Estimation and test for quantile nonlinear cointegrating regression

•A quantile nonlinear cointegration model is proposed.•The parameter estimator follows a nonstandard distribution asymptotically.•A fully modified estimator and a test for linearity are developed.•Monte Carlo results show that the test has good finite sample performance.

In order to investigate the nonlinear relationship among economic variables at each quantile level, this paper proposes a quantile nonlinear cointegration model in which the nonlinear relationship at each quantile level is approximated by a polynomial. The parameter estimator in the proposed model is shown to follow a nonstandard distribution asymptotically due to serial correlation and endogeneity. Therefore, this paper develops a fully modified estimator which follows a mixture normal distribution asymptotically. Moreover, a test statistic for the linearity and its asymptotic distribution are also derived. Monte Carlo results show that the proposed test has good finite sample performance.