14
choices, such as the labor supply decision if that is predetermined with respect to the
recreation choices (Heckman; Feather and Shaw). The third is to treat it as endogenous
to the recreation choices and to estimate it jointly with recreation demands (McConnell
and Strand; Larson and Shaikh 2002). In this case, the marginal value of time function
must satisfy the requirements of choice subject to two constraints (Larson and Shaikh
2001).
The strategy here is to use a simple version of the latter approach, where the
normalized marginal value of time is constant, which satisfies the homogeneity
requirements with respect to money and time budget arguments. This also implies that
the “absolute” marginal value of time, scaled to the levels of actual budgets and prices,
varies across people if they have different prices or budget levels. The reason is that the
relationship between the relative and absolute marginal values of time is
3(p,t,M,T) œ 38 ∙ )(p,M)∕<(t,T); (23)
that is, the absolute marginal value of time is the relative marginal value of time scaled
by the ratio of the deflators used to normalize the money and time budgets (Larson and
Shaikh 2001). The end result is an estimate of the marginal value of time for each person
that is a constant dollar hour per hour, similar to the approach taken in Hausman et al.,
with the per-hour value varying across the sample according to each person's time and
money budgets.
Data
The data used to illustrate the model are from on-site intercepts of whale-watchers at
three sites in Northern California during the winter of 1991-92. Whalewatching is an