Stephen M. Miller error structures with unit roots. In sum. a well-behaved demand- djusting partial-adjustment model of the money market implies an autoregressive crror structure with a unit root for estimated moncy demand equations, potentially explaining the high autocorrelation in the post-1973 money demand regressions Estimation of Equations (7)and (7a)present several econo- metric problems. First, the equations contain right-side endogenous variables. The rates of change in the interest rate nominal and real income, and the price level, since they are based on Equation(3b), follow, in a timing sense, the other variables in the equations, it cluding the left-hand-side money stock. Thus, two-stage estimation appears appropriate, assuming that the rate of change variables are endogenous. But, such an approach implies an exogenous left-hand side variable. Cointegration and error-correction modeling, consid ered in the next section, provide a possible solution to these prob. ems Cointegration and Error-Correction Econometric method precedes econometric practice, some- times with a substantial lead. Fo or exam ple, the possibility of spu us co-movement between variables has been acknowledged for a long time(for example, Jevons 1884, 3), with Yule(1926)conduct ing the first formal analysis(Hendry 1986 provides more details) Nonetheless. econometricians continued to use standard time-series regressions with little concern for whether the relationships were sUch a dichotomy does not occur with the supply-adjusting model, where the error structures of the partial-adjustment and estimating equations are identical Gordon(1984, 414)introduces the error term into the partial-adjustment, rather han the demand, equation with little effect, since the final error structure of the stimating equation is unaffected. Such is not the case for the demand-adjusting EStimation also assumes constant parameters, inviting the Lucas(1976)criti- cism. The speeds of adjustment( that is,中,中;,φa,andφ2y) are especially open to this criticism, since they measure how the interest rate, nominal and real in (1985)makes this point as it applies to the estimation of standard post-1973 money demand functions. In addition, exogenous oil-price shocks cause temporary pertur- bations in the price- level adjustment process. For example, as the price level larger(smaller)changes in D In P than are indicated by previ equilibria. As a consequence, the estimates of and aa are biased (downward) during the time when the oil-price shock is being transmitted to the domestic price levelStephen M. Miller error structures with unit roots. In sum, a well-behaved demand￾adjusting partial-adjustment model of the money market implies an autoregressive error structure with a unit root for estimated money demand equations, potentially explaining the high autocorrelation in the post-1973 money demand regressions.‘j Estimation of Equations (7) and (7a) present several econo￾metric problems. First, the equations contain right-side endogenous variables. The rates of change in the interest rate, nominal and real income, and the price level, since they are based on Equation (3b), follow, in a timing sense, the other variables in the equations, in￾cluding the left-hand-side money stock. Thus, two-stage estimation appears appropriate, assuming that the rate of change variables are endogenous. But, such an approach implies an exogenous left-hand￾side variable. Cointegration and error-correction modeling, consid￾ered in the next section, provide a possible solution to these prob￾lems.7 Cointegration and Error-Correction Econometric method precedes econometric practice, some￾times with a substantial lead. For example, the possibility of spu￾rious co-movement between variables has been acknowledged for a long time (for example, Jevons 1884, 3), with Yule (1926) conduct￾ing the first formal analysis (Hendry 1986 provides more details). Nonetheless, econometricians continued to use standard time-series regressions with little concern for whether the relationships were real or spurious. Spurious regression can occur when the regression ‘Such a dichotomy does not occur with the supply-adjusting model, where the error structures of the partial-adjustment and estimating equations are identical. Gordon (1984, 414) introduces the error term into the partial-adjustment, rather than the demand, equation with little effect, since the final error structure of the estimating equation is unatfected. Such is not the case for the demand-adjusting framework. ‘Estimation also assumes constant parameters, inviting the Lucas (1976) criti￾cism. The speeds of adjustment (that is, a,, $, Q2,, and a,,) are especially open to this criticism, since they measure how the interest rate, nominal and real in￾come, and the price level respond to disequilibria in the money market. Laidler (1985) makes this point as it applies to the estimation of standard post-1973 money demand functions. In addition, exogenous oil-price shocks cause temporary pertur￾bations in the price-level adjustment process. For example, as the price level rises in response to previous excess supplies of money, oil-price increases (decreases) cause larger (smaller) changes in D In P than are indicated by previous money￾market disequilibria. As a consequence, the estimates of Qz and @a are biased upward (downward) during the time when the oil-price shock is being transmitted to the domestic price level. 570