Three Essays in Econometrics

In this thesis, I contribute to the literature on multiple comparisons and specification testing for multivariate models, through the lens of model selection procedures in asset pricing. In the first chapter, I provide a model selection procedure for multivariate models, generalizing the model confidence set (MCS) procedure to systems of N>1 dependent variables. A (1-α) level MCS collects the set of models with equal predictive ability, based on a sequential elimination procedure. I introduce supremum t and Hotelling T^2 statistics which account for correlation between loss differentials. I assess the performance of 14 candidate asset pricing models using monthly data for the period 1972-2013. I find that for out-of-sample tests, only a single model is selected by the procedure, but the MCS often includes multiple models for in-sample tests. Overall, out-of-sample tests and a larger number of more heterogenous test assets provide more information to disentangle models. The procedure shows good size and power properties in simulations. In the second chapter, we propose a multivariate extension of exact specification tests for non-nested models. Our test is finite-sample exact under the assumption of Gaussian errors, and is easily generalized to a multiple-model hypothesis via a combined alternative. We obtain valid inference results using bootstrapped Monte Carlo p-values, even when the distribution under the null hypothesis is intractable. We consider Gaussian and non-Gaussian errors through bootstrapping, and we show that our test possesses good size and power properties via simulations. Finally, we present empirical applications to asset pricing by testing benchmark factor models against single and multiple alternatives. In the third chapter, we offer an empirical assessment of the current beta-pricing literature, using non-nested tests for multivariate models and a MCS approach. Both methods can be used to assess either: (i) the statistical significance of a newly proposed non-nested model, or (ii) the statistical equivalence of their predictions, in the sense of equal predictive ability. We reconcile the MCS procedure of Hansen et al. (2011) with our empirical approach. We find that the test of Khalaf and Richard (2022) rejects many models empirically, while the MCS approach favours the Fama and French (2018) model.

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