Dealing with Endogeneity in Threshold Models Using Copulas: An Illustration to the Foreign Trade Multiplier

Exploring Okun's law asymmetry: An endogenous threshold logistic smooth transition regression approach*

“…Regarding the conditional copula functions, we consider the Gaussian, or Student's-t copulas, which imply bias correction terms that are linear transformations of copula transformations of the threshold variable. As shown in Christopoulos et al (2021), these functions can satisfactorily approximate nonlinear dependence structures between the regression error term and threshold variable. They are also robust to different distribution assumptions for the error term.…”

“…As shown in Christopoulos et al . (2021), these functions can satisfactorily approximate nonlinear dependence structures between the regression error term and threshold variable. They are also robust to different distribution assumptions for the error term.…”

“…To deal with this problem, we follow the procedure recently suggested by Christopoulos et al . (2021). We will augment the LSTR threshold regression with appropriately transformed variables controlling for the endogeneity of $$$ {z}_t $$$.…”

“…This is likely to happen in economic relationships, like the OL, where z t and y t (or v t ) are jointly determined or reflect common sources of shifts (shocks) due to policy changes (see our discussion in Section IV). 10 To deal with this problem, we follow the procedure recently suggested by Christopoulos et al (2021). We will augment the LSTR threshold regression with appropriately transformed variables controlling for the endogeneity of z t .…”

“…To deal with this problem, motivated by the recent work of Kourtellos et al (2016), hereafter KST, we adjust the LSTR regression model by including bias correction terms on its right side as control variables conditional on each regime of the model to account for the threshold variable endogeneity problem. We also draw on the recently suggested method of Christopoulos, McAdam and Tzavalis (2021), which calculates the bias correction terms based on the copulaapproach (which does not necessarily require normality of the threshold variable): the bias correction terms are then given by copula-based transformations of the threshold variable for each regime of the model truncated at the location (threshold) parameter value. 5 Recently, Yu, Liao and Phillips (2019), and Kourtellos et al (2021) also suggested control-function methods to correct for the threshold endogeneity bias in threshold regressions.…”