The Economics of Insurance Fraud Investigation: Evidence of a Nash Equilibrium Stephen P. D’Arcy, FCAS University of Illinois Richard A. Derrig Ph.D. OPAL Consulting LLC Herbert I. Weisberg Correlation Research Inc. NBER Presentation - February 2005

Outline Research Questions Automobile Bodily Injury Coverage and Claim Investigation Notation Nash Equilibrium Tables Results

Research Questions What are the incentives for fraud investigation under the current market structure of automobile insurance in the United States? What happens when different companies are responsible for paying different parts of a bodily injury claim?

Coverage for Automobile Bodily Injury Claims First Party Coverages –Medical Payments –Personal Injury Protection (No-Fault) Third Party Coverages –Bodily Injury (BI) Liability –Uninsured Motorist (UM) Subrogation Our Example is No-Fault PIP and BI

Claim Investigation Tactics Independent Medical Exams (IME) Medical Audit (MA) Special Investigative Unit (SIU) Tracked Since 1995 in Massachusetts Tracked in Recent 2004 IRC Study of Auto Injury Claims countrywide

Notation Cost of claim without any investigation: PIP claim = P i,j (i company has PIP, j company has Liability) Liability claim (excess of PIP) = L i,j Savings from investigations: Savings on PIP claims = SP Savings on Liability claims = SL Savings on Total claim = ST Level of investigation: No investigation = 0 Optimal investigation based on PIP claims = A Optimal investigation based on total claims = B Investigation cost: Cost of an A level investigation = IA Cost of an B level investigation = IB

AB STB STA SPB IB SPA IA Figure 1 Optimal Level of Claim Investigation

Table 1 Single Insurer Case Net Cost of Claim and Investigations Level of Claim Investigation None (0)PIP Based (A)Total Claim Based (B)

Table 2 -Two Insurer Case Net Cost of Claim and Investigations (No Subrogation )

Table 4-Two Insurer Case Net Cost of Claim and Investigations (Subrogation)

Massachusetts Experience I No-Fault State PIP Coverage of $8000 –Medical expenses –Loss of income –Other services and expenses Tort Threshold of $2000 in medical expenses Study of claim investigations –IME costs ≈ SPA (PIP savings) –Implies investigations consider total savings –Total costs reduced net of cost by investigation

Massachusetts Experience II PIP and BI Company Same For Only 20% PIP Claims; Two companies 80% of Claims, a Non-Cooperative Game BI Coverage of $20,000 Compulsory; $100,000 Commonly Purchased –Medical & Income expenses excess of PIP –General Damages “Pain and Suffering” –Attorney Fees for Claimant & Company Study of Claim Investigation: Claim Screen Experiment on 1996 Claims: Four Companies tracked “Fraud Indicators” for each PIP Claim for six months; BI claim matched from database and both coded for relevant data (medicals, providers, injuries, suspicion (automated), investigation, attorney involvement, other data) 1993 Claim Sample and 1996 Population of Detailed Claim Database

DM Fraud Indicators Scoring Functions Graded Output Non-Suspicious Claims Routine Claims Suspicious Claims Complicated Claims

Massachusetts Experience III IME Savings Net of Cost ($350, $75 no show) PIP Only: 0.1% All; 1.6% No Shows; Suspicion: Moderate 2.6%; High -13.8%, None -3.4% PIP & BI: 8.7% All; 4.3% No Shows; Suspicion: Moderate 14.4%; High -4.5%, None -8.0% Study Conclusion: Claim Scoring for Suspicion Helps Maximize Savings Net of Cost by Reducing the Number of Claims Investigated without Savings

AB STB STA SPB IB SPA IA Figure 2 Claim Investigation in Massachusetts MA

Conclusion When viewed in non-cooperative game theoretic framework, insurers have liability reimbursement incentives to under investigate suspicious claims but Massachusetts data points to over investigation. Intelligent claim sorting creates more incentive (more $ available) to investigate for fraud and could move toward Nash equilibrium. Market structure revisions could increase fraud detection and reduce insurance costs

Summary of Tabular Results PIP Sample:1993 AIB1996 DCD1996 CSE Net Savings (PIP) Savings from IME Req but not Completed Savings from Positive IMEs Cost of Negative IMEs 0.2% 0.7% -1.3% -0.2% 0.3% 0.4% -0.9% -0.2% 0.4% 0.2% -0.8% BI + PIP Sample:1993 AIB1996 DCD1996 CSE Net Savings (BI + PIP) Savings from IME Req but not Completed Savings from Positive IMEs Cost of Negative IMEs 3.8% 4.4% 0.1% -0.7% 5.7% 2.8% 3.2% -0.3% 8.9% 4.5% 4.9% -0.5%

IME Performance Data % of Claims with IME Requested Strain/ Sprain Other Injury 1993 AIB1996 DCD 1996 CSE PIP IME (PIP Claims) PIP IME (BI Claims) PIP or BI IME (BI Claims) 18% 34% 41% 23% 35% 40% 20% 52% 57% 32% 53% 58% 14% 45% 51% % of Completed IMEs with Positive Outcomes Strain/ Sprain Other Injury 1993 AIB1996 DCD 1996 CSE PIP IME (PIP Claims) PIP IME (BI Claims) PIP or BI IME (BI Claims) 34% 32% 36% 59% 60% 58% 70% 59% 71% 54% 56% 61%

IME Performance Data IME Requested 1993 AIB1996 DCD1996 CSE PIP IME Requested (PIP Claims) PIP IME Requested (BI Claims) PIP or BI IME Requested (BI Claims) 18% 34% 41% 23% 35% 40% 20% 52% 57% IME Positive Outcomes 1993 AIB1996 DCD1996 CSE PIP IME Completed (PIP Claims) PIP IME Completed (BI Claims) PIP or BI IME Completed (BI Claims) 34% 32% 36% 59% 60% 58% 70%

Net Savings by Suspicion Level Suspicion Level Claim Payment IME Type ClaimsNone (0) Low (1-3) Mod (4-6) High (7-10) All PIP Suspicion Score (CSE Model) PIP All PIPS-3%0%5%-6%0% PIP PIPs with no BIs-2%1%2%-29%-1% PIP PIP & BI Matching-8%-1%7%10%1% BI PIP & BI Matching9%5%8%9%6% PIP+BIPIPPIP & BI Matching4%2%3%7%4% PIP+BIBestPIP & BI Matching6%5%8%-4%7% BI Suspicion Score (NHR Model) PIP PIP & BI Matching2%-2%1%2%1% BI PIP & BI Matching-2%0%11%7%6% PIP+BIPIPPIP & BI Matching-7%4%6%0%4% PIP+BIBestPIP & BI Matching-11%0%14%1%7% Source: 1996 CSE Claims