Three other alternatives place stronger restrictions on the error terms than does the baseline model: In alternative III they are assumed to be homoskedastic
, in alternative IV they are not autocorrelated, and in alternative V their autocorrelation is common across states.
By contrast, the deficiency of a homoskedastic
linear model as a description of nineteenth-century interest rate dynamics--that interest rates are much more volatile at some times than others--would be consistent with any model that implies GARCH effects on interest rates, (7) However, it does seem fair to describe this finding as implying that, at least during some of the nineteenth-century recessions, interest rates were being influenced by some forces that do not operate in usual times, or, perhaps more strongly, that the financial crises emphasized by early students of the business cycle are in some important respects qualitatively different from the factors governing normal interest rate fluctuations.
t], which is homoskedastic
with, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [square root of [h.
This is an effective transformation of the data because it achieves two objectives at once; it will help make the error terms more homoskedastic
and at the same time will make the distribution of the independent variables more normal (Maddala 1977).
Under this hypothesis, the return distribution is homoskedastic
and no ARCH or GARCH effects exist.
and uncorrelated) disturbance term (Anselin, 1988, pp.
Probit (i) is estimated with a homoskedastic
This weighting procedure is expected to produce homoskedastic
disturbances and is in the spirit of Beatty and Ritter |6~.
However, as Mullahy (1998) observed, it is important that the error structure strictly satisfies the homoskedastic
error assumption, otherwise a nonlinear smearing correction can produce seriously biased estimates.
The null hypothesis is that the residuals are homoskedastic
After including lnASSETS, the White (1980) chi-square test statistic fails to reject the null hypothesis of homoskedastic
error terms and correct model specification (p = 0.
White's  test statistic for homoskedastic
error terms is a chi-square equal to 1217.