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

NotationCost of claim without any investigation:

PIP claim = Pi,j (i company has PIP, j company has Liability)

Liability claim (excess of PIP) = Li,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

Claims

$

Total Saving

PIP Saving

Cost of Investigation

A B

STB

STA

SPBIB

SPA

IA

Figure 1Optimal Level of Claim Investigation

Table 1Single Insurer Case

Net Cost of Claim and Investigations

Level of Claim Investigation

None (0) PIP Based (A) Total Claim Based (B)

1,11,10,1 LPP 1101111101

111101

,,,,,

,,,

IAIASLASPASPA

LPP

1101111101

111101

,,,,,

,,,

IBIBSLBSPBSPB

LPP

Insurer 1 Level of Claim Investigation

None (0) PIP Based (A) Total Claim Based (B)

0

11 ,, LP

22 ,, LP

,,

,,,

111

111

IASLA

SPALP

2122 ,,, SLALP

,,

,,,

111

111

IBSLB

SPBLP

2122 ,,, SLBLP

A

1211 ,,, SLALP

,,,

,,

2222

22

IASLASPA

LP

,,

,,,

11

111

IASLA

SPALP

,,,

,,

222

22

IASLASPA

LP

,,

,,,,

112

11111

IBSLA

SLBSPBLP

,,,

,,,

22221

222

IASLASLB

SPALP

Insu

rer

2 L

evel

of

Inv

esti

gati

on

B

1211 ,,, SLBLP

,,,

,,

2222

22

IBSLBSPB

LP

,,

,,,,

112

11111

IASLB

SLASPALP

,,,

,,,

22212

222

IBSLBSLA

SPBLP

,,

,,,

11

111

IBSLB

SPBLP

,,,

,,

222

22

IBSLBSPB

LP

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

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

Insurer 1 Level of Claim Investigation

None (0) PIP Based (A) Total Claim Based (B)

0

1211121101 ,,,,, LLPPP

2221222102 ,,,,, LLPPP

,11,11,1

0,11,21,11,21,10,1

IASLASPA

SPALLPPP

2,12,12,22,1

2,22,10,2

SLASPALL

PPP

,11,11,1

0,11,21,11,21,10,1

IBSLBSPB

SPBLLPPP

2,12,12,22,1

2,22,10,2

SLBSPBLL

PPP

A

1,21,2

1,21,11,21,10,1

SLASPA

LLPPP

,22,22,2

0,22,22,1

2,22,10,2

IASLASPA

SPALL

PPP

,11,21,11,2

1,10,11,21,11,21,10,1

IASLASLASPA

SPASPALLPPP

,22,22,12,2

2,10,22,22,1

2,22,10,2

IASLASLASPA

SPASPALL

PPP

,11,21,11,2

1,10,11,21,11,21,10,1

IBSLASLBSPA

SPBSPBLLPPP

,22,22,12,2

2,10,22,22,1

2,22,10,2

IASLASLBSPA

SPBSPALL

PPP

Insu

rer 2

Lev

el o

f Cla

im In

vest

igat

ion

B

12121211121101 ,,,,,,, SLBSPBLLPPP

,,,,

,,,,,

2222202

2221222102

IBSLBSPBSPB

LLPPP

,11,21,11,2

1,10,11,21,11,21,10,1

IASLBSLASPB

SPASPALLPPP

,22,22,12,2

2,10,22,22,1

2,22,10,2

IBSLBSLASPB

SPASPBLL

PPP

,11,1,

0,11,21,11,21,10,1

IBSLBSPB

SPBLLPPP

,22,2,0,2

2,22,12,22,10,2

IBSLBSPBSPB

LLPPP

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

DMFraud Indicators

Scoring Functions

Graded Output

Non-Suspicious ClaimsRoutine Claims

Suspicious ClaimsComplicated 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

Claims

$

Total Saving

PIP Saving

Cost of Investigation

A B

STB

STA

SPBIB

SPA

IA

Figure 2Claim 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 ResultsPIP

Sample: 1993 AIB 1996 DCD 1996 CSE

Net Savings (PIP)

Savings from IME Req but not Completed

Savings from Positive IMEs

Cost of Negative IMEs

0.2%

0.7%

0.7%

-1.3%

-0.2%

0.3%

0.4%

-0.9%

-0.2%

0.4%

0.2%

-0.8%

BI + PIP

Sample: 1993 AIB 1996 DCD 1996 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 AIB

1996 DCD

1996 CSE 1996 CSE 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 AIB

1996 DCD

1996 CSE 1996 CSE 1996 CSE

PIP IME (PIP Claims)

PIP IME (BI Claims)

PIP or BI IME (BI Claims)

34%

32%

36%

59%

60%

60%

58%

58%

70%

59%

59%

71%

54%

56%

61%

Net Savings by Suspicion Level

Suspicion Level

Claim Payment

IME Type

Claims None (0)

Low (1-3)

Mod (4-6)

High (7-10)

All

PIP Suspicion Score (CSE Model)

PIP PIP All PIPS -3% 0% 5% -6% 0%

PIP PIP PIPs with no BIs -2% 1% 2% -29% -1%

PIP PIP PIP & BI Matching -8% -1% 7% 10% 1%

BI BI PIP & BI Matching 9% 5% 8% 9% 6%

PIP+BI PIP PIP & BI Matching 4% 2% 3% 7% 4%

PIP+BI Best PIP & BI Matching 6% 5% 8% -4% 7%

BI Suspicion Score (NHR Model)

PIP PIP PIP & BI Matching 2% -2% 1% 2% 1%

BI BI PIP & BI Matching -2% 0% 11% 7% 6%

PIP+BI PIP PIP & BI Matching -7% 4% 6% 0% 4%

PIP+BI Best PIP & BI Matching -11% 0% 14% 1% 7%

Source: 1996 CSE Claims