In this paper, we developed a pilot model of the public service production structure of the local government in Japan. “The productivity analysis of the local government in Japan;a production function approach” was previously published by Kinugasa （the Otemon Economic Bulletin, 45（2）, pp. 34-53, 2011）. In the previous manuscript （Kinugasa 2011）, the Cobb-Douglas type production function and the Data Envelopment Analysis （DEA） were estimated to measure the productivity of local governments in Japan. As the next step, we estimate the multi-output production function. Two major purposes supplied by local governments such as cities, towns and villages are defined. The first purpose is “municipal income distribution” and the second is “population growth rate”.
In local governments, there are various types of public services, for example, elementary and secondary education, welfare of persons with disabilities, welfare of the aged, medical services, firefighting, etc. The various public services for citizens must be integrated to estimate the production function of local governments. However, these services are difficult to integrate. We adopted “municipal income distribution” as one integrated indicator that is the consequence of monetary oriented public services by local governments. This indicator is based on the former report by Kinugasa （2011）. Another indicator, “population growth rate” we adopted is not precisely “output of public services”, but is defined as “the result of improvement in the welfare of public services in every local government”. Many people migrate from one region to other region based on comparison of the welfare of public services. Non-monetary oriented public services by local governments are integrated as an indicator of “population growth rate”. From the estimated results and consideration of conditions, the multi-output production function of local governments we propose provides a reasonable result.

JEL Classification: G21, L10, L13