We empirically study the number of facilities at municipality level in Japan observed in telephone directory data from 2011 to 2017. This data is renewed every one year and contains comprehensive individual listings of about 7 million facilities. The distribution of the number of facilities is approximated by an exponential distribution. The annual growth rates follows a Laplace distribution. Observation of the scatter plot for number of facilities and annual growth rate seems to support that growth rate decrease with its size(the number of facilities), indicating deviations from Gibrat's law. This result is similar to what is found for population growth. There are significant positive correlation between two successive annual growth rates, implying that cities with large (small) growth rate tend to be larger (smaller) in the next year. To demonstrate directional patterns of size changes, conditional probabilities of upward versus downward size change given prior size changes are examined. The conditional probability of size increase (decrease) in the next size change after n successive size increase (decrease) is significantly larger than 0.5. Probabilities of successive negative size changes is slightly higher than that of positive size changes. As n becomes larger, the probability gradually increases. The findings suggest that city sizes tend to continue increasing or decreasing.
