The provision of infrastructure: benefit–cost criteria for optimizing local governments

Duranton and Deo (1999) provides additional background and rationalization for how public goods are productive and affect local industry.

I use “regional” and “local” interchangeably as is common in the literature.

There are many competing definitions of MCPF that have generated substantial discussion on the subject. Some of the works that gather the more relevant issues and differences between approaches are discussed in Wildasin (1984), Ballard and Fullerton (1992), Dahlby (2008), and most recently Jacobs (2018). Though the open-economy setting in this paper differs from most prior works, I point out certain guideposts from the literature that are helpful. For example, prior to collecting all marginal benefit terms, the optimization rule in Eq. 8 tracks Stiglitz and Dasgupta (1971), which includes the social marginal value of the provision of the public good since uncompensated demand curves are utilized. This contrasts with simply adding the marginal excess burden to the amount of tax collected under the “Harberger/Browning” approach. Ultimately in the model here, the social marginal value will be capitalized into the price of the fixed factor, so it is accounted for by the rule of provision. However, what I term MCPF is given on the right-hand side of Eq. 12 which is the correct criterion for public expenditure evaluation in this paper. I do so not to introduce a new definition, but to facilitate balancing the marginal benefits with the marginal costs in this setting.

See Krol (1998) for an overview of related literature.

In fact, the assumption of intergovernmental transfers is suggestive of spillovers or fiscal externalities occurring outside the jurisdiction because federal transfers are typical policy instruments used to correct for these issues.

The right of free mobility throughout the federation is protected by the Privileges and Immunities Clause found in the US Constitution (Article IV, Section 2, Clause 1). Additionally, Russia and Canada have similar rights in their respective constitutions (see the Russian Constitution, Rights and Freedoms of Man and Citizen, Chapter 2, Article 27, Clause 1; Constitution of Canada, Canadian Charter of Rights and Freedoms, Mobility Rights, Section 6). The European Union also shares this aspect of federations through the Treaty on the Functioning of the European Union (see the Free movement of workers, services and capital, Part 3, Title IV, Chapter 1, Article 45). As a counterexample to free mobility, China’s use of the Hukou system severely hinders internal migration of households.

Although the actual structure of decisions and taxing authority differ by region, some examples of regional transportation infrastructure entities in the USA include: the Metropolitan Transportation Authority or MTA (providing public transportation to Downstate New York and parts of Connecticut through a payroll tax), the Metropolitan Atlanta Rapid Transit Authority or MARTA (providing public transportation for the various counties in the Atlanta metro area funded by a local sales tax), the Metropolitan Transportation Commission or MTC (providing regional transportation planning and financing around San Francisco Bay Area funded by the state of California), the Regional Transportation Council of the North Central Texas Council of Governments (determining the allocation of regional transportation funds for the 12 counties of the Dallas-Fort Worth area). Furthermore, state level departments of transportation such as Caltrans (California) and PennDOT (Pennsylvania) are divided into districts to better serve local constituents.

For simplicity in developing the insights of the model, identical mobile households are considered. Of course, it is possible to assume multiple classes of households with differing utility functions and mobility, but that would provide an inessential complexity to the analysis. However, one important aspect in which households can be considered heterogeneous is in wealth, provided that preference for wealth is separable.

Each of these variables can be thought of as a vector of consumption goods and public goods, respectively.

With labor provided within the locality, this model is a “regional” and not a “metropolitan” Tiebout-type model (Mieszkowski and Zodrow 1989). Regional models generally require three assumptions: 1. the households work within the jurisdiction they reside in, 2. regional governments do not have absolute control of community size, and 3. land is fixed within regions.

Haughwout (2002) notes that the principal beneficiaries of infrastructure investment are households and not firms. Thus, to avoid additional complexity this simplified production process is assumed.

There is an expansive literature on the impact of the assumption to whom the benefits accrue, e.g., whether the public input is a firm-augmenting or a factor-augmenting type input, which is reviewed in Feehan (1989). In particular it depends on whether the production function exhibits constant returns to scale in all inputs or just in the private inputs, i.e., the public good may be congestible in its use by firms that make up the aggregate production function. Matsumoto (1998) investigates this distinction in a tax competition setting with mobile capital and firms.

Wilson (1995) points out that since there are many regions that are small and open, an Arrow-Debreu like separation may be applied, thus households may own the fixed factor, but the decision is unattached to their locational choice of maximizing utility, i.e., they allow market conditions to dictate the optimal mix in their locational decision as consumers of private and public goods. Therefore, households that locate in this locality and own a portion of the fixed factor, or a non-traded good (e.g., houses), within the region also prefer this objective (Sonstelie and Portney 1978; Wildasin 1979).

A useful benchmark for the model would be one with lump-sum taxes and the first-best provision of public goods. Given the established framework, a simple alteration of the tax available provides the necessary conditions. Thus, supposing that instead of a tax on labor the public good is solely financed with a tax on rents—such as Henry George’s single tax, a well-known lump-sum tax—the rule for first-best provision should result. This specification would beAfter optimization following 6 and cancellations, the result is \(F_{z}-C'L=(1-\bar{m})H'\). This result is the rule for the first-best provision of public expenditure. The first term is the value marginal product of the public expenditure. This follows the Kaizuka/Sandmo rule for an aggregate production function (Kaizuka 1965; Sandmo 1972). The second term is the marginal rate of substitution of the public expenditure to the private good multiplied by the number of households, which follows Samuelson (1954). The right side is the local price adjustment for the matching grant times the first derivative of the cost function with respect to the numeraire, or the marginal rate of transformation. By setting the matching rate to zero, and simplified to familiar terms this is equivalent to a “generalized Samuelson condition” for first-best provision: \(\hbox {VMP}_{z}+\sum \hbox {MRS}=\hbox {MRT}\) (Brueckner and Wingler 1984). The tax on rents is required for the optimal tax system under the assumptions of the model.

The Allen–Uzawa elasticity of substitution shows how the change in the price of the public good changes the level of labor, holding the input prices and the output quantity constant. The relation between the two elasticities is reciprocal under constant returns to scale production functions (Sato and Koizumi 1973; Syrquin and Hollender 1982). Syrquin and Hollender (1982) shows that in the non-constant returns to scale production function the reciprocity rule of the two elasticities does not hold, but is altered by a scale effect on the marginal cost. Given that estimates for public inputs are only available for the Allen–Uzawa elasticity of substitution, these are roughly converted to elasticity of complementarity using the reciprocity rule to give a loose sense of sign and magnitude.

Stiglitz and Dasgupta (1971) is among the first to show that uncompensated demand curves take the effect of public expenditure into account in the rule for provision of public goods financed with distortionary taxes. See footnote 3 for additional discussion on the MCPF.

These results are similar to those found in Feehan and Matsumoto (2002).

The values of these parameters can be found in a number of papers and studies. For the purposes here, Krol (1998) provides an incredibly valuable review and collection of papers, including the crucial specification of production and cost function estimates. The various levels of elasticity of complementarity are chosen to demonstrate the operation of both the potential sign and magnitude. The upper and lower extremes of the parameter values seem plausible given the results in Nadiri and Mamuneas (1994), which finds that infrastructure and labor are substitutes, corresponding to the furthest right three columns in Table 1. Additionally, this parameter is also shown to lie between 0.5 and 1 given the results of Canning and Bennathan (2000), after adjustments following Kim (2000).

The demand elasticity of labor has a range from − 0.15 (Hamermesh 1996), to − 0.45 (Deno 1988), to − 0.70 (Hamermesh 1996; Lichter et al. 2015). These values are highly dependent on the time frame of adjustment. The factor share of labor has been falling in recent history, yet is relatively stable over decade long analysis (Lawrence 2015). Finally, the share of marginal benefits that accrues through the impact on production is calculated from estimates from Albouy and Farahani (2017).