Home | Business News | Browse by Publication | I | International Advances in Economic Research

Cyclical asymmetries in unemployment rates: international evidence.

Article Excerpt
Abstract This paper investigates to what extent the observed nonlinearities in the unemployment rates of six major developed economies are the response to cyclical asymmetries. Two classes of models are compared: strict smooth transition autoregressions and models where the transition variable is GDP growth, which is considered a more direct indicator of the business cycle. The empirical evidence points out that nonlinearities in unemployment rates are induced by cyclical asymmetries. It is also found that in most countries the unemployment rate looks stationary and reverts to a long-run equilibrium rate in periods of normal growth, while in extreme cyclical situations it tends to become nonstationary as if each extreme cyclical episode had its own path of equilibrium.

Keywords Nonlinearity * STAR models * Business cycle * Unemployment * Unit roots

JEL Classification E32 * E24 * C52

Introduction

Nonlinear behavior in unemployment has been extensively documented in the literature. To mention just a few examples that include a variety of approaches, Neftci (1984) uses Markov chains to model asymmetric behavior. Montgomery et al. (1998) and Rothman (1998) estimate different classes of nonlinear time series models and compare their fit and forecasting performance. Krolzig et al. (2002) analyze the labor market in the United Kingdom with a regime-switching vector error correction model. Skalin and Terasvirta (2002) use smooth transition autoregressions to explain cyclical asymmetries and moving equilibria in unemployment rates for several OECD countries. Chauvet et al. (2002) set up a dynamic factor model with regime switching to extract the cyclical component of the unemployment rate in the USA.

This paper centers on the source of nonlinearities. It investigates to what extent nonlinear behavior is the response to cyclical asymmetries, or should be interpreted as being caused by idiosyncratic factors specific to the labor market. For doing so, it is assumed that nonlinearities can be captured by a smooth transition autoregression (STAR) model. The STAR model is a special case of an autoregressive process where the parameters depend on a transition variable [s.sub.t]. Given the value of [s.sub.t] the model simplifies into a linear autoregression, so nonlinearities arise because of the changes in [s.sub.t]. Each value of [s.sub.t] defines a regime, which is characterized by the properties of the linear autoregression that stems from it.

In strict univariate STARs the transition variable is a lag of the dependent variable and regimes are endogenously determined. If nonlinear behavior is generated by cyclical asymmetry, however, one would expect to achieve a better model by allowing the changes in the parameters to depend on a direct indicator of the business cycle. This extension leads to a smooth transition autoregression with exogenous transition, see for instance Cancelo and Mourelle (2005a). Such a parameterization can be seen as a special case of the general smooth transition regression model, and seems to be a natural extension of univariate STARs to explain nonlinearities induced by the business cycle. It should be noted that the models with exogenous transition are no longer an univariate representation of the Data Generating Process (DGP) of the dependent variable.

The relative performance of different alternatives for the transition variable in explaining the data provides an indication on whether nonlinearities are generated by cyclical asymmetries. In the affirmative, one would expect that the model with exogenous transition displays the best performance. On the contrary, if nonlinearities are due to idiosyncratic components specific to the labor market, then one should find that standard STARs are better in terms of their adequacy to the data.

The paper is organized as follows. The following section reviews the foundations of STAR models. Next, the modeling strategy is summarized and the final models are reported. Then, the estimated nonlinearities as captured by the models are interpreted in terms of cyclical asymmetries. The final section concludes.

Smooth Transition Autoregressions

In a Smooth Transition Autoregression (STAR) all predetermined variables are lags of the dependent variable and the autoregressive coefficients change with the transition variable [s.sub.t]. There are two extreme regimes, and the degree of smoothness of the transition from one extreme regime to the other is estimated from the data. Granger and Terasvirta (1993), Terasvirta (1998) and van Dijk et al. (2002) describe smooth transition autoregressions in detail.

The model of order p for a stationary and ergodic process [u.sub.t] is defined as

[u.sub.t] = [[pi].sub.0] + [p.summation over (i=l)] [[pi].sub.i][u.sub.t-i] + F([s.sub.t])[[[theta].sub.0] + [p.summation over (i=l)][[theta].sub.i][u.sub.t-i]] + [e.sub.t] (1)

where F([s.sub.t]) is a transition function that satisfies 0[less than or equal to]F[less than or equal to]1. This paper centers on the so-called Logistic STAR or LSTAR, where F([s.sub.t]) is the logistic function

F([s.sub.t]) = 1/[1 + exp[-[gamma]([s.sub.t] - c)]], [gamma] > (2)

In Eq. 2 F(-[infinity])=0 and F(+[infinity]) = 1, so the extreme regimes are defined for very high and very low values of [s.sub.t]; c is a location parameter such that F(c)=0.5; and [gamma] is a slope parameter that determines how rapid the transition between extreme regimes is.

LSTAR models are expected to offer a suitable framework for capturing the effects of cyclical asymmetries, in the sense that the extreme "good" and "bad" states correspond to very high and very low values of the transition variable. Other transition functions, notably the exponential function, have been considered in the literature of cyclical asymmetries, see...