Disequilibrium Macroeconomics adjusted coefficient of determination(R)exceeds the Durbin-Wat son statistic(Granger and Newbold 1974 and Plosser and Schwert Cointegration analysis addresses the spurious regression prob lem, attempting to identify conditions for which regression rela ionships are not spurious(Eugle and Granger 1987; Granger 1986; and Hendry 1986). When two time-series variables are cointegrated, their secular trends move subject to an equilibrium constraint, and the cyclical components of the series conform to a dynamic speci- fication in the class of error-correction models The problem of spurious regression emerges because most economic time series exhibit non-stationary tendencies. Thus, the high R may reflect correlated trends rather than underlying eco- mic relationships; the low Durbin-Watson statistic may indicate non-stationary residuals. One specification check for spurious regression involves first-differenced regressions. That specification check probably produces stationary residuals. The question emerges as to whether relationships found in regressions on levels remain under the first-differenced specification. But, first-differencing re- moves the low-frequency (long-run)information. Cointegration and error-correction modeling reintroduces the low-frequency informa tion into first-differenced regressions in a statistically acceptable way Consider two time-series x, and y, that are non-stationary in their levels but stationary in their first differences. The series are cointegrated when a factor B exists, such that z, y, -Bx, is sta tionary. If it does exist, then the cointegration factor must be unique in the two-variable case, since altering it to(B+ 8) introduces an additional term(-Sxt), which is non-stationary by definition. Since the temporal characteristics of zt and its components are so differ- ent, a special relationship exists between cointegrated variables. To it,y, and Bx, must exhibit low-frequency(long-run)components that cancel, producing a stationary series zr. The long- run(equilib- rium)relationship may emerge from economic theory, where z measures short-term deviations from the trend (equilibrium) rela In sum, cointegration and error-correction modeling is a two- step procedure. The first step estimates the cointegration equation which captures the long- run(trend)relationships, if any, between the variables of interest. The errors from the cointegration regres sion are then used in the second step to estimate the error-correc- tion model, which captures the short-run (cyclical)relationships among the variableDisequilibrium Macroeconomics adjusted coefficient of determination (R’) exceeds the Durbin-Wat￾son statistic (Granger and Newbold 1974 and Plosser and Schwert 1978). Cointegration analysis addresses the spurious regression prob￾lem, attempting to identify conditions for which regression rela￾tionships are not spurious (Engle and Granger 1987; Granger 1986; and Hendry 1986). When two time-series variables are cointegrated, their secular trends move subject to an equilibrium constraint, and the cyclical components of the series conform to a dynamic speci￾fication in the class of error-correction models. The problem of spurious regression emerges because most economic time series exhibit non-stationary tendencies. Thus, the high R2 may reflect correlated trends rather than underlying eco￾nomic relationships; the low Durbin-Watson statistic may indicate non-stationary residuals. One specification check for spurious regression involves first-differenced regressions. That specification check probably produces stationary residuals. The question emerges as to whether relationships found in regressions on levels remain under the first-differenced specification. But, first-differencing re￾moves the low-frequency (long-run) information. Cointegration and error-correction modeling reintroduces the low-frequency informa￾tion into first-ditlerenced regressions in a statistically acceptable way. Consider two time-series xt and yt that are non-stationary in their levels but stationary in their first differences. The series are cointegrated when a factor B exists, such that z, = yt - Bx, is sta￾tionary. If it does exist, then the cointegration factor must be unique in the two-variable case, since altering it to (B + 6) introduces an additional term (-6x,), which is non-stationary by definition. Since the temporal characteristics of z, and its components are so differ￾ent, a special relationship exists between cointegrated variables. To wit, yt and Bx, must exhibit low-frequency (long-run) components that cancel, producing a stationary series zt. The long-run (equilib￾rium) relationship may emerge from economic theory, where zt measures short-term deviations from the trend (equilibrium) rela￾tionship. In sum, cointegration and error-correction modeling is a two￾step procedure. The first step estimates the cointegration equation, which captures the long-run (trend) relationships, if any, between the variables of interest. The errors from the cointegration regres￾sion are then used in the second step to estimate the error-correc￾tion model, which captures the short-run (cyclical) relationships among the variables. 571