MAHIMA CHAWLAELIZABETH GORDON

The Adoption Market: How can the number of parent-child matchings be increased?

Overview

How does the domestic US adoption market work?

What are the problems with the adoption market?

Literature solution: Auctions & Subsidies

Our solution: Add a monthly fee to waiting time

Defining Terms

High quality child (HQ): Healthy and Young

Low quality child (LQ): Unhealthy and Old

Matching: a pairing between adoptive parent(s) and child that results in legal adoption of child

Acceptable Threshold: the minimum quality child that adoptive parents are willing to adopt for a given monetary cost of waiting

How does the domestic adoption system work?

2-sided market Public and private adoption agenciesPrice cap for adoptionSteps for adopting a child:

1. Select an adoption agency2. Complete screening and home-study (fee required)3. Social worker searches for, identifies and evaluates

multiple potential children (search and information exchange period)

4. Child’s social worker makes final decision on adoptive parents

The problem in the adoption market

What is the problem? Shortage of high quality children and surplus of low quality

children indicate the market is not clearing

Why is this a problem? The goal of the adoption markets is to maximize the number of

matchings Shortage of HQ children = parents left without a child Surplus of LQ children = children left without a parent

Looking forward… Can we increase the number of matchings in the adoption market

by making previously unacceptable matches acceptable and matching unmatched children to unmatched parents?

What causes this problem?

Literature says the problem is the result of adoptive parents’ preferences Young children > Old children Healthy children > Unhealthy children

Result: Demand for HQ children > Demand for LQ children

However, this only causes a problem when a price cap is introduced…

How does the shortage of HQ children arise?

Price Cap

Demand

Supply

Quantity

Price

$30,000

Shortage

How does the surplus of LQ children arise?

Quality of Baby

ANA

Stage 1

x

2x

# babies

T*

Quality of Baby

NA

A

Stage n

x

(n+1)x

# babies

T*

A

Stage 0

x

Quality of Baby

# babies

T*

NA

T* =adoptive parents’ acceptable threshold with no monetary cost of waiting A = children adoptedNA = children not adopted

How can the number of matchings in the adoption market be increased?

Literature solution• Blackstone presents an auction and subsidy

solution to match otherwise unmatched children and adoptive parents

Our solution• We suggest adding a monthly fee, paid from

adoptive parents to the social worker, during the search and information exchange period of adoption

How is the adoption market currently like an auction?

Blackstone likens adoption market to fixed-price all-pay auction

Fixed-price: Fixed fee for adoption based on costs; these are not related to quality of the child No benefit to paying more, no option to pay less

All-pay: Fees paid and time spent waiting are sunk costs unrelated to whether adoptive parents receive a child. Unmatched parents still pay fees

Blackstone’s proposed auction solution…

An all-pay simultaneous ascending auction with a bid cap All-pay: ensures parents with a strong motive

will participate Simultaneous: results in more aggressive

bidding revenue maximizing larger endowment

Bid Cap: incentivizes low-income prospective parents to participate

Blackstone’s auction solution continued…

Adoptive parents submit bid for a child or split their bid among multiple children

Multiple bidding rounds until one set of adoptive parents remains receives child

End of each round, bids are pooled and allocated as a subsidy to low quality children based on health costs

Result: Unmatched parents unable to obtain a high quality child begin bidding on endowed low quality children increase matchings

Quality of Baby

NA

A

Stage n

x

(n+1)x

# babies

T*

Quality of Baby

NA

A

Stage n

x

(n+1)x

# babies

T*

A

Changing “effective quality” of a child with endowments

Effective quality = child’s quality relative to adoptive parents’ threshold

Problems with Blackstone’s auction and endowment solution

Placing a price/bid on a baby is often seen as socially unethical

It is unclear how ties are broken when the bid cap is reached by multiple bidders in a round.

Difficult to implement logistically and disseminate information

Makes the adoption market one-sided instead of two-sided

Motivations for our solution

Recall our solution: Add a monthly fee to search period

Search theory: “studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting”

McCall has a paper on job search and suggests “as c increases, the length of search decreases”o c = Marginal cost of generating another job offero Reservation wage declines over time as worker runs out of

money while searching

Applying McCall’s job search to the adoption market

Proposal: By adding a monthly cost to the search period, we can reduce the length of search period and thus increase the number of matches in the adoption market

The monthly fee equivalent to “c”Reservation wage equivalent to acceptable

thresholdReservation price is the maximum that an

adoptive parent is willing to pay to obtain a child

Current system of fixed fees

Adoptive parents face fixed monetary costs regardless of waiting period No monetary cost to preferring HQ children No monetary costs to having a high acceptable

thresholdIncentive to remain in search period until

either a HQ child is obtained or frustration lowers acceptable threshold long search period

Result: shortage of high quality children and surplus of low quality children

How does a monthly fee affect length of search period?

By adding a monthly fee, the search period becomes a fixed amount of time dependent on adoptive parents’ initial reservation price

Reservation price declines over time as adoptive parents shell out money

As time approaches n, adoptive parents will risk leaving the market unmatched

How would you react to approaching time n?

Time

Reservation price

n

Understanding quality as a spectrum

While we have been defining children as “HQ” and “LQ”, it is important to remember that a child’s quality falls on a spectrum. Quality child A ~ Quality child B

B

x

Quality of Baby

# babies

T*

A

Time

Acceptable Threshold Tipping

point

Lowest acceptable quality

Time

Reservation price

R0

Why impose a monthly fee?

T*

n

Recall that the acceptable threshold is the minimum child quality that adoptive parents are willing to adopt for a given monetary cost of waiting

As time approaches n:1. Reservation price falls2. Remaining search period decreases3. Probability of finding a child above

the initial acceptable threshold decreases

4. Taking into account added cost to waiting time, acceptable threshold falls

Result: increase in the number of low quality children matched

Conclusion

Goal: Increase the number of matchings in the adoption market

Our Solution: add a monthly fee to the search period, ultimately lowering the parents’ acceptable threshold and increasing the number of matchings

Further steps: What is the optimal size of this fee to be effective?

References

Blackstone, E., A. Buck, and S. Hakim. "Privatizing Adoption and

Foster Care: Applying Auction and Market Solutions." Children

and Youth Services Review 26.11 (2004): 1033-049.

Blackstone, E., A. Buck, S. Hakim, and U. Spiegel. "Market Segmentation in Child Adoption." International Review of Law and Economics 28.3 (2008): 220-25.

Goodwin, Michele. "The Free-Market Approach to Adoption: The Value of a Baby." Boston College Third World Law Journal 26.1 (2006): 61-79.

Landes, Elisabeth M., and Richard A. Posner. "The Economics of the Baby Shortage." The Journal of Legal Studies 7.2 (1978): 323-48. McCall, John J. "Economics of Information and Job Search." The

Quarterly Journal of Economics 84.1 (1970): 113-26.