An Empirical Study of City Sizes

我们构建了自己的大都市数据集来估计日本城市集聚经济的规模。在总生产函数的估计中，我们的主要发现如下。(1)小城市的集聚经济规模较小，20万以上城市的集聚经济规模较大。人口在20万至40万之间的城市具有特别大的集聚经济：在柯布-道格拉斯生产函数的情况下，城市规模扩大一倍，生产率将提高约25%。人口超过40万的城市生产率提高约7%，人口不足20万的城市生产率提高约1%。(2)在我们对都市生产函数的横截面估计中，社会间接资本的系数要么在统计上不显著，要么为负。因此我们省略了可变的生产函数。我们还估计了一种修正的柯布-道格拉斯形式，其中集聚效应与社会间接资本以高度非线性的方式相互作用。这种情况下的集聚效应比简单的柯布-道格拉斯情况要小得多。利用集聚经济的估计，我们检验了最优城市规模是否满足亨利·乔治定理。我们发现，所有城市的土地总价值与庇古补贴总额相比都非常高，但东京的这一比例略低于日本17个最大城市的平均水平。因此，没有证据支持东京太大的假设。但请注意，这种比较是根据比率进行的。由于东京比其他城市大得多，城市租金差异和庇古补贴之间的绝对差异可能非常大。

We construct our own metropolitan data set to estimate the magnitudes of agglomeration economies for Japanese cities. In the estimation of aggregate production functions our major findings are as follows.(1) Agglomeration economies are small for small cities but fairly large for cities with population larger than 200,000. Cities with population between 200,000 and 400,000 have especially large agglomeration economies : doubling the size of a city increases productivity by about 25% in the Cobb-Douglas production function case. The productivity increase is about 7% for cities with more than 400,000 residents and about 1% for cities with less than 200,000 residents.(2) In our cross-section estimation of a metropolitan production function, the coefficient for social overhead capital is either statistically insignificant or negative. We therefore omit the variable production function. We have also estimated a modified Cobb-Douglas form in which the agglomeration effect interacts with social overhead capital in a highly nonlinear manner. Agglomeration effects are substantially smaller in this case than in the simple Cobb-Douglas case.Using the estimates for agglomeration economies, we have tested if the Henry George Theorem for optimal city size is satisfied. We found that the total land values are very high compared with the total Pigouvian subsidies in all cities, but the ratio for Tokyo is slightly below the average for 17 largest cities in Japan. Thus, there is no evidence supporting the hypothesis that Tokyo is too large. Note however that this comparison is made in terms of ratios. Because Tokyo is much larger than other cities, the absolute difference between the differential urban rent and the Pigouvian subsidy could be extremely large.