On the Validity of Tests for Asymmetry in Residual-Based Threshold Cointegration Models

Karl-Heinz Schild,Karsten Schweikert

doi:10.3390/econometrics7010012

Karl-Heinz Schild, Karsten Schweikert

Open Access

https://doi.org/10.3390/econometrics7010012

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Abstract

This paper investigates the properties of tests for asymmetric long-run adjustment which are often applied in empirical studies on asymmetric price transmissions. We show that substantial size distortions are caused by preconditioning the test on finding sufficient evidence for cointegration in a first step. The extent of oversizing the test for long-run asymmetry depends inversely on the power of the primary cointegration test. Hence, tests for long-run asymmetry become invalid in cases of small sample sizes or slow speed of adjustment. Further, we provide simulation evidence that tests for long-run asymmetry are generally oversized if the threshold parameter is estimated by conditional least squares and show that bootstrap techniques can be used to obtain the correct size.

Highlights

Almost all economic processes, like production, refinement or trading, involve some kind of transmission of input prices to output prices
We demonstrate by means of simulation experiments that tests for asymmetry in self-exciting threshold autoregressive (SETAR)
We still notice oversizing from requiring evidence for cointegration, we find that the test for asymmetry in the momentum threshold autoregressive (MTAR)

Summary

Introduction

Like production, refinement or trading, involve some kind of transmission of input prices to output prices. In the original residual-based cointegration model by Engle and Granger (1987), the only type of cointegrating relation allowed was a static linear equation whose stationarity was assessed by a single adjustment coefficient As this is unable to capture asymmetries in the price transmission, Enders and Granger (1998) and Enders and Siklos (2001) devised a concept of threshold cointegration which allows the cointegrating relation to revert to its long-term equilibrium with two different speeds of adjustment. We demonstrate by means of simulation experiments that tests for asymmetry in SETAR and MTAR models excessively reject their null hypothesis of symmetry in small samples and for slow adjustment rates.

Models and Tests

Simulations

Findings

Summary and Concluding Remarks