1971), Goodman ( 1978, 1988) and Palmquist ( 1984) included both socioeconomic status and race ratio variables in their regression equations. Which neighborhood variables should be included in the regression depends not only on the researcher's interests and emphasis but also on the social background of a country or city. For two reasons, this study includes only the educational level of adults and population density as neighborhood variables. First, more than 98% of the population of Taiwan is of identical race and the country has no racial problem. Second, the quality of elementary and junior high schools plays no significant role on households' choice of location for a dwelling unit, since regulations on school district boundaries are not strictly enforced in this country. Regarding the distance variable, previous researchers used linear, quadratic or exponential functions for distance, implicitly assuming that the city is monocentric, with a single CBD. As a result, the estimated coefficient became insignificant since most modern cities contain more than one business or cultural center. We believe that the essence of accessibility to CBD in the monocentric model is correct but that its assumptions are unrealistic. People do value access, but they might significantly value access to places other than the CBD. Holding all other characteristics of a dwelling unit constant, the price gradient should fall when the distance to a major employment center, which may not be the CBD, increases. To reflect the multiple centers in the Taichung area, a linear spline function on the distance variable will be used in this study to show the complexity of determining housing price.
The use of spline functions ( Suits, Mason and Chan, 1978) enables us to present a complex functional form in a simple manner and to identify any local extremes in the price gradient. The equation for estimation of housing price by incorporating a linear spline function is shown as below:
s.t. ai+1 = ai + bi(X + ̄i+1-X + ̄i) for all i (13.2)
P = selling price of dwelling X = distance from the CBD X + U+304i = beginning value of X for interval i