# Presentation: 223391

## Credit and Identity Theft

- Charles M. Kahn
- and
- William Roberds

## Basic idea of paper

- Present theory of fraud, including ID theft, in credit transactions
- ID theft arises endogenously as a form of opportunistic behavior
- Outgrowth of Kahn, McAndrews, and Roberds (IER 2005)

## Fraud risk vs. credit risk

- Payments fraud has grown with the use of electronic forms of payment (FTC report: 12% victimized)
- Fraud risk quite small compared to credit risk (for credit cards, 5 BP versus 400 BP)
- Nonetheless, fraud risk a critical concern for industry

## Modeling identity

- Usually modeled as history of agents’ actions
- We must go further: problem is to *link* a particular history with individual making a current transaction

## Modeling identity

- Individual’s identity will be denoted by a unique (infinite) sequence of ones and zeros.
- We will describe technology for distinguishing an individual from an impersonator

## Modeling identity

- In his role as a producer an individual’s identity is unproblematic
- The difficulty is to link the production history with a particular attempt at consumption

## The framework

*N *agents, infinitely lived, risk neutral, with common discount factor 
- Each agent identified with a “location” where he can produce a unique, specialized, non-storable good at a cost *s*

## The framework

- Each period one agent wakes up “hungry” for the good of a particular producer
- Consumption of that good by that agent provides him utility *u*; any other consumption in the period gives the consumer 0 utility

## The framework

- Note: no double coincidence of wants
- Therefore no possibility of barter (if *s > 0)*
- Some arrangement needed for intertemporal trade

## The framework

- The value of *u* is common to all agents.
- The value of *s* is distributed in the population with distribution *F*
-  0< *F(u) <*1
- A producer’s value of *s* (his “type”) is unchanging over time, and is private information to the producer

## The framework

- The hungry agent can travel to the location of his preferred supplier
- The hungry agent’s own location is not automatically revealed
- Refusal to supply a good is observable

## Timing

- At time 0, agents learn their own costs, and have the opportunity to form club (binding commitment)
- Agents in club receive goods *from* club members, but must supply goods *to* other club members
-  ** denotes fraction of population in club

## Enforcement

- Agreements can be enforced by court: assume has power to punish *one* individual up to an amount *X (large)*, *provided he can be identified *
- Thus “fraud risk” but no “credit risk”

## Events within a period

- Hungry agent and supplier randomly chosen
- Hungry agent journeys to supplier’s location
- Hungry agent’s identity is verified
- If verification successful, trade occurs

## Baseline: costless identification

**Result: **Provided *X *_*>*_* u*,  all individuals with  *s *_*<*_* u  *join club  (club size ***F*(*u*) )
- A member’s expected utility is
- 			*V*(*s*) = *** **–1** **** *(*u – s*)
- Constrained efficient (cross-subsidy not allowed)

## Verification technology

- Examine a sample of *n* bits of individual’s identity at cost *k* per bit sampled
- No type I error;  probability of a false match of *z**n*
- Optimal sampling increases with *s* and falls with *k, z, *or **

## Equilibrium

- Find the cutoff level of supply cost for membership such that
- all members join voluntarily and are willing to supply
- each chooses his preferred monitoring sample
- all non-members prefer to remain outside the club (and attempt impersonation)

## Credit club equilibrium

**Result: **If *X *_>_ *u*
- For small *k*, equilibria exist with ***F*(*u*).
- As *k* shrinks, **approaches*F*(*u*).

## Credit card technology

- The *credit card* is a manufactured “pseudo-identity”: a string of bits, verifiable at lower cost than the identity itself.
- The credit card club makes an initial check of identity, then issues the member a card
- Subsequent suppliers verify the card rather than the person.

## Equilibrium

- Analogous definition: Agents voluntarily choose between:
- joining the club (being monitored initially, and supplying to all card holders after monitoring their cards)
- not joining (not supplying, instead attempting credit card fraud)

## Types of fraud

- Thus either the card or the person can be imitated: “existing account” vs. “new account” fraud

## Key result

- Equilibrium with credit cards exists under same conditions as before, and dominates equilibrium with independent verification of buyers

## Benefits of card arrangement

- Cards allow club members to share information gleaned in initial screening
- More intense verification possible; more frauds are excluded
- Size of club expands; high cost producers induced to join club

## Costs of card arrangement

- Shared information info on buyer IDs may be incorrect, leading to
- New account fraud
- Existing account fraud

## Policy implications

- Popular notion is sometimes advanced that more sophisticated cards can “solve the problem” of ID theft—
- But more sophisticated cards may actually contribute to the problem by making credit card payment more prevalent, increasing incentives for fraud.

## Policy implications

- Proposed privacy legislation may also fail to curb ID theft—
- By constraining ID samples, such legislation may encourage new account fraud (“impersonation” in the model)

## Policy implications

- Key policy tradeoff
- Gathering & sharing more information on buyers leads to better allocation of credit, but
- Amassing such data necessarily entails private & social costs (loss of privacy)

## Key ideas of paper

- Credit-based transactions systems are systems for efficiently sharing information among sellers (esp. ID of buyers)
- ID theft a problem because it exploits exactly this source of efficiency
- Transactions systems must balance costs of fraud against costs (private & social) of ID verification