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The Annals of Regional Science

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13-06-2017 | Original Paper

A note on production taxation and public-input provision

Authors: Mutsumi Matsumoto, Kota Sugahara

Published in: The Annals of Regional Science | Issue 2/2017

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Abstract

Gugl and Zodrow (Natl Tax J 68:767–802, 2015) derive a general condition for (in)efficient public-input provision under production-tax financing. Their condition is described in terms of log modularity of production technology. This paper shows that in the case of “factor-augmenting” public inputs, the Gugl–Zodrow condition can be characterized in terms of the technical changes caused by public-input provision.

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Reviews of the related studies are available from Matsumoto and Feehan (2010), Matsumoto (2010) and Gugl and Zodrow (2015).

While listing studies in other research fields is beyond the scope of this paper, we note that there are empirical studies in which the impacts of public inputs are estimated under the factor-augmenting specification. Examples include Haughwout and Inman (2001), Haughwout (2002), Bronzini and Piselli (2009) and Park and Von Rabenau (2011). While Arrow and Kurz (1970, pp. 110–111) argue that education, R&D activities and transportation will cause IRS by raising the productivities of private factors, these empirical studies deal with a wide variety of public services and infrastructures.

That is, the benefit of public inputs is limited to the supplier country or region. This assumption follows the previous theoretical and empirical studies of factor-augmenting public inputs.

In the next section, we introduce the factor-augmenting specification (CRS in private factors only). It should be emphasized that the GZ condition is independent of returns to scale of the production function. Although GZ (p. 772) assume CRS in all factors including public inputs, this assumption does not play any crucial role in deriving their condition for expenditure (in)efficiency.

If local firms earn profit, it is distributed to local residents. The sum of labor income and profit is equal to \((1-t)F-rK\), while capital income is equal to \(r\overline{K} \). In GZ, there is a rent on public inputs that accrues as firms’ profit. On the other hand, due to the difference in the specification of production technology, the public-input rent is absent in our Sect. 3; see Eq. (9).

The GZ condition is valid for the factor-augmenting specification (see footnote 4). Still, one might notice that the base of production taxation depends on returns to scale of the production function. This tax is a uniform levy on capital and labor in our Sect. 3. In GZ where CRS in all factors including public inputs is assumed, the rent on public inputs is also subject to taxation.

Differentiating (2) and applying (4) and (5) to the outcome yields that \(\partial t/\partial B=(1-t)(F_B /F)\). This, together with (6), gives the expression of \({\textit{dK}}/{\textit{dB}}\) in the main text.

In the tax competition literature, it has been recognized that the degree of returns to scale of production functions plays an important role in the normative nature of public-input provision (under-provision or over-provision). If CRS in all factors including public inputs is assumed as in GZ (see footnote 4), the possibility of over-provision cannot be excluded even under capital-tax financing; see also Noiset (1995) for over-provision of public inputs.

Although capital-tax financing may not cause under-provision in the GZ model (see footnote 8), their numerical examples show that the level of public-input provision is higher under production taxation than under capital taxation. This is because a larger, less mobile tax base is available under production taxation.

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Title: A note on production taxation and public-input provision
Authors: Mutsumi Matsumoto
Kota Sugahara
Publication date: 13-06-2017
Publisher: Springer Berlin Heidelberg
Published in: The Annals of Regional Science / Issue 2/2017
Print ISSN: 0570-1864
Electronic ISSN: 1432-0592
DOI: https://doi.org/10.1007/s00168-017-0837-2

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