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Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald statistics constructed from these estimators have asymptotic x [superscript] 2 distributions. These and previously proposed estimators of cointegrating vectors are used to study long-run U.S. money (M1) demand. M1 demand is found to be stable over 1900-1989; the 95 percent confidence intervals for the income elasticity and interest rate semielasticity are (0.88, 1.06) and (-0.13, -0.08), respectively. Estimates based on the postwar data alone, however, are unstable, with variances which indicate substantial sampling uncertainty. Copyright 1993 by The Econometric Society.