In the Linear Expenditure System (Stone) applied to the nonmarket goods setting, the
parameter interpreted as a “subsistence quantity” of each good may be negative, and in
fact must be negative for access value to be finite (Kling). Another, more commonly
used functional form in empirical practice, the Cobb-Douglas demand system (LaFrance
1986), implies that goods are necessities, with infinite access values, when they are own
price-inelastic.
In each of these demand systems, the findings of infinite access value for some
parameter ranges are artifacts of the convergence properties of the demand systems as
own price for a good rises and quantity consumed goes to zero. This problem diminishes
their appeal for empirical nonmarket valuation where determining the total value of
resource-based activities is the goal.
In contrast, the “semilog” demand system, which relates log of quantity consumed
to the levels of the independent variables, has finite access values, even though the
Hicksian choke price is infinite and quantity consumed goes to zero only in the limit.
This makes the semilog model a more attractive option for empirical recreation demand
analysis, and it is often used in single equation models. However, LaFrance (1990) has
shown that demand systems based on this functional form are quite restrictive, with
cross-price effects that are either zero or the same across all goods, and income effects
that are also either zero or the same for all goods.
This paper proposes a variation of the semilog demand system, the “Double
Semilog” (DS) system, which retains its attractive features with respect to measuring
access values, while achieving somewhat greater flexibility with respect to cross-price
and income elasticities. The key differences between the DS and semilog systems are (a)
each good can have a different income elasticity in the DS system, whereas all goods
have the same income elasticity in the semilog system; and (b) elasticities for price and
quality in the DS system are essentially the elasticities in the semilog system with the
addition of an income elasticity adjustment.