Empirical evidence of joint nonlinearity in economic area and US economic variables using two modified multivariate nonlinearity tests

Abstract

This article examines the joint nonlinearity of 15 subsets of US and economic area (EA) economic variables using two modified multivariate nonlinearity tests recently developed in the literature. Clear evidence of joint nonlinearity in both US and EA economic variables is found. Our results thus cast doubts on the adequacy of using linear multivariate (VAR-type) models, structural or not, in applied economics.

Keywords:

• VAR models
• principal component analysis
• nonlinearity testing
• TSAY test
• ARCH test

JEL Classification:

• C12
• C32

Acknowledgement

The author would like to thank Ron Smith for helpful comments and suggestions.

Notes

¹ It is worth mentioning that even some structural economic models (e.g. dynamic stochastic general equilibrium (DSGE) models) can allow for a VAR representation under mild conditions (see Alvarez-Lois et al., 2008 for details).

² The data-sets come from the St. Louis Federal Reserve Economic Database and the Area Wide Model Database. All relevant variables are seasonally adjusted. The data-sets are available from the author upon request.

³ For example, Smets and Wouters (2007) used a data-set spanning the period 1966Q1–2000Q4 (156 obs.), Adolfson et al. (2007) used the period 1970Q1–2002Q4 (132 obs.) and Liu and Mumtaz (2011) used the period 1970Q1–2009Q1 (157 obs.).

⁴  The maximum lag order is restricted to 6. Note that the HQ is a little bit more benevolent in determining the lag order of VAR models as compared to the BIC. Additional lags may eliminate remaining serial correlation in residuals which is desirable when using neglected nonlinearity tests (see Lumsdaine and Ng, 1999 for details).

⁵ Note that although both nonlinearity tests fall into a category of nonconstructive tests, which means that after rejecting the null, they do not give us any indication about the correct (nonlinear) model, Vávra (2013) shows that these tests have reasonable power against, for instance, regime-switching VAR/DSGE models.

⁶ The rejection frequency is calculated as , where is the p-value of a given test statistic obtained in the ith time window and using the jth stopping rule, and is an indicator function. So, the rejection frequency equal to 1 means that a given test statistic rejects the null hypothesis of linearity in all 60 time windows, regardless of the stopping rule.