Mostly harmful econometrics

The statements below are often misleading, sometimes even detrimental; yet they are often reprinted in econometrics textbooks. While some of these concepts have limited pædagogical value (e.g. simplifying a formula for the sake of clarity), when used in real research, they may invalidate the results and potentially cause a rejection of a manuscript by a discerning referee. Many of these assumptions and tests are considered too strict, modern econometrics typically employs their more general analogues that work under weaker assumptions as the stricter assumptions almost never hold in real-world scenarios. Tests relying on more stringent assumptions have been superseded by more reliable alternatives that do not require these far-fetched conditions.

1. Homoskedasticity assumption.
   • It is never observed in the real world.
   • Popular homoskedasticity tests are not omnibus, and parametric conditional variance modelling is unreliable.
   • All results must be robust to heteroskedasticity of arbitrary from. The function sandwich::vcovHC(...) in R and the option , vce(hc3) (or , vce(robust)) in Stata achieve that for most models.
   • There are estimators that are more efficient under heteroskedasticity (e.g. Robinson estimator, Newey’s generated optimal instruments, Kitamura—Tripathi smoothed empirical likelihood (SEL), Dominguez—Lobato estimator, Ai—Chen sieve minimum distance (SMD)), but they involve non-parametric estimation at some point.
2. Normality of errors.
   • The normality of the GMM estimator is a consequence, a property that emerges that is yet to be earned under certain regularity conditions.
3. Judging a model by the R² metric.
   • R² makes no sense without the homoskedasticity assumption and provides no information about the specification validity or regressor relevance. The adjusted R² is even worse.
4. Using determinants for evaluation, interpretation, and testing.
   • In statistics, determinants of random matrices are almost never exactly zero, and not all matrices are square.
5. Accepting the hull hypothesis.
   • One can have multiple competing null hypotheses, and none may be rejected. It is incorrect to draw mutually exclusive conclusions from such tests.
6. Testing hypotheses about estimators or estimates.
   • Hypotheses should pertain to the unknown constants of nature, not to known numbers derived from the data.
7. Wrong logical negations.
   • If the base category is females, its logical negation is not females. Some data sets might contain missing values, other partitions are possible etc.
8. Marginal interpretation of coefficients on dummies / causal interpretation of time-invariant dummies.
   • There is no marginal change of the response variable associated with a marginal change of the region indicator, nor a causal effect of being male. These should be interpreted as conditional group-mean differences (or conditional gaps).
9. Exact interpretation of t- and F-statistics.
   • When the number of parameters is large and the sample size is small, heavy-tailed distributions offer better empirical test sizes. However, when the conditional distribution of the error given the covariates is unknown, the improvement is minor improvement, and the parametric is very coarse.
10. Not thinking about small sample sizes / thinking too much about the sample size.
    • Try collecting large datasets. Do not report asymptotic results when the number of observations is not large. If a data set is small, focus on finite-sample calibration, resampling, empirical coverage etc. If a data set is large, do not waste time correcting for the finite sample size.
11. Exact interpretation of Stock—Yogo critical values.
    • These weak-instrument statistics are exact only under the unrealistic assumption of conditional homoskedasticity.
12. Hausman test for endogeneity testing.
    • The Hausman test is valid only under the surreal assumption of conditional homoskedasticity. Use the control-function-based Wald or Hansen’s GMM-based J-test.
13. Sargan’s validity test.
    • This test is valid only under the surreal assumption of conditional homoskedasticity.
14. Cragg—Donald matrix rank test.
    • This test is valid only under the surreal assumption of conditional homoskedasticity.
15. Separate joint significance tests for the first-stage regression.
    • Use the Kleibergen—Paap (2006) robust rk statistic, Anderson—Rubin GMM statistic, or report the underidentification / weak identification statistics with a caveat that these results give a general indication of the instrument relevance.
16. Zellner’s seemingly unrelated regressions (SUR) via GLS.
    • The standard two- or three-step SUR procedure is reliable only under the surreal assumption of conditional homoskedasticity.
17. Random-effects panel models.
    • These models require three (!) surreal assumptions about the conditional distribution of model errors. If a referee insists on their use due to standard practice in the field, test the conditional random-effect hypothesis via GMM and report the results. (It is almost certain that this hypothesis be rejected.)
18. Hausman test for panel models.
    • The Hausman test is valid only under the surreal assumption of conditional homoskedasticity. Use Hansen’s GMM-based J-test.