Disequilibrium Macroeconomics As a first step, I examine tri-variate cointegration regressions of the natural logarithm of the money stock onto the natural loga- rithms of real GNP and the implicit price deflator. The results ap pear in Table 2.The high adjusted coefficent of determination and low Durbin-Watson statistics suggest possible spurious regression and make the cointegration investigation a fruitful exercise(Hendry 1986). The DF and ADF tests do not reject the null hypothesis of non-stationary errors in any case, although consistent with Engle and Granger(1987), the M2 series comes closest. The DF and ADF statistics for cointegration regressions with three or more variables are given in Engle and Yoo(1987) As a second step, I introduce sequentially the four-to-six-month commercial-paper rate and the dividend-price ratio to form four variable cointegration regressions. The results also appear in Table 2. Now, the M2 equations reject non-stationary errors for the DF test when the four-to six-month commercial-paper rate is added and for the adf test when the dividend-price ratio is added each at the 10% level. Further, deleting insignificant coefficients from the lagged differences in the aDf tests produces a significant ADF sta- tistic(that is,-4.22)for the M2 equation including the four-to-six- month commercial-paper rate I conclude that the natural logarithms of M2, y, P, and re are cointegrated. The cointegration equation measures the long-run equilibrium relationship between the variables. The residuals from the cointegration equation measure the short-run deviations fro long-run equilibrium Table 3 reports the errors(that is, actual M2 minus its fitted alue from the cointegration regression) for the post-1973 period where shifting money demand considerations emerge. For purposes of comparison, the errors for the MI cointegration regression als appear. Several observations emerge. First, the much discussed missing money(that is, long- run equilibrium money demand ex ceeding the available money stock during 1974 and 1975 does not appear; positive errors occur through 1975: iii. Second, much evi- ence exists of the money stock falling short of long-run equilibrium money demand in the late 1970s and early 1980s--negative errors from 1978: ii through 1981: iv. Third, the available money stock ex ceeds the long-run equilibrium demand during the early and mid- 1980s-positive errors with one exception from 1982: i through The table does not report standard t-statistics, since the standard errors are misleading in cointegration equations(Engle and Granger 1987Disequilibrium Macroeconomics As a first step, I examine tri-variate cointegration regressions of the natural logarithm of the money stock onto the natural loga￾rithms of real GNP and the implicit price deflator. The results ap￾pear in Table 2.12 The high adjusted coefficent of determination and low Durbin-Watson statistics suggest possible spurious regression and make the cointegration investigation a fruitful exercise (Hendry 1986). The DF and ADF tests do not reject the null hypothesis of non-stationary errors in any case, although consistent with Engle and Granger (1987), the M2 series comes closest. The DF and ADF statistics for cointegration regressions with three or more variables are given in Engle and Yoo (1987). As a second step, I introduce sequentially the four-to-six-month commercial-paper rate and the dividend-price ratio to form four￾variable cointegration regressions. The results also appear in Table 2. Now, the M2 equations reject non-stationary errors for the DF test when the four-to-six-month commercial-paper rate is added and for the ADF test when the dividend-price ratio is added, each at the 10% level. Further, deleting insignificant coefficients from the lagged differences in the ADF tests produces a significant ADF sta￾tistic (that is, -4.22) for the M2 equation including the four-to-six￾month commercial-paper rate. I conclude that the natural logarithms of M2, y, P, and r, are cointegrated. The cointegration equation measures the long-run equilibrium relationship between the variables. The residuals from the cointegration equation measure the short-run deviations from long-run equilibrium. Table 3 reports the errors (that is, actual M2 minus its fitted value from the cointegration regression) for the post-1973 period, where shifting money demand considerations emerge. For purposes of comparison, the errors for the Ml cointegration regression also appear. Several observations emerge. First, the much discussed missing money (that is, long-run equilibrium money demand ex￾ceeding the available money stock) during 1974 and 1975 does not appear; positive errors occur through 1975:iii. Second, much evi￾dence exists of the money stock falling short of long-run equilibrium money demand in the late 1970s and early 1980s-negative errors from 1978:ii through 1981:iv. Third, the available money stock ex￾ceeds the long-run equilibrium demand during the early and mid- 1980s-positive errors with one exception from 1982:i through “The table does not report standard t-statistics, since the standard errors are misleading in cointegration equations (Engle and Granger 1987). 575