Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

Abstract

Estimators and tests are developed and analyzed for a general class of vector error correction models which allow for asymmetric and non-linear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are we believe useful in general for analysis of non-stationary non-linear time series models. We provide a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. With respect to testing, this makes implementation of testing involved, and bootstrap versions of the tests are proposed in order to facilitate their usage. The asymptotic results regarding the QML estimators extend and improve results in Kristensen and Rahbek (2010, Journal of Econometrics) where estimation, but not testing, of symmetric non-linear error correction was considered. A simulation study shows that the …nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

Interest rate pass-through: a nonlinear vector error-correction approach

“…Lags are chosen based on bivariate estimates of full rank models and then once a lag is chosen it is fixed for the rank tests. Rank tests are conducted within the CVAR model because inference in nonlinear VECMs requires the long-run coefficient β to be identified under the null (Kristensen and Rahbek, 2013). For consistency, the CVAR is also used for Note: LR statistics are reported against the alternative of full rank, r = 2.…”

“…Although critical values are known for the CVAR and can be simulated for the nonlinear VECM, the bootstrap procedure is robust to heteroskedasticity (Boswijk et al, 2013). In general the bootstrap samples are generated using the residuals obtained under the null, but for the hypothesis of linearity this can be problematic (for details, see Kristensen and Rahbek, 2013) and therefore, the residuals under the alternative are used instead.…”

“…To get around this problem, the restricted likelihood is estimated first and the coefficients are used as starting values for maximizing the unrestricted likelihood. I thank Dennis Kristensen for providing me with the code for the simulation study in Kristensen and Rahbek (2013). …”

“…In fact, exogeneity of the market rate is a testable hypothesis within the model. Estimation and analysis is based on Kristensen and Rahbek (2013), who provide a rigorous discussion of testing and inference -as well as the asymptotic distributions for the relevant test statistics -within a general class of nonlinear VECMs.…”

“…It also allows for explicit tests of some commonly made assumptions such as exogeneity of the market rate. Since the asymptotic distributions for conducting inference in this framework were only recently derived by Kristensen and Rahbek (2013), this framework has yet to be used in the IRPT literature.…”