Cointegration Vector Estimation by Panel DOLS and Long‐run Money Demand*

Abstract We study the panel dynamic ordinary least square (DOLS) estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individual‐specific time trends, individual‐specific fixed effects and time‐specific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T →∞, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of s linear constraints has a limiting χ 2 ( s ) distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T →∞ and then letting N →∞. In a series of Monte‐Carlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel DOLS to estimate coefficients of the long‐run money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e. = 0.26) and the estimated interest rate semi‐elasticity is −0.02 (asymptotic s.e. = 0.01).