the revisionist history of the Phillips curve of King and Watson (1994). The idea is that, although there is no long-run trade-off between inflation and unemployment (i.e., these two I(1) series are not cointegrated), there might exist a relationship in the short to medium run, due to adjustment lags and labor market rigidities. We build up a bivariate VAR for inflation and unemployment, in which a demand shock is defined as a shock which moves the two series in opposite directions. The VAR impulse response function then allows the persistence effect of shocks onto inflation and unemployment to be computed, from which we derive an assessment of the degree of symmetry in the transmission of monetary policy through the labor market in Europe. Quite restrictive assumptions are required for the sacrifice ratios to be of similar magnitude across countries. Furthermore, we cannot provide evidence of a structural convergence process in Europe. Finally, we show that the sacrifice ratios have been rising since the mid-eighties for the four countries we study, which means that the cost of disinflationary policies is higher today (when the inflation rate is already low) than it used to be. This suggests that the short-run inflation-unemployment trade-off is non-linear with respect to inflation.

Asymmetric Time Series and Temporal Aggregation

The detection of nonlinearities could depend on the sampling frequency. Asymmetric monthly series may become symmetric when aggregated to quarterly or annual frequencies. We test against nonlinearity using the nonlinear autoregressive asymmetric moving average (ARasMA) model, which nests the linear ARMA model as a special case. Using monthly, quarterly, and annual Swedish unemployment series, we find support for symmetry/linearity in the annual series but not in the monthly and quarterly series.

A Bayesian Approach to Understanding Time Series Data

This paper explores the use of Bayesian models to analyze time series data. The Bayesian approach produces output that can be readily understood by actuaries and included in their own experience studies. We illustrate this Bayesian approach by analyzing U.S. unemployment rates, a macroeconomic time series. Understanding time series of macroeconomic variables can help actuaries in pricing and reserving their products. For example, a change in the level and/or variance of the unemployment series is of interest to actuaries, because its movement can explain a changing pattern of lapse rates of incidence rates. Our Bayesian analysis, based on models developed by McCulloch and Tsay (1993, 1994), allows for shifts in the level and in the error variance of a process. We develop a measure of model fit, based on the Akaike Information Criterion, that can be used in choosing between alternative models. Posterior prediction intervals for the fitted values are also created to pictorially show the range of paths that could result from the choice of a particular model.

Testing for Seasonal Stability in Unemployment Series: International Evidence

Recently, it has been shown that seasonal and business cycles are related and a similar economic mechanism is at work in producing both types of cycles (Miron 1996). Thus, an analysis of seasonal fluctuations sheds light on the nature of the business cycle. This paper uses the classical test developed by Hylleberg et al. and the LM-type tests proposed by Canova and Hansen (1995) to investigate seasonal behavior in the unemployment series of Australia, Canada, Japan, New Zealand, the US and a number of OECD countries. The main findings are that the Australian, Austrian and Canadian series are non-stationary at all seasonal frequencies, French, Japan, the NZ and the UK series are stationary at all seasonal frequencies and the USA series is stationary only at the annual frequency. The test results for other series are mixed, suggesting that further analysis is required to reach a definite conclusion. The series, except for France, Japan, New Zealand and the UK, appear to possess unstable seasonal patterns, indicating changing business cycle conditions.

Unemployment persistence: does the size of the shock matter?

One of the stylized facts of unemployment is that shifts in its mean rate between decades and half-decades account for most of its variance. In this paper, we use a statistical analysis based on Markov switching regression models to identify the dates of infrequent changes in the mean of the unemployment rate series of fifteen countries. We find that in most countries, unemployment persistence is much reduced once the (infrequently) changing mean rate, induced by large shocks to unemployment, has been removed. We conclude that the observed persistence in unemployment appears to be consistent with multiple equilibria models and models with an endogeneous natural rate. © 1998 John Wiley & Sons, Ltd.

Challenges facing natural rate theory

This paper attempts to test the natural rate hypothesis by looking at historical unemployment data for France, the UK and the US. We find that the unemployment series can be described as stationary around an infrequently changing mean. Moreover, that the speed of convergence towards mean unemployment is slower when unemployment is high and differs across the three countries: the two European countries having more persistence. We do not find any evidence that the persistence of a change in unemployment is a function of the size of the change. We conclude that the data are consistent with multiple equilibria models where large shocks bring the economy from one equilibrium to another, and also with models with a moving natural rate.