IV threshold cointegration tests and the Taylor rule

Abstract

The usual cointegration tests often entail nuisance parameters that hinder precise inference. This problem is even more pronounced in a nonlinear threshold framework when stationary covariates are included. In this paper, we propose new threshold cointegration tests based on instrumental variables estimation. The newly suggested IV threshold cointegration tests have standard distributions that do not depend on any stationary covariates. These desirable properties allow us to formally test for threshold cointegration in a nonlinear Taylor rule. We perform this analysis using real-time U.S. data for several sample periods from 1970 to 2005. In contrast to the linear model, we find strong evidence of cointegration in a nonlinear Taylor rule with threshold effects. Overall, we find that the Federal Reserve is far more policy active when inflation is high than when inflation is low. In addition, we reaffirm the notion that the response to counteract high inflation was weakest in the 1970s and strongest in the Greenspan era.

Testing for Nonlinear Threshold Cointegration in the Monetary Model of Exchange Rates with a Century of Data

“…We let w t = (w 1t , w 2t )′ for our instrument. The resulting t-test statistics for ρ 1 and ρ 2 will have asymptotic standard normal distributions in each case; see Enders, Lee, and Strazicich (2007) and Enders, Im, Lee, and Strazicich (2009). 7…”

“…Lags of Δe t , Δ(m t * − m t ), and Δ(y t * − y t ) can be included as necessary to correct for serial correlations. There are clear advantages to using ADL models; see Li and Lee (2008), and Enders, Im, Lee, and Strazicich (2009) for more details. Following these methods, we consider two threshold indicators.…”

“…We first adopt the ADL-OLS threshold cointegration test developed by Li and Lee (2008) and consider two different threshold models. Following this, we utilize the ADL-IV threshold cointegration test developed by Enders, Im, Lee, and Strazicich (2009). The ADL-IV threshold cointegration test has the distinct advantage that we can include relative output as a stationary covariate to increase power, while the test statistic maintains a standard distribution.…”

“…While RW (2002) omit the output deviation variable in these cases, we want to include this variable as a stationary covariate in our cointegration tests to increase power. In these cases, we utilize the instrumental variables based autoregressive distributed lag (ADL-IV) threshold cointegration test as suggested in Enders, Im, Lee and Strazicich (2009). The ADL-IV threshold cointegration test is well suited to this task, since the test statistics are unaffected by including stationary covariates.…”

Saudi Non-Oil Exports before and after COVID-19: Historical Impacts of Determinants and Scenario Analysis

“…Thus, the third approach is preferable from the practical point of view. Note that applying the instrumental variable method in the cointegration and ECM framework is not unusual in the literature[140][141][142][143][144].…”