Confidence Interval for the Value of Time

This paper describes how the subjective value of time is the ratio of the marginal rate of substitution between travel time and travel cost. In investment appraisal and analysis, measurement of value of time is necessary to establish the individual’s willingness to pay and in coming up with valid demand forecasts to justify expenditures of scarce public investment. This paper will explore the building of confidence intervals for the subjective value of time applying methods that make inferences about the ratio of normal means, that is, by direct substitution of Fieller’s probability density function and the proposed t-test method. The theory, however, does not prescribe exactly how to choose the endpoints for the confidence interval. An obvious criterion is to minimize the length of the interval, which is not a problem as it is symmetrical if the resulting distribution is normal. As the resulting distribution of the value of time is generally skewed, the paper will propose a method of minimizing its confidence interval. The proposed approach in building the confidence interval and in minimizing the length of the confidence interval are then applied to data taken from a long-distance survey conducted in Japan.