result shows that an inverted u-shaped relationship between cartels and degree of concentration. However, when the effect of capital concentration is controlled, we were unable to confirm clearly correlation between them. Concerning relation to R&D, it was observed that the likelihood of cartels in industries with high intensity in R&D was lower than that of industries with low intensity in R&D.

Suslow (2005) analyzed factors influencing the length of cartel operation via applying a survival analysis technique using 71 cartels in 45 industries over periods from 1920 to 1939, for which there were clear written agreements on collaboration to limit its production and to raise its prices. According to the analysis, declines in industry production and fluctuations in the economy posed a significant burden in relation to the perpetuation of cartels. The length of cartels was found to have been extended in cases where contracts stipulated penalties for violating cartel rules. Furthermore, factors relating to the provision of patents and cross-licenses also significantly affected the perpetuation of cartels. Conversely, the length of cartels was significantly shortened in cases where the cartel handled a large number of products. Regarding the number of cartel participants (the number of countries or businesses participating cartels) and length of existence, the length of cartel reduced as the number of participants grew but this relationship was insignificant.

Jacquemin et al. (1981) constructed an economic model for the persistence of export cartels which were legalized by the Japanese government, and conducted an empirical analysis to seek what factors determined the length of periods of these cartels. The cartels examined by the above researches were ones which were prevalent after the depression in 1964 and 1965 from 1967 to the first oil shock in 1972. Their data include degree of market concentration, volume of production and volume of export from 40 industries (6-digit category defined by Ministry of International Trade and Industry and the 4-digit category defined in Japan Standard Industry Classification (JSIC)). Based on the data, the average persistence periods of the legal cartels were 10 years, the average degree of market concentration of industries with the legal cartels was 59.5%, and that of all the manufacturing industries was 62.7%. The average degree of concentration in the industries with the legal cartels was not significantly low from that of all the manufacturing industries. Their results show that the degree of market concentration has a negative impact on the persistence periods of the legal cartels, but it is insignificant. Theoretically speaking, as a greater number of firms which participates in a cartel increases, the cartel will become unstable. $ ^{4} $ The authors give an interpretation for three results that even when there are a large number of firms in a cartel, legalized cartels tend to maintain their stability. Regarding the relationship between cartels and the degree of product differentiation, the results show that it was easy for cartels to sustain when their products were of similar quality. Regarding the growth in demand, while it was not statistically significant, a high demand growth rate makes the period of cartels shorter. As for types of cartels and its relationship to the persistence period, as the cases of cartels on prices and value of production in all the cartel cases increase, the persistence of the cartels decreases significantly. However, this effect declined in an absolute value for