Extensions of the Pesaran, Shin and Smith (2001) Bounds Testing Procedure

We replicate the Pesaran et al. (J Appl Economet 16(1):289–326, 2001) bounds testing procedure (BTP) and extend it with 6 new cases, 4 of which involve a quadratic trend. We provide critical values for the BTP of the lagged regressors in levels under the framework of unrestricted error-correction models (UECMs) to account for degenerate cases of co-integration. Further, we extend the BTP with 11 cases for the quantile UECMs of Cho et al. (J Econom 188(1):281–300, 2015) and present critical values for interdecile and interquartile BTPs for the unrestricted cases. Moreover, we extend the Shin et al. (Festschrift in Honor of Peter Schmidt, Springer, New York, 2014) methodology to account for nonlinear, or asymmetric, responses of the dependent variables to its covariates (NARDL) and for distributional, or location, asymmetry (QARDL of Cho et al. 2015) of the dependent variable. This is the quantile nonlinear ARDL, or QNARDL. We provide codes that generate critical values for different sample sizes of the BTPs. These critical values are utilized in an empirical application of a dynamic equity valuation model for the S&P Global Index. Misspecifying a nonlinear relationship as linear produces misleading results and policy implications. There is strong evidence of (1) trading activity based on fundamentals and (2) the existence of a stable equilibrium relationship for the price-to-book (PB) ratio of the market index and its fundamentals. During periods of high PB relative to its fundamental values, convergence to equilibrium is faster than during periods of relatively low PB. There is also evidence of momentum trading, i.e., of traders that rely on positive feedback.