The Effects of Operating and Capital Subsidies on Total Factor Productivity: A Decomposition Approach

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Past studies relied on ad hoc associations to establish relationships between productivity on one hand and operating and capital subsidies on the other. This article deviates from these studies. It builds on recent research based on private cost to derive a total factor productivity formula that includes subsidy effects. It specifies an empirical model to estimate the required parameters to apply the formula. The application to urban transit systems shows that the effects of these subsidies on productivity through technical change reinforce the decline in productivity. Sakano, Obeng, and Azam (1997) applied the stochastic frontier method to public transit data and decomposed allocative inefficiency between internal factors and subsidies. They found that the internal factors contributed more toward allocative inefficiencies, and subsidies accounted for less than 25% of the technical inefficiencies in transit firms. These authors also found operating subsidies to be the major sources of the inefficiencies and that capital subsidies mostly acted as a counterbalancing factor in reducing the inefficiencies. These findings suggest that both subsidies play opposing roles in affecting performance and inefficiency and that while capital subsidies increase partial productivity measures, operating subsidies may reduce them. These effects of subsidies on partial productivity will also affect total factor productivity (TFP). Therefore, there is a link between operating and capital subsidies and TFP, and we must find a way to decompose the changes in TFP such that we can identify the effects of subsidies. This decomposition is the motivation for this article; we develop a decomposition method for TFP that permits the contributions of subsidies to be isolated and apply the method to public transit data. The article, therefore, makes contributions in both methodology and application. The basis of the decomposition is an extension of the methods discussed in Obeng (1994), Obeng and Azam (1997), and Sakano, Obeng, and Azam (1997) to derive a TFP measure that depends on subsidies.' These methods hold that firms maximize output subject to a net cost constraint, where net cost is total cost less operating and capital subsidies. The dual of this constrained output maximization is that firms minimize their private cost subject to a production function constraint. This objective is different from those frequently adopted in the public transit