Results

Overview

The results address the central question: do firms that the government selects for less-competitive mechanisms have lower costs than firms that only compete in public auctions? The answer depends on the type of project. For complex contracts involving sewage work, the answer is yes, the selected firms are genuinely more efficient. For simple pavement contracts (the majority), the answer is no, selected firms are actually more expensive.

This section presents the results in three parts: (1) the cost CDF comparison from the structural model, (2) the efficiency index estimates from SFA, and (3) the geographic distribution of efficiency across Mexican states.

Part 1: Cost CDF Comparison

Reading a CDF in This Context

The cumulative distribution function \(\hat{F}_j(c)\) gives the fraction of firms of type \(j\) with pseudo-cost below \(c\). A CDF that lies to the left means that a larger share of firms in that group can complete the project at any given cost threshold, i.e., that type has systematically lower costs.

More formally, if \(\hat{F}_1(c) > \hat{F}_0(c)\) for all \(c\) in the support, then Type 1 first-order stochastically dominates Type 0 in terms of cost, meaning Type 1 draws lower costs at every quantile. When the CDFs cross, the comparison is ambiguous and depends on the part of the distribution under consideration.

First-order stochastic dominance (FOSD) of Type 1 over Type 0 in cost means: \[F_1(c) \geq F_0(c) \quad \text{for all } c\]

This implies that a randomly drawn Type 1 firm has a lower cost than a randomly drawn Type 0 firm with probability greater than 1/2. In the procurement context, it means the government’s selection of Type 1 firms is, on average, cost-justified.

Why CDFs at multiple quantiles? The paper reports CDFs at the 25th, 50th, and 75th percentiles of the project-size distribution. This controls for project size, since larger contracts may have systematically different cost structures. The toggle below shows CDFs at the median project size (most representative).

Why CDF comparisons rather than mean costs? Means can be sensitive to outliers, especially when pseudo-costs may have kernel estimation error in the tails. CDFs are more robust and allow visual inspection of the entire distribution.

Cost CDFs: Simple vs. Complex Projects

Interpreting the CDF Results

Simple projects (no sewage, ~62% of public contracts): The Type 0 CDF lies to the left of the Type 1 CDF. This means that at every cost threshold, a larger share of Type 0 firms can complete the project at or below that cost. Government-selected firms (Type 1) are less cost-efficient for routine pavement work. The government would obtain lower-cost contractors by defaulting to public auctions for these contracts.

Complex projects (with sewage, ~38% of public contracts): The pattern reverses. The Type 1 CDF lies to the left of the Type 0 CDF. Government-selected firms have lower costs when the project involves sewage infrastructure. This is consistent with economies of scope: firms with prior experience in multi-task contracts (combining pavement with drainage or utility work) have lower costs for complex projects, even after conditioning on project characteristics.

NoteWhy does the result flip for complex projects?

One interpretation is that the government’s selection criterion is (partially) valid for complex projects but not for simple ones. A second interpretation is that Type 1 firms have invested in capabilities, including equipment, workforce, and project management, that are only cost-advantageous when projects involve multiple types of work. For homogeneous pavement without sewage, their specialized advantages disappear, and their higher overhead makes them more expensive.

A third possibility is reverse causality: governments learned, over time, which firms perform well on complex projects and selectively directed those firms toward I3P contracts. If so, the efficiency advantage of Type 1 firms on complex projects is partly a consequence of the selection process itself, as governments learned by doing. The structural model cannot distinguish between these interpretations, but all of them are consistent with the finding.

Part 2: Stochastic Frontier Efficiency Index

The SFA estimates a cost frontier, the minimum cost achievable given output and input prices, and recovers firm-level deviations from it. The Battese-Coelli index \(BC = e^{-\hat{\eta}} \in (0,1]\) summarizes efficiency, with higher values indicating less excess cost.

Efficiency Index Distributions by Firm Type

Interpreting the Efficiency Index

The density plot shows the full distribution of \(BC\) efficiency scores for each firm type. The vertical dotted lines mark the means.

NoteWhat does BC = 0.60 mean?

A BC efficiency index of 1.0 means the firm is on the cost frontier — its actual cost equals the minimum achievable cost. A value of 0.60 means the minimum cost is 60% of the firm’s actual cost: the firm spends more than it needs to, relative to the best-practice firms in Mexico operating under the same conditions.

The SFA results show that Type 1 firms overuse inputs by 7.5 percentage points more than Type 0 firms, on average, and this difference is statistically significant. This aggregate finding is driven by the composition of the sample: the majority of public auction contracts do not include sewage work, and simple pavement projects are precisely the type where Type 1 firms are less cost-competitive. When the full sample is pooled, the cost disadvantage of Type 1 firms on simple projects dominates.

Part 3: Geographic Distribution of Efficiency

The map below shows the average BC efficiency index by Mexican state (weighted by contract volume). States with more contracts contribute more to their state average. Brighter colors (toward gold) indicate higher average efficiency; darker colors (navy) indicate more excess cost.

The state-level average reflects the composition of firms participating in public auctions in that state’s municipalities. States with few contracts have less precise estimates; the contract count is available in the hover tooltip.

Large variation across states may reflect: 1. Local market conditions: thin contractor markets in less populated states may have fewer efficient firms 2. Sample composition: states with more Type 1 bidders may show higher average efficiency if Type 1 firms are more efficient in complex projects 3. Contract mix: states with more complex (sewage-inclusive) contracts may show different average efficiency than states with mostly simple pavement work

Summary of Main Results

Simple contracts Complex contracts (sewage)
Type 1 pseudo-costs vs. Type 0 Higher (worse ✗) Lower (better ✓)
Type 1 efficiency index vs. Type 0 Lower (worse ✗) Higher (better ✓)
CDF dominance Type 0 dominates Type 1 dominates
Share of public auctions ~62% ~38%
Policy implication Switch to public auction Discretion may be justified

The combined evidence from the structural model (CDFs) and the SFA (efficiency index) points consistently in the same direction. For most I3P contracts, the simple, routine pavement projects, the government would obtain lower-cost contractors by opening the process to public competition. For the minority of contracts involving sewage work, the selected firms appear to have genuine cost advantages, possibly reflecting cumulative experience with multi-task construction.