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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 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.