Scale effects on long-run economic growth

Daishoku Kanehara
MQ Discussion Series
September 2016
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Empirical studies about scale effect indicate in decades-long data there is no scale effect, but in a very long-run data scale effect is clearly observed. In this study, we construct a uni…ed model that can explain both two empirical results, focusing on the length of the data sets of empirical studies. We construct horizontal lab-equipment R&D growth model with exogenously growing efficient labor, the rate of which is determined by the initial land size. In this model, we derive the period-2 cycle, which has scale effect on average, but which faces with strong scale effect and weak scale effect with R&D reciprocally. The scale effect of this R&D period can difficult to be observed. We also verify the existence condition of the period-2 cycle numerically, and this is consistent with both the duration of monopoly power guaranteed by patents and the "medium-term cycle" pointed out in Comin and Gertler (2006). Since, by the patent citation data, the length of one period is expected to be about a decade, if the data set contains more R&D periods than strong scale effect periods and the labor force is less important in final good production, it is not easy to observe the existence of scale effect in decades-long data. On the other hand, if we use (very) long-run data like several centuries-long data or so, there exists a clear link between the scale of the economy and the growth rate. Therefore, this model can explain the seemingly inconsistent several empirical studies about scale effect. This also implies that to measure scale effect in a proper way it is necessary to use (very) long-run data.

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