Estimating The Opportunity Cost Of Time When Labor Supply Decisions Are Institutionally Constrained

Policy decisions concerning options for the recreational use of natural resources typically call for recreation demand and benefit measures that are not revealed by market prices and must therefore be estimated. Travel cost models use a proxy for the unobserved market price to estimate recreation demand. The "price" is typically equal to the sum of time and monetary costs of traveling to the recreation site in addition to any site access fees. This price proxy allows individual recreation demand schedules and their corresponding benefits to be estimated. The time element of the price proxy is converted to its price equivalent and is referred to as the "opportunity cost of time". Conventional methods use the marginal wage as the rate of conversion. Bockstael, Strand and Hanemann (1987) observe, however, that the opportunity cost of time is equal to the wage rate only when individuals are able to choose the hours they work. When individuals face institutional constraints on their labor supply decision , the marginal value of time is unobservable and is generally not equal to the wage rate. The choice of a time valuation method influences demand estimates of any time-intensive good such as recreation. Time valuation methods that ignore the effects of institutional constraints when time valuation behavior is, in fact, influences by such effects, will generate biased opportunity time cost estimates. The price proxy used in the travel cost model inherits any time value bias resulting from uncontrolled effects of institutional constraints. A biased price proxy in turn contaminates recreation demand estimates. Freeman (1993, p. 449) intuitively demonstrates that demand for recreation is underestimated when time cost estimates are too high and is overestimated when time cost estimates are too low. Empirical studies by Cesario (1976) support the institution that demand forecasts and benefit estimates of recreational service flows are highly sensitive to competing estimates of opportunity time costs. A time valuation approach that generates accurate time cost estimates for both constrained and institutionally unconstrained workers is needed in order to derive accurate recreation demand and benefit estimates. Consumer decision theory of time allocation suggests that individual's opportunity time costs are influences by the imposition of constraints on their labor supply decisions. Prevailing time valuation approaches, however, either ignore institutional constraints or account for their influence but place overly-restrictive assumptions on the determination of who is actually constrained. The deficiencies in existing time valuation methods stem from survey designs that collect employment information too limited in scope to allow for the appropriate treatment of institutional constraints. Conventional time valuation methods preclude assessment of the effects of labor constraints on time values because recreation surveys typically collect only limited employment data on individuals' wage rates and observed work hours. With no information on institutional constraints, time is often valued at the observed wage rate (or at some fraction of the wage rate) and added to monetary costs to construct a price proxy for all respondents. When wage rates are not available, predicted wage rates are sometimes used (see Smith, Desvouges and McGivney, 1983). The recreation demand equation is then estimated as a function of the price proxy. The majority of previous recreation demand and benefit analyses have relied on survey data that provides no information on labor supply constraints. It can be shown that conventional estimation procedures ignoring labor supply constraints generate biased time cost estimates where the sample includes individuals working fixed hours. As an alternative to conventional approaches, Bockstael, Strand and Hanemann suggest a theoretically-consistent framework where recreation demand functions incorporate the effects of institutional constraints. In addition tot he usual survey data collected on observed wages and work hours, they differtiate survey respondents on the basis of whether or not they have the discretion to select the number of hours worked and estimate a separate demand equation for each group. For those with flexible work hours who are identified as unconstrained, time is valued at the marginal wage rate as usual, summed with money costs of travel and entered as a single price proxy in a demand function. For those with fixed work hours who are identified as institutionally constrained, however, the convertion rate of time to its monetary equivalent is unobservable. Instead of constructing a single price proxy, time and money are entered as separate arguments in the demand equation for constrained respondents.