Therefore, where, in Dickey-Fuller statistics zero is rejected, the conclusion is drawn up that the variables cointegrate and the Granger regression theory is not applicable.
Since the data cointegrate the Granger causality test may be used only having accordingly adjusted the regression equations (1, 2).
Common trends arise in this RBC model when there are more sectoral economies than productivity shocks (i.e., productivity shocks cointegrate
If the data cointegrate
, II must be of reduced rank, r [less than] N, where N is the number of variables.
The two vectors that clearly cointegrate
are given by the two largest eigenvectors.
However, in most practical situations I(2) variables will cointegrate
to the I(1) level at least.
The results reported in Table 2 indicate that several different estimation methodologies--one using RC estimation on annual data over 1870-1989, another using the same data but based on the use of variables integrated of order one (and, therefore, excluding [g.sub.y]), which (in this case) cointegrate
into a single equilibrium relationship, another using cointegration on quarterly data over 1915-88, and still another using ordinary least squares on phase-averaged data over 1869-1975 with dummy variables to capture shifts in behavior--yield estimates of some of the coefficients of the long-run money demand functions that fall within a fairly narrow range.
They concluded that exports and GNP did not cointegrate
except in the cases of Norway, Iceland, and the Netherlands.
Below we investigate the time-series properties of the data used by Jones, and find that petroleum consumption, the real price of oil, and real GNP all appear to be I(1) processes that do not cointegrate. This implies either that there does not exist a stable long run relationship between the levels of petroleum consumption, oil prices and income, or that there is one or more important variables missing in explaining energy consumption in the long run.
petroleum consumption, the real price of oil, and real GNP appear to be non-stationary I(1) processes that do not cointegrate. This implies that regressions involving only these three variables are spurious.