  In the early 1980s Halbert White inaugurated a "model-robust'' form of
statistical inference based on the "sandwich estimator'' of standard error.
This estimator is known to be "heteroskedasticity-consistent", but it is less
well-known to be "nonlinearity-consistent'' as well. Nonlinearity, however,
raises fundamental issues because in its presence regressors are not ancillary,
hence can't be treated as fixed.
  The consequences are deep: (1)~population slopes need to be re-interpreted as
statistical functionals obtained from OLS fits to largely arbitrary joint
$\xy$~distributions; (2)~the meaning of slope parameters needs to be rethought;
(3)~the regressor distribution affects the slope parameters; (4)~randomness of
the regressors becomes a source of sampling variability in slope estimates;
(5)~inference needs to be based on model-robust standard errors, including
sandwich estimators or the $\xy$~bootstrap. In theory, model-robust and
model-trusting standard errors can deviate by arbitrary magnitudes either way.
In practice, significant deviations between them can be detected with a
diagnostic test.
