Does Institutional Quality Matter for Infrastructure Provision? A Non-parametric Analysis for Italian Municipalities

Abstract

This study explores the relationship between different dimensions of regional institutional quality and the efficient provision of transport infrastructure. A two-stage semi-parametric approach is applied to a large sample of public works procured by about 1700 Italian municipalities in the 2000–2014 period. First, we estimate the performance in contract execution; then, we test the impact of different measures and dimensions of institutional quality at both regional and provincial level. The results provide evidence that the quality of institutional environment matters in infrastructure procurement, though some specific dimensions of institutional quality appear to be more relevant than others in affecting performance in contract execution. Overall, the estimates are robust to alternative measures of institutional quality, alternative model specifications, and different sample selections.

Appendices

Appendix A

This Appendix reports some further statistics and robustness checks of the empirical findings obtained in the paper (Figs. 5, 6 and Tables 9, 10, 11, 12, 13).

Fig. 5

Source: our elaboration on data provided by Nifo and Vecchione (2014)

Pillars of IQI_ REGION_2012 at NUTS 2 level

Fig. 6

Frequency of DEA CRS efficiency estimates (on the left) and kernel density estimates of DEA CRS and DEA CRS bias corrected efficiency estimates (on the right). Source: our elaboration on data provided by AVPC. Note: Figures show the frequency and the kernel density estimates of DEA efficiency scores under CRS assumption, respectively. DEA CRS bias corrected scores are estimated with the procedure proposed by Simar and Wilson (2000). The kernel density functions for the efficiency of contracts for roads are derived from bias corrected DEA efficiency scores using a univariate kernel smoothing distribution and the appropriate bandwidth (Simar and Wilson 2008)

Table 9 Pairwise correlation matrix

Table 10 Conditional distribution of average DEA CRS bias corrected efficiency estimates

Table 11 Robustness check with institutional quality index at NUTS 2 level—semiparametric bootstrap truncated estimates, sub-sample of small municipalities

Table 12 Robustness check with institutional quality pillars at NUTS 2 level– semi-parametric bootstrap truncated estimates, sub-sample of small municipalities

Table 13 Estimates using pillars one by one—semi-parametric bootstrap truncated estimates, full sample

Appendix B

This Appendix reports the analytical formulation of the DEA model. To facilitate the interpretation of the results reported in the paper, the formulation of DEA is presented. A production process using the input vector $\left\{ {x = x_{i} , i = 1, \ldots ,n} \right\} \in \Re_{ + }^{N}$ is considered to produce an output vector $\left\{ {y = y_{s } , s = 1, \ldots , m} \right\} \in \Re_{ + }^{M}$. The production process is constrained by the production possibility set $\varPsi$, which is the set of physically attainable points (x, y) given by:

$$ \varPsi = \left\{ {(x, y) \in \Re_{ + }^{N + M} | = \left( {x,y} \right)\,\, {\text{is feasible}} } \right\} $$

(1)

The efficiency of a generic DMU (i.e. a public work contract) is measured by the distance between the observed input-output mix and the optimal mix located on the frontier of $\varPsi$, which is the boundary of optimal production plans.

The single DMU efficiency score is:

$$ \lambda \left( {x,y} \right) = \inf \left\{ {\lambda |\left( {\lambda x,y} \right) \in \varPsi } \right\} $$

(2)

where a value of $\lambda \left( {x,y} \right) < 1$ indicates the radial distance of the DMU from the full efficient frontier and a value of $\lambda \left( {x,y} \right) = 1$ means that the DMU is efficient. Being $\varPsi$ the frontier and $\lambda \left( {x,y} \right)$ unknown, they should be estimated from a sample of i.i.d. observations ${\mathcal{X}}_{n} = \left\{ {\left( {x_{i} ,y_{i} } \right),i = 1, \ldots ,n} \right\}.$

The DEA non-parametric estimator assumes the convexity of the hull and, thus, under the hypothesis of constant returns to scale (CRS), can be defined as:

$$ \widehat{\varPsi }_{DEA} = \left\{ {\left( {x,y} \right) \in {\mathbb{R}}_{ + }^{N + M} |y \le \mathop \sum \limits_{i = 1}^{n} \gamma_{i} x_{i} ; x \ge \mathop \sum \limits_{i = 1}^{n} \gamma_{i} y_{i} ,for (\gamma_{1} , \ldots ,\gamma_{n} )\, {\rm such that}\, \gamma_{i} \ge 0, i = 1, \ldots ,n } \right\} . $$

(3)

A DEA estimator of the efficiency scores can be calculated by replacing the true production set $\varPsi$ in (2) with the estimator $\hat{\varPsi }_{DEA}$:

$$ \hat{\lambda }_{DEA} \left( {x,y} \right) = \inf \left\{ {\theta |\left( {\theta x,y} \right) \in \hat{\varPsi }_{DEA} } \right\} $$

(4)

where, by construction, $\hat{\lambda }_{DEA} \left( {x,y} \right) \le \lambda \left( {x,y} \right)$ (Simar and Wilson 2008).

To study the effect of environmental variables (or non-discretionary input in the second-stage analysis, Simar and Wilson (2007) suggest applying a semi-parametric two-step bias-corrected truncated estimator where the unobserved regress and $\lambda_{i}$. is replaced by its bias-corrected estimate $\hat{\hat{\lambda }}_{i}$ obtained using DEA with bootstrap and a maximum likelihood truncated estimator. More specifically, the second-stage regression can be summarized as follows:

• 1. Apply maximum likelihood estimator in a truncated regression of $\hat{\hat{\lambda }}_{i}$ on $z_{i}$. to obtain estimates of $(\hat{\beta },\hat{\sigma })$, where $i = 1, \ldots ,n$ is the number of DMUs.

• 2 Repeat the steps from 2.1 to 2.3, L times to obtain b numbers obootstrap estimates of $\left\{ {(\hat{\beta }^{*} ,\hat{\sigma }_{\varepsilon }^{*} )_{b} } \right\}_{b = 1}^{L}$:

  • 2.1 For each DMU $i = 1, \ldots ,n$, draw $\varepsilon_{i}$from the left-truncated $(1 - z_{i} \hat{\beta })$normal distribution;

  • 2.2. Use $\varepsilon_{i}$for each DMUs $i = 1, \ldots ,n$to calculate fitted DEA scores: $\hat{\hat{\lambda }}_{i}^{*} = z_{i} \hat{\beta } + \varepsilon_{i}$;

  • 2.3 Apply maximum likelihood estimator in a truncated regression of $\hat{\hat{\lambda }}_{i}^{*}$on $z_{i}$. to obtain estimates of $(\hat{\beta }^{*} ,\hat{\sigma }^{*} )$.

• 3. Compute the bias-corrected estimator of $\hat{\hat{\beta }}$ as well as the percentile bootstrap confidence intervals at a given level of significance using the bootstrap estimates obtained from the previous step $\left\{ {(\hat{\beta }^{*} ,\hat{\sigma }_{\varepsilon }^{*} )_{b} } \right\}_{b = 1}^{L}$ and the original parameters $(\hat{\beta },\hat{\sigma })$.