Calculating, with income e¤ects, the compensating variation for a state change

One can easily obtain exact closed-form solutions for the compensating variation (and equivalent variation) in the presence of income e¤ects when the policy being evaluated can be described as a change in the state of the world and one is willing to assume the policy change does not change the individual’s epsilon draw. Alternatively, if one assumes the policy changes the epsilon draw, the expectation of the compensating variation is a complicated integral, typically without a closed-form. The assumption that the policy does not a¤ect one’s epsilon draw is common, and often reasonable, but little discussed. keywords: compensating variation, epsilon draw, equivalent variation, random components, state change, state independence forthcoming Environmental and Resource Economics Consider the very common practice of estimating an individual’s compensating variation, cv, or E[cv], for some policy using the estimated parameters of an indirect utility function(s), each with an additive random component. Separate in your mind the issue of estimating the parameters in the utility function(s) from the issue of estimating the cv for some policy after the parameters are estimated. This note is concerned only with the latter problem. More speci…cally, this note is concerned solely with calculating an individual’s cv for a change in the state of the world, a state change. A state is characterized by the levels of all of the exogenous variables that determine utility: an indirect utility function is assumed that identi…es maximum utility as a function of the state.1 A change from the world as it exists to a world with 1 It is critical to distinguish between the indirect utility function and a conditional indirect