Bunching below thresholds to manipulate public procurement

Abstract

Manipulative authorities can bunch tenders just below thresholds to implement noncompetitive procurement practices. I use regression discontinuity manipulation tests to identify the bunching manipulation scheme. I investigate the European Union public procurement data set that covers more than two million contracts. The results show that 10–13% of the examined authorities exhibit a high probability of bunching. These authorities are less likely to employ competitive procurement procedures. Local firms are more likely to win contracts from a bunching authority. The probability that the same firm wins contracts repeatedly is high when an authority has high bunching probability. Empirical results suggest that policy makers can effectively employ regression discontinuity manipulation tests to determine manipulative authorities.

Appendices

Appendix A: The CJM methodology

In this section, I rewrite some of the major equations of CJM and summarize their methodology. The supplementary material supplied by CJM provides detailed proofs and derivations.

CJM proposes a local polynomial density estimator to estimate the probability density function of the estimated cost (c), f(c). The manipulation test is a hypothesis test on the continuity of the density f(c) at the EU threshold, T. The test is formulated as follows:

$$\begin{aligned} H_{o}:\underset{{\scriptstyle c\uparrow T}}{\lim }f(c)=\underset{{\scriptstyle c\downarrow T}}{\lim }f(c) \end{aligned}$$

CJM estimates the density f(c) using a local-density estimator based on the cumulative distribution function of the observed sample. Specifically, the test statistic is

$$\begin{aligned} T_{p}(h)=\frac{{\hat{f}}_{+,p}(h)-{\hat{f}}_{-,p}(h)}{{\hat{V}}_{p}(h)} \end{aligned}$$

where $\hat{V_{p}^{2}}(h)=\hat{V}\left\{ {\hat{f}}_{+,p}(h)-{\hat{f}}_{-,p}(h)\right\}$ is a variance estimator such that $V(x)=e'_{1}A(x)^{-1}B(x)A(x)^{-1}$. $A(x)=f(x)\int _{h^{-1}(X-x)}r_{p}(u)r_{p}(u)'K(u)du$ and $B(x)=f(x)^{3}\int \int _{h^{-1}(X-x)}min(u,v)r_{p}(u)r_{p}(v)'K(u)K(v)dudv.$ Detailed descriptions of the notation and derivations are available at Theorem 1 of CJM (page 3).

$$\begin{aligned} \begin{array}{cc} {\hat{f}}_{-,p}(h)=e'_{1}{\hat{\beta }}_{-,p}(h),&{\hat{f}}_{+,p}(h)=e'_{1}{\hat{\beta }}_{+,p}(h)\end{array} \end{aligned}$$

CJM develops AMSE criterion functions to calculate the optimal bandwidths. The bandwidths are chosen to minimize the AMSE of the following density estimators, separately:

$$\begin{aligned} \begin{array}{ccc} {\hat{h}}_{1,p}=argmin_{h>0}AMSE\left\{ {\hat{f}}_{-,p}(h)\right\}&and&{\hat{h}}_{r,p}=argmin_{h>0}AMSE\left\{ {\hat{f}}_{+,p}(h)\right\} \end{array}. \end{aligned}$$

Appendix B: The distribution of manipulating authorities within EU countries

Figure 6 displays the percentages of authorities with p-values below 0.05 in each country with adequate number of observations.

Fig. 6

Distribution of manipulating authorities within EU Countries

Appendix C: Binomial test results

This section displays the binomial test results for alternative windows and alternative initial window sample sizes. The test is conducted for different sample sizes in the initial window. Each test presents results or 10 windows. Table 3 displays the binomial manipulation test results.

Table 3 Binomial test results p-values of binomial tests (H0: prob =.5)