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related effects. To test for size- and price-related slope seasonality, we
test cross-equation equality restrictions on the βs in the regression of
equation <5) for the MV, PR, SIZE, PRICE, and MVPR portfolios. The test
results appear in table 6.
As seen in tables 3, 5, and 6, there are significant size-related effects
in the estimates of β2 for the MV portfolios, although β2 does not exhibit
a significant size-related effect for the SIZE portfolios. The rejection of
the cross-equation equality restriction on β2 for the MV portfolios, com-
bined with the inability to reject the cross-equation equality restriction on
β2 for the SIZE portfolios, is evidence that the size-related effect in 82
for the MV portfolios is actually a price-related effect. In contrast, look-
ing at tables 4 through 6, we see a significant price-related effect in the
estimates of β2 for the PR and PRICE portfolios. The failure to reject the
cross-equation equality restriction on β2 for the SIZE portfolios while
rejecting it for the MV, PR, PRICE, and MVPR portfolios is evidence that the
factor-related slope seasonality is an effect related to price but not
size. " This is consistent with the LPSH.
One could argue that we are overstating the significance of the tests of
the cross-equation equality restrictions for β2 because β2 is the shift in
β during the post-yearend period and we reject the cross-equation equality
restriction for β3 (which is our estimate of the market model β exclusive of
the TOY shifts). This may indicate that the relative and not the absolute
shifts in β2 are important in determining whether size or price i s driving
the seasonality in β. However, closer inspection of the results in tables 3
and 5 indicates that this is not a problem. The coefficient for β3 for the
lowest (highest) market-value quintile of the MV portfolios is close to that
of β3 for SIZEl (SIZES). On the other hand, the coefficient for β2 for
the lowest (highest) market-value quintile of the MV portfolios is twice