Asymptotic variance approximations for invariant estimators in uncertain asset-pricing models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: This paper derives explicit expressions for the asymptotic variances of the maximum likelihood and continuously updated GMM estimators under potentially misspecified models. The proposed misspecification-robust variance estimators allow the researcher to conduct valid inference on the model parameters even when the model is rejected by the data. Although the results for the maximum likelihood estimator are only applicable to linear asset-pricing models, the asymptotic distribution of the continuously updated GMM estimator is derived for general, possibly nonlinear, models. The large corrections in the asymptotic variances, which arise from explicitly incorporating model misspecification in the analysis, are illustrated using simulations and an empirical application. Terms of use: Documents inJEL classification: C12; C13; G12

Too good to be true? Fallacies in evaluating risk factor models

“…where CD D (L) is the Cragg and Donald (1997) test of the null that the rank of D is equal to L. 17 It is worth pointing out that this step of the model reduction procedure can be implemented using any available rank test. 18 If the rank is estimated to be 1 ≤ k ≤ K − 1, construct N × k matrices D by selecting all possible combinations of k − 1 risk factors,f , 19 and perform a rank test on each D. Then, choose thef that gives rise to the largest rejection of the reduced-rank hypothesis.…”

“…Also, consistent with the existing studies, the CAPM model is rejected by the data. This requires the use of misspecification-robust standard errors in constructing the t-statistics (see Gospodinov, Kan, and Robotti, 2017a). Finally, the pseudo-R 2 points to some, but not particularly strong, explanatory power.…”

“…For the form of the asymptotic variance of CU-GMM under misspecified models, seeGospodinov, Kan, and Robotti (2017a).…”

“…A similar procedure is proposed inBurnside (2016) where the selected factors are linear combinations of the original factors. By contrast, our procedure selects individual factors and preserves their economic interpretation 17. In order to minimize the probability of rejecting the null of a reduced rank when the true rank of D is deficient and to guard the procedure against the selection of nearly spurious factors (see alsoWright, 2003), we fix the level of the rank test on D to be the same and small (say 1%) for all levels of the subsequent specification test.18 In our simulations inTable 5, we employ the rank test ofKleibergen and Paap (2006) instead of the CD test since the former does not require numerical optimization 19.…”