Benchmarking the performance of US Municipalities

The Harrisburg case was subsequently dismissed.

See Lee and Wilson (1990, 1991) for theoretical analysis of the economic loss created by this type of rent-seeking behavior.

The studies that employ parametric methods typically specify translog response functions. Among the 31 papers listed by Narbón-Perpiñá and De Witte (2018, Table A2) that employ parametric methods to assess local government performance, 25 use a translog specification, and one (Nikolov and Hrovatin 2013) uses a Cobb–Douglas specification (which of course is nested by the translog specification). However, municipal governments vary widely in terms of size, and several studies have noted that the parameters of a translog function are unlikely to be stable when the function is fit globally across units of widely varying size. See, for example, Guilkey et al. (1983) and Chalfant and Gallant (1985) for Monte Carlo evidence, and Cooper and McLaren (1996) and Banks et al. (1997) for empirical evidence involving consumer demand, Wilson and Carey (2004) for empirical evidence involving hospitals, and McAllister and McManus (1993), Mitchell and Onvural (1996), and Wheelock and Wilson (2001, 2012, 2018) for empirical evidence involving banks.

Inequalities involving vectors are defined on an element-by-element basis.

In principle, for some \((x,y)\in \Psi ^\partial \) one might have \(\theta (x,y\mid \Psi )<1\) or \(\lambda (x,y\mid \Psi )>1\) if the frontier is parallel to either all of the input axes or all of the output axes in some regions. However, this is ruled out by additional assumptions required to define a statistical model in which the efficiency measure defined in (3)–(5) are statistically efficiency; see Kneip et al. (1998) and Kneip et al. (2008) for details.

In other words, standard CLT results hold in the FDH case if and only if \(p=1\) and output is fixed and constant, or \(q=1\) and input is fixed and constant.

We include municipalities in the 48 states excluding Alaska and Hawaii. The census regions are illustrated in Fig. 1. We denote the Northeast, Midwest, South and West regions as regions 1, 2, 3 and 4, respectively.

Problems with the CPI are well known, e.g., the CPI covers a small number of items compared to the gross domestic product deflator, but this is not available at local levels. Where a city-specific CPI is not available, we use the CPI for the region in which a given city is located.

Alternative measures of communal service administrative include number of highway miles and square footage of green space. Unfortunately, these data are not readily available for US municipalities.

One might also consider two separate measures of crime, one for violent crime and another for property crimes such as theft. We expect that there would be a high degree of collinearity between these measures, and as discussed below, there is a high degree of collinearity among our six output measures. Consequently, splitting \(Y_3\) into two measures may not add much information.

We use the number of permits issued for individual units, rather than number of buildings for which permits have been issued. In dense urban environments, one might observe multiple units (e.g., condominium units) in a single building for which building permits have been issued.

We use the U.S. Census Bureau’s definition of local government, corresponding to type code 2 in the U.S. Census of Governments’ 14-digit government ID code.

Starting with data from the Annual Survey of State and Local Government Finance, we merge data from other sources listed above. Necessarily, there are mismatches across the various sources, and in particular some of the municipal governments observed in the Annual Survey of State and Local Government Finance in a given year are not observed in one or more of the other sources. Due to this, we must discard observations for 165–363 cities in each year. As one might expect, these are predominantly smaller cities, but due to the skewed distribution of city-sizes in the USA, the discarded observations are a small proportion of the number of smaller cities for which observations remain in our sample. In the end, our sample size is larger than many that have been used in the literature, e.g., Moore et al. (2005) use a sample of 46 US cities observed over 6 years, giving a total sample size of 276 observations, whereas we have 648–800 observations in each of the 4 years covered in our sample.

Specifically, \(Y_*=Y E_y\) where \(E_y\) is the \((q\times 1)\) eigenvector corresponding to the largest eigenvalues of the moment matrix \(Y'Y\).

Färe and Lovell (1988) and Olesen and Petersen (2016) suggest that dimension reduction is only appropriate when the technology is homothetic. However, the technologies simulated by Wilson (2018) are not homothetic, and yet the simulations in Wilson (2018) show that substantial reductions in estimation error can be achieved with dimension reduction as implemented here.

Recall from the discussion in Sect. 2.1 that by construction, \(\theta (x,y\mid \Psi )\le 1\) and \(\gamma (x,y\mid \Psi )\le 1\), while \(\lambda (x,y\mid \Psi )\ge 1\).

To illustrate, consider a municipality operating near the frontier where both X and \(Y_*\) are small. Here, the frontier is very steep, and the municipality may be close to the frontier in the input direction, but far from the frontier in the output direction. For a municipality operating near the frontier but where both X and \(Y_*\) are large, the reverse is true since the frontier is relatively flat in this region. But the hyperbolic measure will be similar in both cases. See Wilson (2011) for additional discussion, and in particular see Wilson (2011, Fig. 6.1).

Note that the test for differences in mean efficiency developed by Kneip et al. (2016) requires independence between the two means to avoid complications arising from covariance. Our tests of different mean efficiencies across regions involve different municipalities in different regions, so there is little reason to suspect independence does not hold. However, our tests of differences in mean efficiency across time in a particular region involve many of the same municipalities observed at two points in time, and consequently covariance is an issue. On the other hand, inertia likely plays a role here, i.e., a municipality that performs poorly (or well) in one period is likely to also perform poorly (or well) in the next period. Consequently, any covariance is likely to be positive, and since we are testing for differences, ignoring positive covariance makes our tests conservative by biasing toward failure to reject the null hypothesis of no difference in mean efficiencies.

Among these tests, only one—for region 2 versus region 3 in 2012—is not statistically significant.

Similar reasoning regarding covariance across time discussed in footnote 18 applies here. To the extent that there is positive covariance between municipalities’ productivity over time, our tests are conservative.