Competing under Information Heterogeneity: Evidence from Auto Insurance

This paper studies imperfect competition in selection markets where competing firms have heterogeneous information about consumers — a layer of asymmetry distinct from the classic buyer-seller information gap. The central questions are: how do inter-firm information asymmetries shape equilibrium pricing, consumer sorting, and market efficiency; and whether a centralized bureau that aggregates and equalizes firms’ risk information can promote competition and improve welfare.

The empirical setting is the Italian mandatory motor vehicle liability insurance market (Responsabilità Civile Auto). The authors use the IPER dataset from IVASS, a nationally representative panel of matched insurer-insuree contracts covering 124,428 liability insurance contracts for new customers in the province of Rome from 2013 to 2021. The panel tracks consumers across insurer switches, enabling construction of individual-specific risk estimates from ex-post claim records using Poisson regressions for claim frequency and log-normal regressions for claim severity. The analysis focuses on the top 10 largest firms plus a composite fringe firm.

The paper’s empirical strategy proceeds in three stages. First, individual risk types are estimated from multi-year claim panels. Second, demand parameters — price sensitivity and firm-level unobserved product attributes — are recovered using a novel fixed-point algorithm (extending Berry et al. 1995) that infers the full offered-price distribution from observed transaction prices alone, without parametric restrictions on price distributions across firms. Third, supply-side parameters — pricing coefficients, signal variances, and cost parameters — are identified by exploiting the monotone mapping between offered prices and private signals, borrowing from the nonparametric auction literature.

The model features firms that each draw a private Gaussian signal about a consumer’s true risk type theta, with firm-specific signal standard deviation sigma_j. Lower sigma_j means higher information precision. Firms set prices as a linear function of their posterior risk rating: p_j = alpha_j + beta_j * E(theta | theta_j, D=j). Firms simultaneously choose pricing coefficients to maximize expected profits.

Key empirical findings: (1) Firms differ substantially in how sensitively their premiums respond to realized consumer risk — a reduced-form measure of information precision — with Figure 2 showing wide cross-firm variation in premium-to-risk coefficients. (2) Structural estimation confirms substantial heterogeneity in signal standard deviations sigma_j across all 11 firms. Firms with less accurate risk-rating algorithms (higher sigma_j) tend to have more efficient cost structures (lower claim-processing cost parameter k_j), generating distinct comparative advantages. (3) Baseline pricing coefficients alpha_j and risk-sensitivity coefficients beta_j vary dramatically across firms. (4) Senior drivers are less price sensitive; urban drivers are more price sensitive. Lower-risk consumers show stronger preferences for Firms 3 and 5, while higher-risk consumers disproportionately choose Firm 8.

Counterfactual simulations assess three information policies relative to the baseline. Under a centralized risk bureau — which collects each firm’s signal, aggregates them weighted by precision, and distributes the combined signal equally — average premiums fall by 21.6% and consumer surplus rises by 15.7%. The efficiency benchmark (firms observe true risk perfectly) yields a 25.7% premium reduction and a 16.9% consumer surplus gain, so the bureau recovers almost all the efficiency gap. The privacy benchmark (all firms restricted to the coarsest signal in the market) raises surplus for high-risk consumers by 6.9% but harms low-risk consumers.

The bureau’s price reduction operates through two channels: it eliminates the market power that accrues to firms with superior private information, and it aligns firms’ risk evaluations, enabling sharper undercutting. The bureau also reduces average costs by 12 euros per contract by enabling more efficient insurer-insuree matching — cost-efficient claim processors can better target the consumer types they have a comparative advantage in serving.

The analysis is confined to new customers in Rome’s provincial market to avoid complications from dynamic pricing and consumer-firm learning. The model abstracts away from optional contract clauses (treated as observable characteristics) and does not model the specific mechanisms generating information heterogeneity.

Q: What is the paper’s core research question? A: The paper asks how information asymmetries between competing firms (not just between buyers and sellers) shape equilibrium pricing strategies, consumer sorting, and market efficiency in a selection market, and whether a centralized bureau that equalizes firms’ access to aggregated risk information can improve competition and welfare. This extends the classic Akerlof-Rothschild-Stiglitz framework by introducing a second layer of asymmetry — across sellers themselves.

Q: Why is the Italian auto insurance market well suited for this study? A: Italy mandates liability insurance for all drivers and prohibits rejections, so the analysis focuses entirely on how consumers sort across insurers rather than on participation margins. The IPER dataset from IVASS is a nationally representative panel tracking policyholders even across insurer switches, providing both premium and ex-post claim records needed to construct individual risk types. The market has roughly 50 competing firms using demonstrably heterogeneous pricing algorithms, documented through a survey of major insurers and reduced-form regressions.

Q: How do the authors measure firm-level information precision in the reduced-form analysis? A: They estimate individual-specific risk types from a panel of claim records using Poisson regressions (claim frequency) and log-normal regressions (claim severity), then regress each firm’s premiums on those estimated risk measures. Firms whose premiums respond more sensitively to realized risk are inferred to have higher information precision. Figure 2 shows that these premium-to-risk coefficients vary significantly across firms — for example, Firm 7’s premiums are considerably more sensitive to risk than Firm 8’s — providing reduced-form evidence of heterogeneous information precision before any structural estimation.

Q: What is the structural model’s signal structure? A: Each firm j draws a private signal theta_j ~ N(theta, sigma_j^2) about a consumer’s true risk type theta, where sigma_j is the firm-specific signal standard deviation. A smaller sigma_j means higher precision. Signals are independent across firms conditional on theta, analogous to common-value auctions where firms receive noisy estimates of a shared unknown value (expected claim payouts). The parameter sigma_j is the key structural object the paper identifies and estimates.

Q: What is novel about the demand estimation strategy? A: Standard demand estimation assumes the same price is offered to all consumers or that the full price menu is observed. Here, only transaction prices are observed — the prices of unchosen insurers are not in the data. The authors apply the Wu and Xin (2024) fixed-point algorithm, which jointly estimates consumers’ sorting probabilities, offered price distributions, and demand parameters by adding an outer loop over sorting propensities to the Berry (1994) contraction mapping. No parametric restrictions are imposed on the offered price distributions, and they are allowed to vary fully across firms.

Q: How are firms’ signal variances identified separately from pricing coefficients? A: There is a one-to-one mapping between a firm’s offered price and its signal (prices increase monotonically in the signal, analogous to bids in auctions). After recovering the offered price distribution from the demand step, the authors observe price dispersion at a fixed risk level. By focusing on average prices conditional on each risk level, signal noise averages out, identifying the pricing coefficients beta_j. The residual price dispersion at fixed risk then identifies signal variance sigma_j^2.

Q: What does structural estimation reveal about the relationship between information precision and cost efficiency? A: Firms with higher signal standard deviations (less precise risk evaluation) tend to have lower claim-processing cost parameters k_j — they are more efficient at handling claims. This creates distinct comparative advantages: some firms excel at risk identification but face higher processing costs, while others process claims cheaply but evaluate risk less precisely. This heterogeneity means information-equalizing policies have differentiated firm-level impacts.

Q: What are the quantitative effects of the centralized risk bureau on premiums and consumer surplus? A: The bureau reduces average premiums by 21.6% relative to baseline and increases consumer surplus by 15.7%. The efficiency benchmark — where firms observe consumers’ true risk perfectly — produces a 25.7% premium reduction and a 16.9% consumer surplus gain. The bureau therefore closes nearly all of the gap to the first-best allocation in surplus terms (15.7% vs. 16.9%).

Q: Through what mechanisms does the bureau reduce prices? A: Two distinct channels are identified. First, equalizing information precision eliminates the informational market power held by firms with superior signals, compelling them to compete more aggressively on price. Second, when all firms share the same risk evaluation of a consumer, they can undercut each other more precisely, which intensifies price competition further. Both channels operate simultaneously under the bureau.

Q: How does the bureau affect consumer surplus distribution across risk types? A: The bureau primarily benefits low-risk consumers because improved information allows firms to price discriminate more accurately on risk type, lowering prices for those who are low risk. High-risk consumers see smaller benefits and may face relatively higher premiums. This contrasts with the privacy benchmark, where restricting all firms to the coarsest signal in the market raises high-risk consumers’ surplus by 6.9% — because it becomes harder for firms to distinguish them from low-risk consumers.

Q: What is the cost efficiency effect of the bureau? A: Under the centralized risk bureau, average costs per contract fall by 12 euros. This reflects more efficient insurer-insuree matching: when firms have equal and better information, those with cost advantages in claims processing can better identify and attract the consumer types they are relatively best equipped to serve. The authors note that given the scale of the Italian auto insurance market (approximately 31 million contracts annually), this per-contract saving implies a substantial aggregate impact.

Q: What happens to firm profits under the bureau, and is the impact uniform? A: Average profits decline overall due to lower prices. However, the impact is heterogeneous across firms. Firms that rely most heavily on superior information precision — often smaller, more specialized firms — experience greater profit losses, since the bureau most directly erodes their competitive advantage.

Q: How does the privacy benchmark differ from the bureau scenario? A: The privacy benchmark simulates a regulation that restricts all firms to using only basic consumer information, setting signal variance to the highest level observed in the market. Unlike the bureau (which improves and equalizes information), this benchmark degrades information uniformly. It produces opposite distributional effects: high-risk consumers gain 6.9% in surplus as cross-subsidization from low-risk to high-risk consumers increases, while low-risk consumers are worse off.

Q: Why does the paper focus on new customers only? A: Focusing on new customers avoids complications from dynamic pricing, where insurers update premiums based on accumulated claim history with a specific consumer, and from consumer-firm learning dynamics. This follows standard practice in the empirical asymmetric information literature, as cited in Chiappori and Salanie (2000) and Crawford et al. (2018).

Q: How does this paper relate to and extend prior work on selection markets? A: Prior empirical work on imperfect competition in selection markets — including Einav et al. (2010), Crawford et al. (2018), and related studies — assumes that competing firms have symmetric information about consumers. This paper is described as introducing the first tractable empirical framework for analyzing selection markets where firms have heterogeneous information. It also incorporates multidimensional cost heterogeneity on the supply side, adding to work by Salanié (2017) and Nelson (2025).

Q: What do the reduced-form regressions reveal about pricing heterogeneity across insurers? A: Firm-level regressions of premiums on observable risk factors show R-squared values ranging from 0.39 to 0.59. Estimated coefficients on key risk factors vary dramatically: being one year older reduces premiums by 0.25 to 1.68 euros depending on the firm; a higher bonus-malus class increases premiums by 12 to 32 euros; one additional accident in the previous five years raises premiums by 74 to 181 euros. These ranges reflect genuine differences in actuarial algorithms, not just sampling variation.

Q: What is the bonus-malus system and why does its saturation matter for the paper’s setting? A: Italy’s bonus-malus (BM) system assigns drivers to one of 18 risk classes based on accident history. Because approximately 80% of policyholders are in the best class (BM class 1), the public BM system provides limited granularity for risk evaluation. This saturation creates strong incentives for firms to develop proprietary risk-rating algorithms, which is the institutional basis for the substantial information heterogeneity that the paper documents and models.

Information Precision (sigma_j): In the paper’s model, the firm-specific parameter measuring the dispersion of a firm’s private signal about a consumer’s true risk type. Firm j draws signal theta_j ~ N(theta, sigma_j^2); 1/sigma_j is information precision. A smaller sigma_j means the firm more accurately identifies consumer risk. This is not merely a theoretical construct — the paper identifies and estimates sigma_j structurally for each of the 11 firms.

Heterogeneous Information: The condition where competing firms hold signals of different precision about the same consumer’s unobserved risk type, introducing asymmetry not just between buyers and sellers (as in Akerlof 1970) but among sellers themselves. This is the paper’s central departure from prior literature on selection markets, which assumed symmetric information among firms.

Centralized Risk Bureau: A policy institution that collects each firm’s analyzed risk signal, aggregates them weighted by each firm’s information precision (producing a combined signal more precise than any individual firm’s signal), and makes the aggregated information equally accessible to all firms. The bureau is the paper’s primary policy counterfactual, and it is modeled as equalizing both the level and heterogeneity of information precision across competitors.

Offered vs. Accepted Price Distribution: A distinction central to the paper’s identification strategy. The accepted price distribution is what is observed in transaction data — prices conditional on the consumer having chosen that firm. The offered price distribution is the full set of prices the firm would charge across all consumers, including those who did not select it. The paper recovers the offered distribution from the accepted distribution using a fixed-point algorithm, without imposing parametric restrictions.

Selection Loop: The paper’s methodological extension of the Berry (1994) BLP contraction mapping for mean utilities. An outer loop iterates over consumers’ sorting propensities to jointly recover offered price distributions, sorting probabilities, and demand parameters when only transaction prices are observed. This technique handles the endogeneity of which prices are accepted.

Risk Rating: The firm’s posterior assessment of a consumer’s expected cost, computed as the posterior mean E(theta | theta_j, D=j) — the expected true risk type conditional on the firm’s private signal and the consumer selecting that firm. Firms set prices as a linear function of their risk rating: p_j = alpha_j + beta_j * E(theta | theta_j, D=j).

Comparative Advantage (information vs. cost): The paper’s finding that firms with lower information precision (higher sigma_j) tend to have more efficient cost structures (lower k_j), and vice versa. This cross-sectional negative correlation between information advantage and cost advantage means that policy interventions that equalize information precision shift the basis of competition from information asymmetry to cost specialization.