An Empirical Study on Relationship between Residents’ Disposable Income and CPI Based on TVECM: Application of Bootstrap SupLM Testing for Threshold Cointegration

Abstract

Based on the fluctuation characteristics of residents’ disposable income and CPI (Consumer Price Index) in different periods, this article introduces a nonlinear threshold cointegration theory, establishes a TVECM (Threshold Vector Error Correction Model) of the residents’ disposable income and CPI. We propose an algorithm to obtain maximum likelihood estimation under the condition of cointegration vector and threshold value which are unknown and then propose a SupLM test for the presence of a threshold. The asymptotic distribution of the SupLM statistic is analyzed, and it appears to depend on the moment functionals, so tabulated critical values are unavailable. We discuss how the residual bootstrap can be used to calculate asymptotic critical values and $p$ values, investigate the size and power of the SupLM test using Monte Carlo simulation, and find that the test works quite well. In the empirical section, we apply our methods to test and estimate the TVECM of residents’ disposable income and CPI. According to the experimental results, the causal relationship between residents’ disposable income and CPI under different mechanisms is tested and compared with the test results under the linear cointegration hypothesis. The empirical results show that the disposable income of residents and CPI belong to a two-mechanism nonlinear threshold cointegration system. When the deviation from the equilibrium state exceeds the threshold value, the system may adjust to the equilibrium state, and the adjustment speed of CPI shall be faster than that of the residents’ disposable income.