As opposed to the fully informed choice-making assumption in classical discrete choice models, the theory of Rational Inattention (RI)1 in discrete choice modelling has been recently proposed in the literature. Matějka and McKay (2015) proposed the RI-multinomial logit (RI-MNL), and Fosgerau et al. (2020) proposed the RI-nested logit (RI-NL) model. These models consider that choice makers are bayesian agents with prior probabilities of choices and process any further information assuming an information processing cost to have the updated/posterior choice probabilities. However, the proposed RI-MNL and RI-NL models are theoretical formulations without any estimable empirical specifications. This paper proposes econometric formulations of RI-MNL and RI-NL models that are estimable using classical maximum likelihood estimation methods and suitable for revealed crossectional choice data. The proposed models are estimated for commuting mode choices in the Greater Toronto and Hamilton Area (GTHA) using data from a household travel survey conducted in the region. Empirical investigation reveals that the induction of RI in the classical discrete choice models (MNL and NL) improves the model fit by large margins. While scale parameterization in classical MNL and NL does not make a better model, the scale parameterization better captures the choice heterogeneity within the RI framework. Between the RI-MNL and RI-NL, the RI-NL is proven to be the best. The RI-NL model can capture asymmetric (between increasing and decreasing values) elasticities of choice attributes.