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Assuming that the regression contains a constant term, which is the usual case, this predictor also can be written as:
While there may be no directional derivatives from the constant term, we could also equivalently model this as orthogonal vectors with the sum of 0.
Note that, by the multinomial formula, this is equivalent to the following constant term formula
29) One possible explanation of why the switch did not lead to any significant shift in the estimated Taylor rule is that while the switch may have lowered the Fed's inflation target expressed in core PCE inflation, it may have also caused the Greenspan Fed to raise its assessment of the economy's real rate of interest, thereby leaving the constant term of the estimated Taylor rule unchanged.
As we see, even only the check for constant terms would detect the error.
Indeed, a substantial constant term in our models represented these unattributed deaths.
The constant term in equation (1) can be thought of as a lump sum tax.
15 Correlation Matrix (percent) Term Default Prepay MKT Reit Cmort PPI Lease Bank Term 100 -49 -0 12 17 -29 -20 1 15 Default 100 -0 13 9 1 9 -14 12 Prepay 100 4 -0 -13 -21 -14 13 MKT 100 47 -30 -19 -12 66 Reit 100 -31 -13 -10 52 CMort 100 17 -5 -38 PPI 100 10 -22 Lease 100 -2 Bank 100 OLS Regression Results with the Dependent Variable of Bank (1/72-12/02) Constant Term Default Prepay MKT Reit CMort PPI -0.
The alternative hypothesis is stationary autoregressive model with constant term.
However, for example, in [4] the constant term of the equation is negative for all mines.
In column 2, we pool the annual data for all the OECD economies, and partially relax the assumption of parameter homogeneity allowing for a different constant term across countries.

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