Title : Extended Two-Way Fixed Effects Quantile Cointegration Regression and Its Application

Author : Ki-Ho Kim(BOK)

The novel quantile regression of Koenker and Basset (1978) has been applied to the microstudies that use cross-sectional data. Recently, it has been applied to the cointegration models that use I(1) time series data (Xiao 2009, Cho et al. 2015). However, applications of panel quantile regression with macro time series data are relatively rare. This paper considers a two-way fixed effects quantile cointegration model with I(1) macro panel data. The model extends the QCM (quantile cointegration model) of Xiao (2009) to incorporate I(1) panel data. Kim (2022) showed that the extension to a fixed effects cointegration models in which data are within transformed in a quantile framework is not a trivial one. It is because the fixed effects quantile estimates do not change at all with respect to quantiles if we use a conventionally within transformed data. This indicates that the fixed effects quantile estimators become inconsistent with the coefficients of that quantiles. This severe problem can be easily fixed by using the Extended Within Group Fixed Effects Quantile Regression Estimator (EWFE). To obtain the EWFE, it is inevitable to include a global constant term as a regressor with within transformed data since the conventional within transformation removes individual invariant covariates such as gender, schooling years, and fixed effects terms. However, Kim (2022) only provides the asymptotics for I(0) panel data. We suggest a panel quantile cointegrating regression with a two-way fixed effects in which dependent and independent variables are all two-way demean transformed. We call the estimator an Extended two-way Fixed Effects Quantile Cointegration Regression Estimator (ETFQC). A simulation study is provided to show the suggested estimator has an efficiency gain over the panel OLS estimator. As an illustrative application of the estimator, we estimate a consumption function with nonstationary regional panel data that includes 8 city areas of local governments in Korea.