Vector Error Correction Models with Stationary and Nonstationary Variables

Abstract

<p style="text-align: justify;"><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">Vector Error Correction Models (VECM) have become a standard tool in empirical economics for analyzing </span><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">nonstationary time series data because they integrate two key concepts in economics: equilibrium and dynamic </span><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">adjustment in a single model. The current standard VECM procedure is limited to time series data with the same </span><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">degree of integration, i.e., all I(1) variables. However, empirical studies often involve time series data with </span><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">different de‐grees of integration, necessitating the simultaneous handling of I(1) and I(0) time series. This paper </span><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">extends the standard VECM to accommodate mixed I(1) and I(0) variables. The conditions for the mixed VECM are </span><span style="font-size: 14pt; font-family: 'times new roman', times, serif;">derived, and consequently, we present a test and estimation for the mixed VECM.</span></p>