The model
Allen and Gale (1997) show that a long-lived intermediary can smooth returns across generations by holding a reserve, and that a competitive spot market unwinds the arrangement. The paper specializes their model to rate-setting and derives four hypotheses that tell an intertemporal smoother from a cross-sectional pricer.
The evidence
An event study of the loss-cost surge of 2021 through 2023 on the two insurers that occupy the two roles, State Farm as the smoother and Progressive as the pricer, read from rate filings, statutory financial statements, and statutory premium records.
The line of sight
the section belongs to the modelthe section belongs to the evidencethe theme passes through the section
1
Introduction
ModelEvidence- Establishes
- Two insurers that sell a near-identical contract file rate changes at linear pass-through slopes near one-half, yet one ran an underwriting account that drained over 25 years while the other’s built. The contrast is the observable signature of two risk-sharing technologies, and the curvature of the pass-through function, not its level, is what separates them.
- Leads to
- Which literatures does the question join?
2
Related Literature
Model- Establishes
- The paper joins the literatures on intermediated intertemporal smoothing, long-term insurance contracts and reclassification risk, underwriting cycles and capital, organizational form in insurance, customer markets and pass-through, and risk classification. Its mechanism is the reserve that transfers resources across cohorts that never share a contract, not the front-loaded contract that insures one cohort.
- Leads to
- What must a model of the two insurers explain?
3
Stylized Facts
Evidence- Establishes
- State Farm is a mutual that sells through captive agents; Progressive is a stock insurer built on risk segmentation. On a linear reading both pass about half of an indicated rate change into the approved rate, while over 2001 through 2025 the smoother’s underwriting account drained, at a mean combined ratio of 106.65, and the pricer’s built, at a mean combined ratio of 92.04.
0.467Linear slope of the approved on the indicated rate change, State Farm
0.497Linear slope of the approved on the indicated rate change, Progressive
−$63.328 billionNet underwriting result, State Farm, 2001 through 2025
+$52.132 billionNet underwriting result, Progressive, 2001 through 2025
- Leads to
- One slope leaves the underwriting outcomes unexplained. What model gives two pass-through functions that share an average slope and differ in curvature?
4
Theoretical Framework
Model- Establishes
- The risky dividend of the Allen and Gale economy becomes the loss-cost realization, the reserve becomes policyholders’ surplus, the smoothed consumption path becomes the smoothed rate, and the option to opt out becomes a policyholder’s option to defect to an insurer that prices to current cost. Four propositions give four hypotheses: the smoother’s pass-through is convex (Hypothesis 1) and the pricer’s concave (Hypothesis 2); the smoother’s underwriting account drains while investment income on its surplus funds it, and the pricer’s builds (Hypothesis 3); and quantity migrates toward the pricer where the pricer is present (Hypothesis 4).
- Exhibits
- Table 1, the correspondence between the two economies · Table 2, the four hypotheses
- Leads to
- On what record can the four hypotheses be read?
5
Data
Evidence- Establishes
- Rate filings that carry an indicated, a filed, and an approved rate change, kept where the filing carries an indication and takes effect within the event of 2021 through 2023; statutory financial statements for 2001 through 2025; and statutory premium by state.
477Filings in the estimation sample, State Farm
802Filings in the estimation sample, Progressive
48States the State Farm sample draws on
50States the Progressive sample draws on
- Exhibits
- Table 3, data sources · Table 4, variable definitions and construction · Table 5, sample construction · Table 6, descriptive statistics
- Leads to
- What in this record identifies a difference in conduct?
6
Empirical Specification and Identification
Evidence- Establishes
- The quantity read is the local slope of the filed on the indicated rate change, recovered by a linear regression, a locally weighted scatterplot smoother, and a changepoint fit that weights down the tail of large indications. One industry-wide loss-cost shock meets both insurers, so the difference between their responses within the event is a difference in conduct; the explanations the design can and cannot set aside are stated in Section 6.3.
- Leads to
- Do the four hypotheses hold?
7
Results
ModelEvidence- Establishes
- The smoother’s pass-through is convex and the pricer’s concave, the concavity resting on the pricer’s high-indication filings and the less settled of the two readings (Hypotheses 1 and 2). Over 2001 through 2025, $73.410 billion of net investment income funded the smoother’s underwriting losses as its surplus rose from $43.691 billion to $169.997 billion, while the pricer’s underwriting gains built and it paid $41.856 billion in dividends to its parent (Hypothesis 3). The pricer’s national market share rose from 7.3 percent in 2004 to 18.60 percent in 2025, beside the smoother’s 18.64 percent (Hypothesis 4).
0.369 to 0.672Local slope of the filed on the indicated rate change below and above the knot of 20.38 percent, State Farm
0.692 to 0.256Local slope of the filed on the indicated rate change below and above the knot of 12.20 percent, Progressive
0.740Difference between the two insurers’ changes in slope at the knot, State Farm less Progressive
7.3 to 18.60 percentNational market share of Progressive, 2004 to 2025
- Exhibits
- Table 7, surplus reconciliation · Figure 1, capital and surplus against an underwriting-only buffer · Figure 2, underwriting and operating margins · Figure 3, filed versus indicated rate change · Figure 4, leverage-controlled pass-through · Figure 5, national market share
- Leads to
- What do the four findings establish together?
8
Discussion
ModelEvidence- Establishes
- The four findings correspond to the four hypotheses under the auxiliary assumptions of Section 4. The near-equal linear slopes are not evidence of similar conduct; they are the averages of opposite curvatures. The findings are consistent with the mechanism, within the limits Section 8 states.
- Leads to
- What follows from the two-insurer contrast?
9
Conclusion
ModelEvidence- Establishes
- Specializing the Allen and Gale framework turns their welfare results into statements about rate-setting conduct and their disintermediation result into a statement about market structure, and on the two insurers both hold. The next step treats the smoother-pricer character as a measured attribute of a firm and reads the curvature of pass-through across the full set of national insurers.
- Appendices
- A, Proofs · B, Changepoint and Leverage-Control Methodology · C, North Carolina Sensitivity