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Article Excerpt
Abstract
This paper applies smooth transition models to capture the nonlinear behavior in the imports data of six major European economies and to assess whether such nonlinearities are related to business cycle asymmetries. Two classes of switch between regimes are considered: endogenously determined transition that assumes nonlinearities are generated by idiosyncratic components specific to foreign trade, and exogenous transition based on GDP growth as a more direct indicator of the cyclical state of the economy. The results support the proposition that the dynamics of imports are nonlinear. In Belgium, France, Spain, and the United Kingdom, regimes change over the business cycle, while in Germany and Italy the switch between regimes is endogenous. National characteristics play a role in defining the position of extreme regimes, the smoothness of the transition, and local dynamics within each state. (JEL C32, E32, F15)
Introduction
Modeling nonlinearities in economic time series related to business cycle asymmetries has long been of interest to applied economists. There has been an explosion of papers on the suitable statistical methods for summarizing and explaining cyclical behavior of macroeconomic data, most of them from a univariate point of view. Three types of models have most commonly been used [Potter, 1999]: the Markov switching model, the Self-Excited Threshold AutoRegression, and the Smooth Transition Model (STM).
STMs have been applied to capture asymmetric cyclical behavior in macroeconomic variables like Gross Domestic Product (GDP), industrial production, and unemployment [van Dijk and Franses, 1999; Skalin and Terasvirta, 1999, 2002; Ocal and Osborn, 2000; Sensier et al., 2002]. Imports have not received too much attention in the literature, probably because empirical work has concentrated on the United States where the volume of international transactions is low compared to GDP. However, international trade represents a significant proportion of economic activity in European countries, and the differences between domestic and imported goods are negligible with regard to that part of imports due to regional trade within the European Union. Therefore, in Europe, imports are expected to be very sensitive to the state of the cycle.
In such a case the usual approach of modeling imports behavior by estimating aggregate demand functions and focusing on price and income elasticities misses some relevant features [Masih and Masih, 2000; Ribeiro, 2001; Sawyer and Sprinkle, 1996, 1997; Sinha and Sinha, 2000]. Even though the latest advances in cointegration techniques have been used to separate long-run effects from short-run responses, and some tests of the stability of the long-run elasticities have been developed [Konno and Fukushige, 2002, 2003], most of the research has been carried out within a linear framework that does not take into account the contribution of business cycle asymmetries.
This paper investigates potential nonlinearities in the imports data of six major European economies: Belgium, France, Germany, Italy, Spain, and the United Kingdom. Following standard practice in the literature, first, Smooth Transition AutoRegressions (STAR) are considered. Next, the basic univariate framework is extended to allow for exogenous determination, so that the switch between regimes is a function of the rate of growth of GDP as a more direct indicator of the business cycle. This variant leads to the Smooth Transition AutoRegression with EXogenous Transition (STAR-EXT) model. The two specifications are compared in terms of their adequacy to the data. Finding that STAR-EXTs are preferred would support the proposition that nonlinearities arise from cyclical asymmetries, while opting for pure STARs would be an indication that they are due to idiosyncratic components specific to foreign trade.
The paper is organized as follows. The following section presents the two variants of smooth transition models. Next, the estimated models for the quarterly rate of growth of imports are reported. Then, the international evidence on the effects of business cycle asymmetries in the imports data is examined. The final section concludes the paper.
Smooth Transition Models
STMs are a special class of state-dependent, nonlinear time series models, where the variable is assumed to vary between two extreme regimes and the smoothness of the transition is estimated from the data. The dependent variable is given by a linear combination of predetermined variables plus a random disturbance, where each coefficient is a function of a state variable. This parameterization permits a variety of dynamic behavior and at the same time, once the state is given, the model is locally linear, which allows an easy interpretation of the local dynamics. Granger and Terasvirta [1993], Terasvirta [1994, 1998], and van Dijk et al. [2002] describe STMs with full particulars.
The basic univariate version of STMs is the Smooth Transition AutoRegression: all predetermined variables are lags of the dependent variable and regimes are endogenously generated by the recent history of the time series itself. The STAR model of order p for a stationary and ergodic process [y.sub.t] is defined as
[y.sub.t] = [[pi].sub.0] + [p.summation over (i = 1)] [[pi].sub.i][y.sub.t - i] + F([y.sub.t - d]) [[[theta].sub.0] + [p.summation over (i = 1)] [[theta].sub.i][y.sub.t - i]] + [u.sub.t]...
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