This relation also confirms the inverse relation between the NLIP and [r.
Blondeau (2001), using a VAR cointegration analysis, also found a long-term relationship between the NLIP, long-term interest rates, and stock market returns over the period 1963-1999.
In order to remedy these limits, following Higgins and Thistle (2000), we propose to extend the study of the NLIP adjustment dynamics to a nonlinear framework.
Concerning the NLIP modeling, under the null hypothesis of linearity, the NLIP adjustment is said to be symmetrical and linear and its dynamics can be reproduced through the following LECM
2,t] are, respectively, the NLIP in logarithm, the stock price also in logarithm, and the interest rate.
An LECM extension can enable the NLIP adjustment to be nonlinear with a time-varying adjustment speed.
In the next section, we focus on the STECM modeling for which the equilibrium is assumed to be linear, unique, and provided by the linear cointegration relationship between the NLIP and financial variables.
In practice, this asymmetry characterizing NLIP deviations from the equilibrium may be understood using the STECM that incorporates the delayed error-correction term [z.
This choice may enable us to reproduce two types of asymmetry (in our case: asymmetry due to the change of the NLIP deviation signs and asymmetry associated to the variation of the NLIP deviation size) with a simple transition function.
9) As discussed above, the LSTECM is useful to replicate the asymmetric adjustment dynamics due to a sign change of the NLIP deviation, whereas the ESTECM is used to reproduce the asymmetric adjustment dynamics in the NLIP size of positive or negative deviations.