Testing nonlinearities in economic growth in the OECD countries: an evidence from SETAR and STAR models

Abstract

This study estimates the Self Exciting Threshold Autoregressive (SETAR) and Smooth Transition Autoregressive (STAR) models and examines the nonlinear and regime switching dynamics of economic growth for a set of 10 OECD countries. The null of linearity in SETAR model is tested using the recursive polynomial F test of Tsay and the bootstrap based supremum, average and exponential average Lagrange Multiplier (LM) tests of Hansen. The F test of Tsay rejects the null of linearity for all the countries, except Spain and Switzerland. The SETAR model of Hansen reinforces the evidence and suggests the rejection of linear model. The STAR model rejects the null of linearity against STAR nonlinearity for all the countries, except Denmark and Switzerland. The sequential F tests for the conditional nulls suggest the LSTAR nonlinearity for Australia, Belgium, France, Sweden and UK, and the ESTAR nonlinearity for Canada, Spain and the USA.

Keywords:

• SETAR
• STAR
• nonlinearities
• regime-switching
• growth

JEL Classification::

• C20
• C30
• C32
• O40
• O47

Acknowledgments

I am grateful to the anonymous Referee of the journal for very useful comments and suggestions. I am, however, solely responsible for any errors and omissions that may remain in this article.

Notes

¹ The Ljung-Box Q-test (Ljung and Box, 1978) is performed to test up to 8th order serial correlation in the residuals of AR model. The AR model for which the Ljung–Box Q-statistic does not reject the null of no serial correlation (at 5% level) is selected as the best-fitting AR model.

² The conventional ARMA and ARIMA models assume (linearity) and consider the entire sequence as one regime. The two-regime TAR model instead postulates that the system nested in model (2) is governed by two separate AR processes. The dynamic properties of the process and the response of output to shocks in expansion are different from those in recession. In a lower regime with and implied and , the follows process, and in a upper regime with and implied and , the series follows a different adjustment process: . The degree of AR persistence is represented by the magnitude and statistical significance of for and for , and such persistence could be asymmetric across states such that for any value of i. So long as , the lower regime with would tend to be more persistent than upper regime with .

³ If these (d and τ) parameters were directly observable, then the estimation of SETAR model would have been quite straightforward. The mean and AR parameters of two separate autoregressions could be estimated using the conditional OLS. Since d and τ are not directly observable, these are treated as parameters and are estimated jointly with other parameters of the model in a nonlinear setting.

⁴ Potter (1995), however, argues that the overall significance of these rejections is uncertain since one is basically minimizing over the probability values.

⁵ The F-statistics do not reject the null of linearity for Spain and Switzerland and, therefore, the recursive residuals are not plotted for these countries. The recursive residuals show approximately two local minima in case of Belgium and Sweden.

⁶ An increase in γ increases the slope of and, thus, the speed of transition. In the limit, as or , the LSTAR collapses to a standard AR(p) model since each value of is constant. Besides, in the limit, as , the STAR and SETAR models become observationally equivalent (Potter, 1995). The degree of autoregressive decay, for intermediate values of γ, depends on the value of . The mean and AR parameters change smoothly between two extremes in response to the changes in . The follows one AR(p) process, , for and , and another process, , for and .

⁷ Intuitively, this is because the inverse-bell shape of the ESTAR transition function is better approximated by a quadratic curve than by a cubic curve (Taylor et al., 2001).

⁸ The results for the estimates of ARMA(p,q) are available from the author on request.

⁹ The classical models assume perfect flexibility in wages and prices, and postulate complete adjustment in prices and no change in the natural rate level of output and employment in response to anticipated policy shocks to aggregate demand. The Keynesian models contrarily assume stickiness in wages and prices and predict partial adjustment in prices and a change in the natural rate level of output and employment in response to the anticipated shocks to aggregate demand.