Along with Rule of a Half (RoH), Log-sum (LS) is probably the most used welfare measure, to assess policy impact on consumer’s welfare. However, they both rely on the assumption of an absence of income effect, this is, fixed marginal utility of income, invariant along with the population. Such a strong presumption facilitates calculations due to the correspondence between LS and Compensating Variation (CV), the exact measure to evaluate changes in consumer surplus. That approach has been usually grounded in two ideas: i) that the household’s transportation expenditure is negligible and; ii) that changes in policies that affect that expenditure are also minor. We can even find this rationalization in the authors that set the microeconomic foundations for the current mode choice models. In McFadden’s (1981) formulation, the choice is only made upon modal costs and attributes since income is canceled out when utility functions are compared to find a maximum. Small and Rosen (1981) approximate compensated demands through their market counterparts and Roy’s identity, explicitly neglecting income effect (for a synthesis of both cases, see Jara- Diaz and Videla, 1987). However, these justifications are questionable. The fact is that transportation expenditure may represent an important share of the total, especially in the case of low-earning households. Furthermore, aggressive pricing policies or a global rise in energy prices might decisively affect income in real terms. Hence, the calculation of benefit measures based on demand models that do not account for the income effect may produce inaccurate results. In this regard, the empirical evidence of the consequences of ignoring it is scarce, and the question of whether LS or RoH are good approximations to the true CV remains open.
To shed light on the issue, the present study closely follows the work of Cherchi and Polak (2004) to test whether or not LS and RoH are good approximations to the true CV under nonlinear effect in the marginal utility of income but using real data instead of synthetic. This is the first contribution of our work, the use of information gathered through a dedicated Stated Preferences survey to evaluate the gap between true CV and both LS and RoH. The second is the inclusion of heterogeneity in Travel Time, one of the fundamental elements that impact travelers’ decisions. This effect of taste is considered through a Multinomial Mixed Logit (MML) model with random parameters, from which the measures will be computed and compared to the case of a Multinomial Logit (MNL).