The aim of this paper is to select appropriate hedonic models for evaluating the externality of paddy fields. The P test, which is a kind of non-nested test, might select inappropriate models because of size distortion. Size distortion means that the size which is assumed in parametric distribution is different from the true size when data does not distribute parametrically. To avoid size distortion, I use the nonparametric bootstrap technique to improve properties of the P test. I call this test a bootstrap P test. I conducted a Monte Carlo simulation which shows that the bootstrap P test overcomes the size distortion, enabling us to select superior models. I used it to select a hedonic model. The log-log and spline regression were selected by bootstrap P test. Also, I evaluated the externality of paddy fields in 1995. The money metric externality was 1.2 trillion in log-log and 1.5 trillion in spline regression in money terms. A 90% confidence interval of externality is also constructed by the bootstrap method. It is [9 trillion/1.5 trillion] (yen) in log-log and [1.2 trillion/1.9 trillion] (yen) in spline regression. It is nearly same as the interval of externality constructed from the data in 1985 as reported by Asano and Tanaka (1996).

　In the long run, the cycle and amplitude in the cyclical fluctuation of economic time-series change accordingly with society, policy, technological progress and so on. But the research on variable cyclical fluctuation is very limited. Therefore, a new method to calculate the change was developed in this study. The change characteristics of cycle and amplitude were combined: the constant, increase and decrease to create 16 sample data series for 25 years in month units, and furthermore, the hen's egg retail price in Tottori City, Japan, for 22 years from 1975 to 1996 in month units were used to study the extraction method of variable cyclical fluctuation. Firstly, auto-correlation coefficient and provisional cycle were calculated by the removal of seasonal and trend fluctuations series, and a threefold period of provisional cycle was regarded as the calculation section series. The principal cycle of the calculation section series was decided by means of power-spectral analysis and F-test (p≦1%). After the detection of harmonic fluctuations, the cyclical fluctuation of the section data was calculated following Fourier-series. Afterwards, a month unit was moved forward for the next calculation. Then reserve variable cyclical fluctuation was calculated by arithmetic means of section cyclical fluctuations. Finally, a functional equation for the time of the arithmetic mean of section cycles and amplitudes was acquired by regression analysis and introduced into Fourier-series to extract the cyclical fluctuation of variable cycle and amplitude.
　The deviation between variable cyclical fluctuation and original sample series or the series removed of seasonal and trend fluctuation was smaller than that of fixed cyclical fluctuation. It seems that the extraction method for the cyclical fluctuation of the variable cycle and amplitude is practical, and this variable cyclical fluctuation closely assimilates real fluctuation.